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aria-hidden="true" height="50" width="50"> <span class="mw-logo-container skin-invert"> <img class="mw-logo-wordmark" alt="Wikipedie" src="/static/images/mobile/copyright/wikipedia-wordmark-cs.svg" style="width: 7.5em; height: 1.1875em;"> <img class="mw-logo-tagline" alt="Wikipedie: Otevřená encyklopedie" src="/static/images/mobile/copyright/wikipedia-tagline-cs.svg" width="118" height="13" style="width: 7.375em; height: 0.8125em;"> </span> </a> </div> <div class="vector-header-end"> <div id="p-search" role="search" class="vector-search-box-vue vector-search-box-collapses vector-search-box-show-thumbnail vector-search-box-auto-expand-width vector-search-box"> <a href="/wiki/Speci%C3%A1ln%C3%AD:Hled%C3%A1n%C3%AD" class="cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only search-toggle" title="Prohledat tuto wiki [f]" accesskey="f"><span class="vector-icon mw-ui-icon-search mw-ui-icon-wikimedia-search"></span> <span>Hledání</span> </a> <div class="vector-typeahead-search-container"> <div class="cdx-typeahead-search cdx-typeahead-search--show-thumbnail cdx-typeahead-search--auto-expand-width"> <form action="/w/index.php" id="searchform" class="cdx-search-input cdx-search-input--has-end-button"> <div id="simpleSearch" class="cdx-search-input__input-wrapper" data-search-loc="header-moved"> <div class="cdx-text-input cdx-text-input--has-start-icon"> <input class="cdx-text-input__input" type="search" name="search" placeholder="Hledat na Wikipedii" aria-label="Hledat na Wikipedii" autocapitalize="sentences" title="Prohledat tuto wiki [f]" accesskey="f" id="searchInput" > <span class="cdx-text-input__icon cdx-text-input__start-icon"></span> </div> <input type="hidden" name="title" value="Speciální:Hledání"> </div> <button class="cdx-button cdx-search-input__end-button">Hledat</button> </form> </div> </div> </div> <nav class="vector-user-links vector-user-links-wide" aria-label="Osobní nástroje"> <div class="vector-user-links-main"> <div id="p-vector-user-menu-preferences" class="vector-menu mw-portlet emptyPortlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> </ul> </div> </div> <div id="p-vector-user-menu-userpage" class="vector-menu mw-portlet emptyPortlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> </ul> </div> </div> <nav class="vector-appearance-landmark" aria-label="Vzhled"> <div id="vector-appearance-dropdown" class="vector-dropdown " title="Změnit vzhled velikosti písma, šířky stránky a barvy" > <input type="checkbox" id="vector-appearance-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-appearance-dropdown" class="vector-dropdown-checkbox " aria-label="Vzhled" > <label id="vector-appearance-dropdown-label" for="vector-appearance-dropdown-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only " aria-hidden="true" ><span class="vector-icon mw-ui-icon-appearance mw-ui-icon-wikimedia-appearance"></span> <span class="vector-dropdown-label-text">Vzhled</span> </label> <div class="vector-dropdown-content"> <div id="vector-appearance-unpinned-container" class="vector-unpinned-container"> </div> </div> </div> </nav> <div id="p-vector-user-menu-notifications" class="vector-menu mw-portlet emptyPortlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> </ul> </div> </div> <div id="p-vector-user-menu-overflow" class="vector-menu mw-portlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="pt-sitesupport-2" class="user-links-collapsible-item mw-list-item user-links-collapsible-item"><a data-mw="interface" href="https://donate.wikimedia.org/?wmf_source=donate&wmf_medium=sidebar&wmf_campaign=cs.wikipedia.org&uselang=cs" class=""><span>Podpořte Wikipedii</span></a> </li> <li id="pt-createaccount-2" class="user-links-collapsible-item mw-list-item user-links-collapsible-item"><a data-mw="interface" href="/w/index.php?title=Speci%C3%A1ln%C3%AD:Vytvo%C5%99it_%C3%BA%C4%8Det&returnto=Limita" title="Doporučujeme vytvořit si účet a přihlásit se, ovšem není to povinné" class=""><span>Vytvoření účtu</span></a> </li> <li id="pt-login-2" class="user-links-collapsible-item mw-list-item user-links-collapsible-item"><a data-mw="interface" href="/w/index.php?title=Speci%C3%A1ln%C3%AD:P%C5%99ihl%C3%A1sit&returnto=Limita" title="Doporučujeme vám přihlásit se, ovšem není to povinné. [o]" accesskey="o" class=""><span>Přihlášení</span></a> </li> </ul> </div> </div> </div> <div id="vector-user-links-dropdown" class="vector-dropdown vector-user-menu vector-button-flush-right vector-user-menu-logged-out" title="Další možnosti" > <input type="checkbox" id="vector-user-links-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-user-links-dropdown" class="vector-dropdown-checkbox " aria-label="Osobní nástroje" > <label id="vector-user-links-dropdown-label" for="vector-user-links-dropdown-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only " aria-hidden="true" ><span class="vector-icon mw-ui-icon-ellipsis mw-ui-icon-wikimedia-ellipsis"></span> <span class="vector-dropdown-label-text">Osobní nástroje</span> </label> <div class="vector-dropdown-content"> <div id="p-personal" class="vector-menu mw-portlet mw-portlet-personal user-links-collapsible-item" title="Uživatelské menu" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="pt-sitesupport" class="user-links-collapsible-item mw-list-item"><a href="https://donate.wikimedia.org/?wmf_source=donate&wmf_medium=sidebar&wmf_campaign=cs.wikipedia.org&uselang=cs"><span>Podpořte Wikipedii</span></a></li><li id="pt-createaccount" class="user-links-collapsible-item mw-list-item"><a href="/w/index.php?title=Speci%C3%A1ln%C3%AD:Vytvo%C5%99it_%C3%BA%C4%8Det&returnto=Limita" title="Doporučujeme vytvořit si účet a přihlásit se, ovšem není to povinné"><span class="vector-icon mw-ui-icon-userAdd mw-ui-icon-wikimedia-userAdd"></span> <span>Vytvoření účtu</span></a></li><li id="pt-login" class="user-links-collapsible-item mw-list-item"><a href="/w/index.php?title=Speci%C3%A1ln%C3%AD:P%C5%99ihl%C3%A1sit&returnto=Limita" title="Doporučujeme vám přihlásit se, ovšem není to povinné. [o]" accesskey="o"><span class="vector-icon mw-ui-icon-logIn mw-ui-icon-wikimedia-logIn"></span> <span>Přihlášení</span></a></li> </ul> </div> </div> <div id="p-user-menu-anon-editor" class="vector-menu mw-portlet mw-portlet-user-menu-anon-editor" > <div class="vector-menu-heading"> Stránky pro odhlášené editory <a href="/wiki/N%C3%A1pov%C4%9Bda:%C3%9Avod" aria-label="Více informací o editování"><span>dozvědět se více</span></a> </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="pt-anoncontribs" class="mw-list-item"><a href="/wiki/Speci%C3%A1ln%C3%AD:Moje_p%C5%99%C3%ADsp%C4%9Bvky" title="Seznam editací provedených z této IP adresy [y]" accesskey="y"><span>Příspěvky</span></a></li><li id="pt-anontalk" class="mw-list-item"><a href="/wiki/Speci%C3%A1ln%C3%AD:Moje_diskuse" title="Diskuse o editacích provedených z této IP adresy [n]" accesskey="n"><span>Diskuse</span></a></li> </ul> </div> </div> </div> </div> </nav> </div> </header> </div> <div class="mw-page-container"> <div class="mw-page-container-inner"> <div class="vector-sitenotice-container"> <div id="siteNotice"></div> </div> <div class="vector-column-start"> <div class="vector-main-menu-container"> <div id="mw-navigation"> <nav id="mw-panel" class="vector-main-menu-landmark" aria-label="Projekt"> <div id="vector-main-menu-pinned-container" class="vector-pinned-container"> </div> </nav> </div> </div> <div class="vector-sticky-pinned-container"> <nav id="mw-panel-toc" aria-label="Obsah" data-event-name="ui.sidebar-toc" class="mw-table-of-contents-container vector-toc-landmark"> <div id="vector-toc-pinned-container" class="vector-pinned-container"> <div id="vector-toc" class="vector-toc vector-pinnable-element"> <div class="vector-pinnable-header vector-toc-pinnable-header vector-pinnable-header-pinned" data-feature-name="toc-pinned" data-pinnable-element-id="vector-toc" > <h2 class="vector-pinnable-header-label">Obsah</h2> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-toc.pin">přesunout do postranního panelu</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-toc.unpin">skrýt</button> </div> <ul class="vector-toc-contents" id="mw-panel-toc-list"> <li id="toc-mw-content-text" class="vector-toc-list-item vector-toc-level-1"> <a href="#" class="vector-toc-link"> <div class="vector-toc-text">(úvod)</div> </a> </li> <li id="toc-Limita_funkce" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Limita_funkce"> <div class="vector-toc-text"> <span class="vector-toc-numb">1</span> <span>Limita funkce</span> </div> </a> <ul id="toc-Limita_funkce-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Limita_posloupnosti" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Limita_posloupnosti"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>Limita posloupnosti</span> </div> </a> <ul id="toc-Limita_posloupnosti-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Limita_v_metrickém_prostoru" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Limita_v_metrickém_prostoru"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Limita v metrickém prostoru</span> </div> </a> <ul id="toc-Limita_v_metrickém_prostoru-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Limita_v_topologickém_prostoru" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Limita_v_topologickém_prostoru"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>Limita v topologickém prostoru</span> </div> </a> <ul id="toc-Limita_v_topologickém_prostoru-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Nevlastní_limita_v_nevlastním_bodě" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Nevlastní_limita_v_nevlastním_bodě"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>Nevlastní limita v nevlastním bodě</span> </div> </a> <ul id="toc-Nevlastní_limita_v_nevlastním_bodě-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Příklady" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Příklady"> <div class="vector-toc-text"> <span class="vector-toc-numb">6</span> <span>Příklady</span> </div> </a> <ul id="toc-Příklady-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Poznámky" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Poznámky"> <div class="vector-toc-text"> <span class="vector-toc-numb">7</span> <span>Poznámky</span> </div> </a> <ul id="toc-Poznámky-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Reference" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Reference"> <div class="vector-toc-text"> <span class="vector-toc-numb">8</span> <span>Reference</span> </div> </a> <ul id="toc-Reference-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Související_články" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Související_články"> <div class="vector-toc-text"> <span class="vector-toc-numb">9</span> <span>Související články</span> </div> </a> <ul id="toc-Související_články-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Externí_odkazy" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Externí_odkazy"> <div class="vector-toc-text"> <span class="vector-toc-numb">10</span> <span>Externí odkazy</span> </div> </a> <ul id="toc-Externí_odkazy-sublist" class="vector-toc-list"> </ul> </li> </ul> </div> </div> </nav> </div> </div> <div class="mw-content-container"> <main id="content" class="mw-body"> <header class="mw-body-header vector-page-titlebar"> <nav aria-label="Obsah" class="vector-toc-landmark"> <div id="vector-page-titlebar-toc" class="vector-dropdown vector-page-titlebar-toc vector-button-flush-left" > <input type="checkbox" id="vector-page-titlebar-toc-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-page-titlebar-toc" class="vector-dropdown-checkbox " aria-label="Přepnout obsah" > <label id="vector-page-titlebar-toc-label" for="vector-page-titlebar-toc-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only " aria-hidden="true" ><span class="vector-icon mw-ui-icon-listBullet mw-ui-icon-wikimedia-listBullet"></span> <span class="vector-dropdown-label-text">Přepnout obsah</span> </label> <div class="vector-dropdown-content"> <div id="vector-page-titlebar-toc-unpinned-container" class="vector-unpinned-container"> </div> </div> </div> </nav> <h1 id="firstHeading" class="firstHeading mw-first-heading"><span class="mw-page-title-main">Limita</span></h1> <div id="p-lang-btn" class="vector-dropdown mw-portlet mw-portlet-lang" > <input type="checkbox" id="p-lang-btn-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-p-lang-btn" class="vector-dropdown-checkbox mw-interlanguage-selector" aria-label="Přejděte k článku v jiném jazyce. Je dostupný v 79 jazycích" > <label id="p-lang-btn-label" for="p-lang-btn-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--action-progressive mw-portlet-lang-heading-79" aria-hidden="true" ><span class="vector-icon mw-ui-icon-language-progressive mw-ui-icon-wikimedia-language-progressive"></span> <span class="vector-dropdown-label-text">79 jazyků</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-af mw-list-item"><a href="https://af.wikipedia.org/wiki/Limiet" title="Limiet – afrikánština" lang="af" hreflang="af" data-title="Limiet" data-language-autonym="Afrikaans" data-language-local-name="afrikánština" class="interlanguage-link-target"><span>Afrikaans</span></a></li><li class="interlanguage-link interwiki-am mw-list-item"><a href="https://am.wikipedia.org/wiki/%E1%8C%A5%E1%8C%8D" title="ጥግ – amharština" lang="am" hreflang="am" data-title="ጥግ" data-language-autonym="አማርኛ" data-language-local-name="amharština" class="interlanguage-link-target"><span>አማርኛ</span></a></li><li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D9%86%D9%87%D8%A7%D9%8A%D8%A9_(%D8%B1%D9%8A%D8%A7%D8%B6%D9%8A%D8%A7%D8%AA)" title="نهاية (رياضيات) – arabština" lang="ar" hreflang="ar" data-title="نهاية (رياضيات)" data-language-autonym="العربية" data-language-local-name="arabština" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-ast mw-list-item"><a href="https://ast.wikipedia.org/wiki/Llende_matem%C3%A1tica" title="Llende matemática – asturština" lang="ast" hreflang="ast" data-title="Llende matemática" data-language-autonym="Asturianu" data-language-local-name="asturština" class="interlanguage-link-target"><span>Asturianu</span></a></li><li class="interlanguage-link interwiki-az mw-list-item"><a href="https://az.wikipedia.org/wiki/Limit_(riyaziyyat)" title="Limit (riyaziyyat) – ázerbájdžánština" lang="az" hreflang="az" data-title="Limit (riyaziyyat)" data-language-autonym="Azərbaycanca" data-language-local-name="ázerbájdžánština" class="interlanguage-link-target"><span>Azərbaycanca</span></a></li><li class="interlanguage-link interwiki-ba mw-list-item"><a href="https://ba.wikipedia.org/wiki/%D0%A1%D0%B8%D0%BA%D0%BB%D3%99%D0%BC%D3%99_(%D0%BC%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D0%BA%D0%B0)" title="Сикләмә (математика) – baškirština" lang="ba" hreflang="ba" data-title="Сикләмә (математика)" data-language-autonym="Башҡортса" data-language-local-name="baškirština" class="interlanguage-link-target"><span>Башҡортса</span></a></li><li class="interlanguage-link interwiki-be mw-list-item"><a href="https://be.wikipedia.org/wiki/%D0%9B%D1%96%D0%BC%D1%96%D1%82_(%D0%BC%D0%B0%D1%82%D1%8D%D0%BC%D0%B0%D1%82%D1%8B%D0%BA%D0%B0)" title="Ліміт (матэматыка) – běloruština" lang="be" hreflang="be" data-title="Ліміт (матэматыка)" data-language-autonym="Беларуская" data-language-local-name="běloruština" class="interlanguage-link-target"><span>Беларуская</span></a></li><li class="interlanguage-link interwiki-bg mw-list-item"><a href="https://bg.wikipedia.org/wiki/%D0%93%D1%80%D0%B0%D0%BD%D0%B8%D1%86%D0%B0_(%D0%BC%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D0%BA%D0%B0)" title="Граница (математика) – bulharština" lang="bg" hreflang="bg" data-title="Граница (математика)" data-language-autonym="Български" data-language-local-name="bulharština" class="interlanguage-link-target"><span>Български</span></a></li><li class="interlanguage-link interwiki-bh mw-list-item"><a href="https://bh.wikipedia.org/wiki/%E0%A4%B8%E0%A5%80%E0%A4%AE%E0%A4%BE_(%E0%A4%97%E0%A4%A3%E0%A4%BF%E0%A4%A4)" title="सीमा (गणित) – Bhojpuri" lang="bh" hreflang="bh" data-title="सीमा (गणित)" data-language-autonym="भोजपुरी" data-language-local-name="Bhojpuri" class="interlanguage-link-target"><span>भोजपुरी</span></a></li><li class="interlanguage-link interwiki-bn mw-list-item"><a href="https://bn.wikipedia.org/wiki/%E0%A6%B8%E0%A7%80%E0%A6%AE%E0%A6%BE_(%E0%A6%97%E0%A6%A3%E0%A6%BF%E0%A6%A4)" title="সীমা (গণিত) – bengálština" lang="bn" hreflang="bn" data-title="সীমা (গণিত)" data-language-autonym="বাংলা" data-language-local-name="bengálština" class="interlanguage-link-target"><span>বাংলা</span></a></li><li class="interlanguage-link interwiki-bs mw-list-item"><a href="https://bs.wikipedia.org/wiki/Limes_(matematika)" title="Limes (matematika) – bosenština" lang="bs" hreflang="bs" data-title="Limes (matematika)" data-language-autonym="Bosanski" data-language-local-name="bosenština" class="interlanguage-link-target"><span>Bosanski</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/L%C3%ADmit" title="Límit – katalánština" lang="ca" hreflang="ca" data-title="Límit" data-language-autonym="Català" data-language-local-name="katalánština" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-ckb mw-list-item"><a href="https://ckb.wikipedia.org/wiki/%DA%95%D8%A7%D8%AF%DB%95_(%D9%85%D8%A7%D8%AA%D9%85%D8%A7%D8%AA%DB%8C%DA%A9)" title="ڕادە (ماتماتیک) – kurdština (sorání)" lang="ckb" hreflang="ckb" data-title="ڕادە (ماتماتیک)" data-language-autonym="کوردی" data-language-local-name="kurdština (sorání)" class="interlanguage-link-target"><span>کوردی</span></a></li><li class="interlanguage-link interwiki-cv mw-list-item"><a href="https://cv.wikipedia.org/wiki/%D0%A7%D0%B8%D0%BA%C4%95_(%D0%BC%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D0%BA%D0%B0)" title="Чикĕ (математика) – čuvaština" lang="cv" hreflang="cv" data-title="Чикĕ (математика)" data-language-autonym="Чӑвашла" data-language-local-name="čuvaština" class="interlanguage-link-target"><span>Чӑвашла</span></a></li><li class="interlanguage-link interwiki-cy mw-list-item"><a href="https://cy.wikipedia.org/wiki/Terfan_(mathemateg)" title="Terfan (mathemateg) – velština" lang="cy" hreflang="cy" data-title="Terfan (mathemateg)" data-language-autonym="Cymraeg" data-language-local-name="velština" class="interlanguage-link-target"><span>Cymraeg</span></a></li><li class="interlanguage-link interwiki-da mw-list-item"><a href="https://da.wikipedia.org/wiki/Gr%C3%A6nsev%C3%A6rdi_(matematik)" title="Grænseværdi (matematik) – dánština" lang="da" hreflang="da" data-title="Grænseværdi (matematik)" data-language-autonym="Dansk" data-language-local-name="dánština" class="interlanguage-link-target"><span>Dansk</span></a></li><li class="interlanguage-link interwiki-diq mw-list-item"><a href="https://diq.wikipedia.org/wiki/Limit" title="Limit – Zazaki" lang="diq" hreflang="diq" data-title="Limit" data-language-autonym="Zazaki" data-language-local-name="Zazaki" class="interlanguage-link-target"><span>Zazaki</span></a></li><li class="interlanguage-link interwiki-el mw-list-item"><a href="https://el.wikipedia.org/wiki/%CE%8C%CF%81%CE%B9%CE%BF_(%CE%BC%CE%B1%CE%B8%CE%B7%CE%BC%CE%B1%CF%84%CE%B9%CE%BA%CE%AC)" title="Όριο (μαθηματικά) – řečtina" lang="el" hreflang="el" data-title="Όριο (μαθηματικά)" data-language-autonym="Ελληνικά" data-language-local-name="řečtina" class="interlanguage-link-target"><span>Ελληνικά</span></a></li><li class="interlanguage-link interwiki-en mw-list-item"><a href="https://en.wikipedia.org/wiki/Limit_(mathematics)" title="Limit (mathematics) – angličtina" lang="en" hreflang="en" data-title="Limit (mathematics)" data-language-autonym="English" data-language-local-name="angličtina" class="interlanguage-link-target"><span>English</span></a></li><li class="interlanguage-link interwiki-eo mw-list-item"><a href="https://eo.wikipedia.org/wiki/Limeso" title="Limeso – esperanto" lang="eo" hreflang="eo" data-title="Limeso" data-language-autonym="Esperanto" data-language-local-name="esperanto" class="interlanguage-link-target"><span>Esperanto</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/L%C3%ADmite_(matem%C3%A1tica)" title="Límite (matemática) – španělština" lang="es" hreflang="es" data-title="Límite (matemática)" data-language-autonym="Español" data-language-local-name="španělština" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-eu mw-list-item"><a href="https://eu.wikipedia.org/wiki/Limite" title="Limite – baskičtina" lang="eu" hreflang="eu" data-title="Limite" data-language-autonym="Euskara" data-language-local-name="baskičtina" class="interlanguage-link-target"><span>Euskara</span></a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%D8%AD%D8%AF_(%D8%B1%DB%8C%D8%A7%D8%B6%DB%8C)" title="حد (ریاضی) – perština" lang="fa" hreflang="fa" data-title="حد (ریاضی)" data-language-autonym="فارسی" data-language-local-name="perština" class="interlanguage-link-target"><span>فارسی</span></a></li><li class="interlanguage-link interwiki-fi mw-list-item"><a href="https://fi.wikipedia.org/wiki/Raja-arvo" title="Raja-arvo – finština" lang="fi" hreflang="fi" data-title="Raja-arvo" data-language-autonym="Suomi" data-language-local-name="finština" class="interlanguage-link-target"><span>Suomi</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/Limite_(math%C3%A9matiques)" title="Limite (mathématiques) – francouzština" lang="fr" hreflang="fr" data-title="Limite (mathématiques)" data-language-autonym="Français" data-language-local-name="francouzština" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-ga mw-list-item"><a href="https://ga.wikipedia.org/wiki/Teorainn_(matamaitic)" title="Teorainn (matamaitic) – irština" lang="ga" hreflang="ga" data-title="Teorainn (matamaitic)" data-language-autonym="Gaeilge" data-language-local-name="irština" class="interlanguage-link-target"><span>Gaeilge</span></a></li><li class="interlanguage-link interwiki-gan mw-list-item"><a href="https://gan.wikipedia.org/wiki/%E6%A5%B5%E9%99%90" title="極限 – čínština (dialekty Gan)" lang="gan" hreflang="gan" data-title="極限" data-language-autonym="贛語" data-language-local-name="čínština (dialekty Gan)" class="interlanguage-link-target"><span>贛語</span></a></li><li class="interlanguage-link interwiki-gcr mw-list-item"><a href="https://gcr.wikipedia.org/wiki/Limit_(mat%C3%A9matik)" title="Limit (matématik) – Guianan Creole" lang="gcr" hreflang="gcr" data-title="Limit (matématik)" data-language-autonym="Kriyòl gwiyannen" data-language-local-name="Guianan Creole" class="interlanguage-link-target"><span>Kriyòl gwiyannen</span></a></li><li class="interlanguage-link interwiki-gl mw-list-item"><a href="https://gl.wikipedia.org/wiki/L%C3%ADmite_matem%C3%A1tico" title="Límite matemático – galicijština" lang="gl" hreflang="gl" data-title="Límite matemático" data-language-autonym="Galego" data-language-local-name="galicijština" class="interlanguage-link-target"><span>Galego</span></a></li><li class="interlanguage-link interwiki-hak mw-list-item"><a href="https://hak.wikipedia.org/wiki/Khi%CC%8Dt-han_(S%C3%BA-ho%CC%8Dk)" title="Khi̍t-han (Sú-ho̍k) – čínština (dialekty Hakka)" lang="hak" hreflang="hak" data-title="Khi̍t-han (Sú-ho̍k)" data-language-autonym="客家語 / Hak-kâ-ngî" data-language-local-name="čínština (dialekty Hakka)" class="interlanguage-link-target"><span>客家語 / Hak-kâ-ngî</span></a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/wiki/%D7%92%D7%91%D7%95%D7%9C_(%D7%9E%D7%AA%D7%9E%D7%98%D7%99%D7%A7%D7%94)" title="גבול (מתמטיקה) – hebrejština" lang="he" hreflang="he" data-title="גבול (מתמטיקה)" data-language-autonym="עברית" data-language-local-name="hebrejština" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-hi mw-list-item"><a href="https://hi.wikipedia.org/wiki/%E0%A4%B8%E0%A5%80%E0%A4%AE%E0%A4%BE_(%E0%A4%97%E0%A4%A3%E0%A4%BF%E0%A4%A4)" title="सीमा (गणित) – hindština" lang="hi" hreflang="hi" data-title="सीमा (गणित)" data-language-autonym="हिन्दी" data-language-local-name="hindština" class="interlanguage-link-target"><span>हिन्दी</span></a></li><li class="interlanguage-link interwiki-hr mw-list-item"><a href="https://hr.wikipedia.org/wiki/Limes_(matematika)" title="Limes (matematika) – chorvatština" lang="hr" hreflang="hr" data-title="Limes (matematika)" data-language-autonym="Hrvatski" data-language-local-name="chorvatština" class="interlanguage-link-target"><span>Hrvatski</span></a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/Hat%C3%A1r%C3%A9rt%C3%A9k" title="Határérték – maďarština" lang="hu" hreflang="hu" data-title="Határérték" data-language-autonym="Magyar" data-language-local-name="maďarština" class="interlanguage-link-target"><span>Magyar</span></a></li><li class="interlanguage-link interwiki-hy mw-list-item"><a href="https://hy.wikipedia.org/wiki/%D5%8D%D5%A1%D5%B0%D5%B4%D5%A1%D5%B6_(%D5%B4%D5%A1%D5%A9%D5%A5%D5%B4%D5%A1%D5%BF%D5%AB%D5%AF%D5%A1)" title="Սահման (մաթեմատիկա) – arménština" lang="hy" hreflang="hy" data-title="Սահման (մաթեմատիկա)" data-language-autonym="Հայերեն" data-language-local-name="arménština" class="interlanguage-link-target"><span>Հայերեն</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Limit_(matematika)" title="Limit (matematika) – indonéština" lang="id" hreflang="id" data-title="Limit (matematika)" data-language-autonym="Bahasa Indonesia" data-language-local-name="indonéština" class="interlanguage-link-target"><span>Bahasa Indonesia</span></a></li><li class="interlanguage-link interwiki-io mw-list-item"><a href="https://io.wikipedia.org/wiki/Limito" title="Limito – ido" lang="io" hreflang="io" data-title="Limito" data-language-autonym="Ido" data-language-local-name="ido" class="interlanguage-link-target"><span>Ido</span></a></li><li class="interlanguage-link interwiki-is mw-list-item"><a href="https://is.wikipedia.org/wiki/Markgildi" title="Markgildi – islandština" lang="is" hreflang="is" data-title="Markgildi" data-language-autonym="Íslenska" data-language-local-name="islandština" class="interlanguage-link-target"><span>Íslenska</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Limite_(matematica)" title="Limite (matematica) – italština" lang="it" hreflang="it" data-title="Limite (matematica)" data-language-autonym="Italiano" data-language-local-name="italština" class="interlanguage-link-target"><span>Italiano</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E6%A5%B5%E9%99%90" title="極限 – japonština" lang="ja" hreflang="ja" data-title="極限" data-language-autonym="日本語" data-language-local-name="japonština" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-jam mw-list-item"><a href="https://jam.wikipedia.org/wiki/Limit_(matimatix)" title="Limit (matimatix) – jamajská kreolština" lang="jam" hreflang="jam" data-title="Limit (matimatix)" data-language-autonym="Patois" data-language-local-name="jamajská kreolština" class="interlanguage-link-target"><span>Patois</span></a></li><li class="interlanguage-link interwiki-ka badge-Q70893996 mw-list-item" title=""><a href="https://ka.wikipedia.org/wiki/%E1%83%96%E1%83%A6%E1%83%95%E1%83%90%E1%83%A0%E1%83%98_(%E1%83%9B%E1%83%90%E1%83%97%E1%83%94%E1%83%9B%E1%83%90%E1%83%A2%E1%83%98%E1%83%99%E1%83%90)" title="ზღვარი (მათემატიკა) – gruzínština" lang="ka" hreflang="ka" data-title="ზღვარი (მათემატიკა)" data-language-autonym="ქართული" data-language-local-name="gruzínština" class="interlanguage-link-target"><span>ქართული</span></a></li><li class="interlanguage-link interwiki-kab mw-list-item"><a href="https://kab.wikipedia.org/wiki/Talast_(Tusnakt)" title="Talast (Tusnakt) – kabylština" lang="kab" hreflang="kab" data-title="Talast (Tusnakt)" data-language-autonym="Taqbaylit" data-language-local-name="kabylština" class="interlanguage-link-target"><span>Taqbaylit</span></a></li><li class="interlanguage-link interwiki-kk mw-list-item"><a href="https://kk.wikipedia.org/wiki/%D0%A8%D0%B5%D0%BA" title="Шек – kazaština" lang="kk" hreflang="kk" data-title="Шек" data-language-autonym="Қазақша" data-language-local-name="kazaština" class="interlanguage-link-target"><span>Қазақша</span></a></li><li class="interlanguage-link interwiki-km mw-list-item"><a href="https://km.wikipedia.org/wiki/%E1%9E%9B%E1%9E%B8%E1%9E%98%E1%9E%B8%E1%9E%8F" title="លីមីត – khmérština" lang="km" hreflang="km" data-title="លីមីត" data-language-autonym="ភាសាខ្មែរ" data-language-local-name="khmérština" class="interlanguage-link-target"><span>ភាសាខ្មែរ</span></a></li><li class="interlanguage-link interwiki-kn mw-list-item"><a href="https://kn.wikipedia.org/wiki/%E0%B2%AA%E0%B2%B0%E0%B2%BF%E0%B2%AE%E0%B2%BF%E0%B2%A4%E0%B2%BF" title="ಪರಿಮಿತಿ – kannadština" lang="kn" hreflang="kn" data-title="ಪರಿಮಿತಿ" data-language-autonym="ಕನ್ನಡ" data-language-local-name="kannadština" class="interlanguage-link-target"><span>ಕನ್ನಡ</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EA%B7%B9%ED%95%9C" title="극한 – korejština" lang="ko" hreflang="ko" data-title="극한" data-language-autonym="한국어" data-language-local-name="korejština" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-la mw-list-item"><a href="https://la.wikipedia.org/wiki/Limes_(mathematica)" title="Limes (mathematica) – latina" lang="la" hreflang="la" data-title="Limes (mathematica)" data-language-autonym="Latina" data-language-local-name="latina" class="interlanguage-link-target"><span>Latina</span></a></li><li class="interlanguage-link interwiki-lmo badge-Q17437796 badge-featuredarticle mw-list-item" title="nejlepší článek"><a href="https://lmo.wikipedia.org/wiki/Limit_(matematega)" title="Limit (matematega) – lombardština" lang="lmo" hreflang="lmo" data-title="Limit (matematega)" data-language-autonym="Lombard" data-language-local-name="lombardština" class="interlanguage-link-target"><span>Lombard</span></a></li><li class="interlanguage-link interwiki-lt mw-list-item"><a href="https://lt.wikipedia.org/wiki/Riba_(matematika)" title="Riba (matematika) – litevština" lang="lt" hreflang="lt" data-title="Riba (matematika)" data-language-autonym="Lietuvių" data-language-local-name="litevština" class="interlanguage-link-target"><span>Lietuvių</span></a></li><li class="interlanguage-link interwiki-lv mw-list-item"><a href="https://lv.wikipedia.org/wiki/Robe%C5%BEa_(matem%C4%81tika)" title="Robeža (matemātika) – lotyština" lang="lv" hreflang="lv" data-title="Robeža (matemātika)" data-language-autonym="Latviešu" data-language-local-name="lotyština" class="interlanguage-link-target"><span>Latviešu</span></a></li><li class="interlanguage-link interwiki-mk mw-list-item"><a href="https://mk.wikipedia.org/wiki/%D0%93%D1%80%D0%B0%D0%BD%D0%B8%D1%87%D0%BD%D0%B0_%D0%B2%D1%80%D0%B5%D0%B4%D0%BD%D0%BE%D1%81%D1%82" title="Гранична вредност – makedonština" lang="mk" hreflang="mk" data-title="Гранична вредност" data-language-autonym="Македонски" data-language-local-name="makedonština" class="interlanguage-link-target"><span>Македонски</span></a></li><li class="interlanguage-link interwiki-mr mw-list-item"><a href="https://mr.wikipedia.org/wiki/%E0%A4%B8%E0%A5%80%E0%A4%AE%E0%A4%BE_(%E0%A4%97%E0%A4%A3%E0%A4%BF%E0%A4%A4)" title="सीमा (गणित) – maráthština" lang="mr" hreflang="mr" data-title="सीमा (गणित)" data-language-autonym="मराठी" data-language-local-name="maráthština" class="interlanguage-link-target"><span>मराठी</span></a></li><li class="interlanguage-link interwiki-ms mw-list-item"><a href="https://ms.wikipedia.org/wiki/Had_(matematik)" title="Had (matematik) – malajština" lang="ms" hreflang="ms" data-title="Had (matematik)" data-language-autonym="Bahasa Melayu" data-language-local-name="malajština" class="interlanguage-link-target"><span>Bahasa Melayu</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Limiet" title="Limiet – nizozemština" lang="nl" hreflang="nl" data-title="Limiet" data-language-autonym="Nederlands" data-language-local-name="nizozemština" class="interlanguage-link-target"><span>Nederlands</span></a></li><li class="interlanguage-link interwiki-nn mw-list-item"><a href="https://nn.wikipedia.org/wiki/Grense_i_matematikk" title="Grense i matematikk – norština (nynorsk)" lang="nn" hreflang="nn" data-title="Grense i matematikk" data-language-autonym="Norsk nynorsk" data-language-local-name="norština (nynorsk)" class="interlanguage-link-target"><span>Norsk nynorsk</span></a></li><li class="interlanguage-link interwiki-no mw-list-item"><a href="https://no.wikipedia.org/wiki/Grenseverdi" title="Grenseverdi – norština (bokmål)" lang="nb" hreflang="nb" data-title="Grenseverdi" data-language-autonym="Norsk bokmål" data-language-local-name="norština (bokmål)" class="interlanguage-link-target"><span>Norsk bokmål</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Granica_(matematyka)" title="Granica (matematyka) – polština" lang="pl" hreflang="pl" data-title="Granica (matematyka)" data-language-autonym="Polski" data-language-local-name="polština" class="interlanguage-link-target"><span>Polski</span></a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/Limite" title="Limite – portugalština" lang="pt" hreflang="pt" data-title="Limite" data-language-autonym="Português" data-language-local-name="portugalština" class="interlanguage-link-target"><span>Português</span></a></li><li class="interlanguage-link interwiki-ro mw-list-item"><a href="https://ro.wikipedia.org/wiki/Limit%C4%83_(matematic%C4%83)" title="Limită (matematică) – rumunština" lang="ro" hreflang="ro" data-title="Limită (matematică)" data-language-autonym="Română" data-language-local-name="rumunština" class="interlanguage-link-target"><span>Română</span></a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%9F%D1%80%D0%B5%D0%B4%D0%B5%D0%BB_(%D0%BC%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D0%BA%D0%B0)" title="Предел (математика) – ruština" lang="ru" hreflang="ru" data-title="Предел (математика)" data-language-autonym="Русский" data-language-local-name="ruština" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-scn mw-list-item"><a href="https://scn.wikipedia.org/wiki/L%C3%ACmiti" title="Lìmiti – sicilština" lang="scn" hreflang="scn" data-title="Lìmiti" data-language-autonym="Sicilianu" data-language-local-name="sicilština" class="interlanguage-link-target"><span>Sicilianu</span></a></li><li class="interlanguage-link interwiki-sh mw-list-item"><a href="https://sh.wikipedia.org/wiki/Limes_(matematika)" title="Limes (matematika) – srbochorvatština" lang="sh" hreflang="sh" data-title="Limes (matematika)" data-language-autonym="Srpskohrvatski / српскохрватски" data-language-local-name="srbochorvatština" class="interlanguage-link-target"><span>Srpskohrvatski / српскохрватски</span></a></li><li class="interlanguage-link interwiki-simple mw-list-item"><a href="https://simple.wikipedia.org/wiki/Limit_(mathematics)" title="Limit (mathematics) – Simple English" lang="en-simple" hreflang="en-simple" data-title="Limit (mathematics)" data-language-autonym="Simple English" data-language-local-name="Simple English" class="interlanguage-link-target"><span>Simple English</span></a></li><li class="interlanguage-link interwiki-sk mw-list-item"><a href="https://sk.wikipedia.org/wiki/Limita" title="Limita – slovenština" lang="sk" hreflang="sk" data-title="Limita" data-language-autonym="Slovenčina" data-language-local-name="slovenština" class="interlanguage-link-target"><span>Slovenčina</span></a></li><li class="interlanguage-link interwiki-sq mw-list-item"><a href="https://sq.wikipedia.org/wiki/Limiti" title="Limiti – albánština" lang="sq" hreflang="sq" data-title="Limiti" data-language-autonym="Shqip" data-language-local-name="albánština" class="interlanguage-link-target"><span>Shqip</span></a></li><li class="interlanguage-link interwiki-sr mw-list-item"><a href="https://sr.wikipedia.org/wiki/%D0%93%D1%80%D0%B0%D0%BD%D0%B8%D1%87%D0%BD%D0%B0_%D0%B2%D1%80%D0%B5%D0%B4%D0%BD%D0%BE%D1%81%D1%82" title="Гранична вредност – srbština" lang="sr" hreflang="sr" data-title="Гранична вредност" data-language-autonym="Српски / srpski" data-language-local-name="srbština" class="interlanguage-link-target"><span>Српски / srpski</span></a></li><li class="interlanguage-link interwiki-sv mw-list-item"><a href="https://sv.wikipedia.org/wiki/Gr%C3%A4nsv%C3%A4rde" title="Gränsvärde – švédština" lang="sv" hreflang="sv" data-title="Gränsvärde" data-language-autonym="Svenska" data-language-local-name="švédština" class="interlanguage-link-target"><span>Svenska</span></a></li><li class="interlanguage-link interwiki-ta mw-list-item"><a href="https://ta.wikipedia.org/wiki/%E0%AE%8E%E0%AE%B2%E0%AF%8D%E0%AE%B2%E0%AF%88_(%E0%AE%95%E0%AE%A3%E0%AE%BF%E0%AE%A4%E0%AE%AE%E0%AF%8D)" title="எல்லை (கணிதம்) – tamilština" lang="ta" hreflang="ta" data-title="எல்லை (கணிதம்)" data-language-autonym="தமிழ்" data-language-local-name="tamilština" class="interlanguage-link-target"><span>தமிழ்</span></a></li><li class="interlanguage-link interwiki-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/Limit" title="Limit – turečtina" lang="tr" hreflang="tr" data-title="Limit" data-language-autonym="Türkçe" data-language-local-name="turečtina" class="interlanguage-link-target"><span>Türkçe</span></a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/%D0%93%D1%80%D0%B0%D0%BD%D0%B8%D1%86%D1%8F" title="Границя – ukrajinština" lang="uk" hreflang="uk" data-title="Границя" data-language-autonym="Українська" data-language-local-name="ukrajinština" class="interlanguage-link-target"><span>Українська</span></a></li><li class="interlanguage-link interwiki-ur mw-list-item"><a href="https://ur.wikipedia.org/wiki/%D8%AD%D8%AF_(%D8%B1%DB%8C%D8%A7%D8%B6%DB%8C)" title="حد (ریاضی) – urdština" lang="ur" hreflang="ur" data-title="حد (ریاضی)" data-language-autonym="اردو" data-language-local-name="urdština" class="interlanguage-link-target"><span>اردو</span></a></li><li class="interlanguage-link interwiki-uz mw-list-item"><a href="https://uz.wikipedia.org/wiki/Limit" title="Limit – uzbečtina" lang="uz" hreflang="uz" data-title="Limit" data-language-autonym="Oʻzbekcha / ўзбекча" data-language-local-name="uzbečtina" class="interlanguage-link-target"><span>Oʻzbekcha / ўзбекча</span></a></li><li class="interlanguage-link interwiki-vec mw-list-item"><a href="https://vec.wikipedia.org/wiki/Limite" title="Limite – benátština" lang="vec" hreflang="vec" data-title="Limite" data-language-autonym="Vèneto" data-language-local-name="benátština" class="interlanguage-link-target"><span>Vèneto</span></a></li><li class="interlanguage-link interwiki-vi mw-list-item"><a href="https://vi.wikipedia.org/wiki/Gi%E1%BB%9Bi_h%E1%BA%A1n_(to%C3%A1n_h%E1%BB%8Dc)" title="Giới hạn (toán học) – vietnamština" lang="vi" hreflang="vi" data-title="Giới hạn (toán học)" data-language-autonym="Tiếng Việt" data-language-local-name="vietnamština" class="interlanguage-link-target"><span>Tiếng Việt</span></a></li><li class="interlanguage-link interwiki-vls mw-list-item"><a href="https://vls.wikipedia.org/wiki/Limiet" title="Limiet – vlámština (západní)" lang="vls" hreflang="vls" data-title="Limiet" data-language-autonym="West-Vlams" data-language-local-name="vlámština (západní)" class="interlanguage-link-target"><span>West-Vlams</span></a></li><li class="interlanguage-link interwiki-wuu mw-list-item"><a href="https://wuu.wikipedia.org/wiki/%E6%9E%81%E9%99%90%EF%BC%88%E6%95%B0%E5%AD%A6%EF%BC%89" title="极限（数学） – čínština (dialekty Wu)" lang="wuu" hreflang="wuu" data-title="极限（数学）" data-language-autonym="吴语" data-language-local-name="čínština (dialekty Wu)" class="interlanguage-link-target"><span>吴语</span></a></li><li class="interlanguage-link interwiki-zh mw-list-item"><a href="https://zh.wikipedia.org/wiki/%E6%9E%81%E9%99%90_(%E6%95%B0%E5%AD%A6)" title="极限 (数学) – čínština" lang="zh" hreflang="zh" data-title="极限 (数学)" data-language-autonym="中文" data-language-local-name="čínština" class="interlanguage-link-target"><span>中文</span></a></li><li class="interlanguage-link interwiki-zh-yue mw-list-item"><a href="https://zh-yue.wikipedia.org/wiki/%E6%A5%B5%E9%99%90_(%E6%95%B8%E5%AD%B8)" title="極限 (數學) – kantonština" lang="yue" hreflang="yue" data-title="極限 (數學)" data-language-autonym="粵語" data-language-local-name="kantonština" class="interlanguage-link-target"><span>粵語</span></a></li> </ul> <div class="after-portlet after-portlet-lang"><span class="wb-langlinks-edit wb-langlinks-link"><a href="https://www.wikidata.org/wiki/Special:EntityPage/Q177239#sitelinks-wikipedia" title="Editovat mezijazykové odkazy" class="wbc-editpage">Upravit odkazy</a></span></div> </div> </div> </div> </header> <div class="vector-page-toolbar"> <div class="vector-page-toolbar-container"> <div id="left-navigation"> <nav aria-label="Jmenné prostory"> <div id="p-associated-pages" class="vector-menu vector-menu-tabs mw-portlet mw-portlet-associated-pages" > <div class="vector-menu-content"> <ul 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hreflang="en"><span>Wikimedia Commons</span></a></li><li id="t-wikibase" class="wb-otherproject-link wb-otherproject-wikibase-dataitem mw-list-item"><a href="https://www.wikidata.org/wiki/Special:EntityPage/Q177239" title="Odkaz na propojenou položku datového úložiště [g]" accesskey="g"><span>Položka Wikidat</span></a></li> </ul> </div> </div> </div> </div> </div> </div> </nav> </div> </div> </div> <div class="vector-column-end"> <div class="vector-sticky-pinned-container"> <nav class="vector-page-tools-landmark" aria-label="Nástroje ke stránce"> <div id="vector-page-tools-pinned-container" class="vector-pinned-container"> </div> </nav> <nav class="vector-appearance-landmark" aria-label="Vzhled"> <div id="vector-appearance-pinned-container" class="vector-pinned-container"> <div id="vector-appearance" class="vector-appearance vector-pinnable-element"> <div class="vector-pinnable-header vector-appearance-pinnable-header vector-pinnable-header-pinned" data-feature-name="appearance-pinned" 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class="mw-content-ltr mw-parser-output" lang="cs" dir="ltr"><div class="uvodni-upozorneni hatnote noprint">Tento článek je o limitě funkce nebo zobrazení. O limitě a kolimitě v teorii kategorií pojednává článek <a href="/wiki/Limita_(teorie_kategori%C3%AD)" title="Limita (teorie kategorií)">Limita (teorie kategorií)</a>.</div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/Soubor:Limit-at-infinity-graph.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/6/66/Limit-at-infinity-graph.png/220px-Limit-at-infinity-graph.png" decoding="async" width="220" height="144" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/66/Limit-at-infinity-graph.png/330px-Limit-at-infinity-graph.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/66/Limit-at-infinity-graph.png/440px-Limit-at-infinity-graph.png 2x" data-file-width="619" data-file-height="405" /></a><figcaption></figcaption></figure> <p><b>Limita</b> je <a href="/wiki/Matematika" title="Matematika">matematická</a> konstrukce vyjadřující, že se hodnoty zadané <a href="/wiki/Funkce_(matematika)" title="Funkce (matematika)">funkce</a> nebo <a href="/wiki/Posloupnost" title="Posloupnost">posloupnosti</a> blíží libovolně blízko k nějakému bodu. Právě tento bod je pak označován jako limita. Tato skutečnost se u funkcí zapisuje <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \lim _{x\rightarrow a}f(x)=A}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <munder> <mo movablelimits="true" form="prefix">lim</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>x</mi> <mo stretchy="false">→</mo> <mi>a</mi> </mrow> </munder> <mi>f</mi> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mi>A</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \lim _{x\rightarrow a}f(x)=A}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/01012d9f7d062f11ff185521f93c6d776d3768fa" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:13.099ex; height:3.843ex;" alt="{\displaystyle \lim _{x\rightarrow a}f(x)=A}"></span> a u posloupností <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \lim _{n\to \infty }a_{n}=A}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <munder> <mo movablelimits="true" form="prefix">lim</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> <mo stretchy="false">→</mo> <mi mathvariant="normal">∞</mi> </mrow> </munder> <msub> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msub> <mo>=</mo> <mi>A</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \lim _{n\to \infty }a_{n}=A}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d3fa48c4f6501b5b590c911426e6265d71101ded" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:11.949ex; height:3.676ex;" alt="{\displaystyle \lim _{n\to \infty }a_{n}=A}"></span>. </p><p>Dle toho, zda se uvažuje o funkci nebo o posloupnosti, hovoříme o <a href="/wiki/Limita_funkce" title="Limita funkce">limitě funkce</a> nebo <a href="/wiki/Limita_posloupnosti" title="Limita posloupnosti">limitě posloupnosti</a>. Pojem limity lze definovat na <a href="/wiki/Re%C3%A1ln%C3%A9_%C4%8D%C3%ADslo" title="Reálné číslo">reálných číslech</a>, obecnější definice má smysl na libovolném <a href="/wiki/Metrick%C3%BD_prostor" title="Metrický prostor">metrickém prostoru</a> a ještě obecnější definice na libovolném <a href="/wiki/Topologick%C3%BD_prostor" title="Topologický prostor">topologickém prostoru</a>. Tam, kde má smysl více definic, jsou tyto definice ekvivalentní (například reálná čísla jsou metrickým i topologickým prostorem). </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Limita_funkce">Limita funkce</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Limita&veaction=edit&section=1" title="Editace sekce: Limita funkce" class="mw-editsection-visualeditor"><span>editovat</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Limita&action=edit&section=1" title="Editovat zdrojový kód sekce Limita funkce"><span>editovat zdroj</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="uvodni-upozorneni hatnote"> Podrobnější informace naleznete v článku <a href="/wiki/Limita_funkce" title="Limita funkce">Limita funkce</a>.</div> <p>Číslo <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle A\in \mathbb {R} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>A</mi> <mo>∈</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">R</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A\in \mathbb {R} }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/bd0221fc4bfd182ed1f4829b01e80cce13959e55" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:6.262ex; height:2.176ex;" alt="{\displaystyle A\in \mathbb {R} }"></span> je <b>limitou funkce</b> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle f:\mathbb {R} \rightarrow \mathbb {R} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>f</mi> <mo>:</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">R</mi> </mrow> <mo stretchy="false">→</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">R</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle f:\mathbb {R} \rightarrow \mathbb {R} }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/85e6e186aabef9e51814bbce62e625dc67e825f2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:10.186ex; height:2.509ex;" alt="{\displaystyle f:\mathbb {R} \rightarrow \mathbb {R} }"></span> v bodě <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle a\in \mathbb {R} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>a</mi> <mo>∈</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">R</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle a\in \mathbb {R} }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b044c60e01b54c7116ee355431f37ed846badc53" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:5.749ex; height:2.176ex;" alt="{\displaystyle a\in \mathbb {R} }"></span>, jestliže pro libovolné <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \varepsilon >0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>ε</mi> <mo>></mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \varepsilon >0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e04ec3670b50384a3ce48aca42e7cc5131a06b12" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:5.344ex; height:2.176ex;" alt="{\displaystyle \varepsilon >0}"></span> existuje <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \delta >0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>δ</mi> <mo>></mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \delta >0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/595d5cea06fdcaf2642caf549eda2cfc537958a9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:5.31ex; height:2.343ex;" alt="{\displaystyle \delta >0}"></span> takové, že pro každé <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle x\in D_{f}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>x</mi> <mo>∈</mo> <msub> <mi>D</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>f</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle x\in D_{f}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3029cdd2f249918d8f7c504343853c821fd480f6" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:7.231ex; height:2.843ex;" alt="{\displaystyle x\in D_{f}}"></span> takové, že <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle 0<\left|x-a\right|<\delta }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mn>0</mn> <mo><</mo> <mrow> <mo>|</mo> <mrow> <mi>x</mi> <mo>−</mo> <mi>a</mi> </mrow> <mo>|</mo> </mrow> <mo><</mo> <mi>δ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 0<\left|x-a\right|<\delta }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/050877ce3ad11b37470435a1e041a5a1d6910bdd" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:15.102ex; height:2.843ex;" alt="{\displaystyle 0<\left|x-a\right|<\delta }"></span> (<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle x}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>x</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle x}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/87f9e315fd7e2ba406057a97300593c4802b53e4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.33ex; height:1.676ex;" alt="{\displaystyle x}"></span> leží v <a href="/wiki/Okol%C3%AD_(matematika)" title="Okolí (matematika)">prstencovém okolí</a> bodu <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle a}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>a</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle a}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ffd2487510aa438433a2579450ab2b3d557e5edc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.23ex; height:1.676ex;" alt="{\displaystyle a}"></span>) platí <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \left|f(x)-A\right|<\varepsilon }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow> <mo>|</mo> <mrow> <mi>f</mi> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> <mo>−</mo> <mi>A</mi> </mrow> <mo>|</mo> </mrow> <mo><</mo> <mi>ε</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \left|f(x)-A\right|<\varepsilon }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1b90a127d9145f59432c731eec38093e957d01d5" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:14.477ex; height:2.843ex;" alt="{\displaystyle \left|f(x)-A\right|<\varepsilon }"></span>. </p> <div class="mw-heading mw-heading2"><h2 id="Limita_posloupnosti">Limita posloupnosti</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Limita&veaction=edit&section=2" title="Editace sekce: Limita posloupnosti" class="mw-editsection-visualeditor"><span>editovat</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Limita&action=edit&section=2" title="Editovat zdrojový kód sekce Limita posloupnosti"><span>editovat zdroj</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="uvodni-upozorneni hatnote"> Podrobnější informace naleznete v článku <a href="/wiki/Limita_posloupnosti" title="Limita posloupnosti">Limita posloupnosti</a>.</div> <p>Číslo <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle A\in \mathbb {R} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>A</mi> <mo>∈</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">R</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A\in \mathbb {R} }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/bd0221fc4bfd182ed1f4829b01e80cce13959e55" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:6.262ex; height:2.176ex;" alt="{\displaystyle A\in \mathbb {R} }"></span> je <b>limitou posloupnosti</b> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \{a_{n}\}_{n=1}^{\infty }}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo fence="false" stretchy="false">{</mo> <msub> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msub> <msubsup> <mo fence="false" stretchy="false">}</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> <mo>=</mo> <mn>1</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">∞</mi> </mrow> </msubsup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \{a_{n}\}_{n=1}^{\infty }}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a28a0eda962ff3986e2b8abba0cad913ee837c75" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:8.092ex; height:3.009ex;" alt="{\displaystyle \{a_{n}\}_{n=1}^{\infty }}"></span>, jestliže pro libovolné <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \varepsilon >0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>ε</mi> <mo>></mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \varepsilon >0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e04ec3670b50384a3ce48aca42e7cc5131a06b12" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:5.344ex; height:2.176ex;" alt="{\displaystyle \varepsilon >0}"></span> existuje <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle n_{0}\in \mathbb {N} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mo>∈</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">N</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle n_{0}\in \mathbb {N} }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a1784c411bfa17be1e10d891101eb365daabda47" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:6.968ex; height:2.509ex;" alt="{\displaystyle n_{0}\in \mathbb {N} }"></span> takové, že pro každé <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle n\geq n_{0}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>n</mi> <mo>≥</mo> <msub> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle n\geq n_{0}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/fff23d9c13da1b2a7ec6f7fab8fa413b129c6b6c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:6.942ex; height:2.343ex;" alt="{\displaystyle n\geq n_{0}}"></span> platí <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle |a_{n}-A|<\varepsilon }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <msub> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msub> <mo>−</mo> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mo><</mo> <mi>ε</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle |a_{n}-A|<\varepsilon }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3f9981da389ab05ac53b38adba616b6e29f3f228" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:12.507ex; height:2.843ex;" alt="{\displaystyle |a_{n}-A|<\varepsilon }"></span>. </p> <div class="mw-heading mw-heading2"><h2 id="Limita_v_metrickém_prostoru"><span id="Limita_v_metrick.C3.A9m_prostoru"></span>Limita v metrickém prostoru</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Limita&veaction=edit&section=3" title="Editace sekce: Limita v metrickém prostoru" class="mw-editsection-visualeditor"><span>editovat</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Limita&action=edit&section=3" title="Editovat zdrojový kód sekce Limita v metrickém prostoru"><span>editovat zdroj</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Prvek <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle x}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>x</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle x}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/87f9e315fd7e2ba406057a97300593c4802b53e4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.33ex; height:1.676ex;" alt="{\displaystyle x}"></span> <a href="/wiki/Metrick%C3%BD_prostor" title="Metrický prostor">metrického prostoru</a> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle X}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>X</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle X}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/68baa052181f707c662844a465bfeeb135e82bab" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.98ex; height:2.176ex;" alt="{\displaystyle X}"></span> s metrikou <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \rho }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>ρ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \rho }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1f7d439671d1289b6a816e6af7a304be40608d64" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:1.202ex; height:2.176ex;" alt="{\displaystyle \rho }"></span> je <b>limitou posloupnosti</b> jeho prvků <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \{x_{n}\}_{n=1}^{\infty }}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo fence="false" stretchy="false">{</mo> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msub> <msubsup> <mo fence="false" stretchy="false">}</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> <mo>=</mo> <mn>1</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">∞</mi> </mrow> </msubsup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \{x_{n}\}_{n=1}^{\infty }}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/02d3ffd73dbe0cdd90a51b461341f72fdc95734d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:8.192ex; height:3.009ex;" alt="{\displaystyle \{x_{n}\}_{n=1}^{\infty }}"></span>, právě když platí <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \lim _{n\rightarrow \infty }\rho (x_{n},x)=0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <munder> <mo movablelimits="true" form="prefix">lim</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> <mo stretchy="false">→</mo> <mi mathvariant="normal">∞</mi> </mrow> </munder> <mi>ρ</mi> <mo stretchy="false">(</mo> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msub> <mo>,</mo> <mi>x</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \lim _{n\rightarrow \infty }\rho (x_{n},x)=0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/78625dccddcdb59ce67d02d0cb75c8fbb6fc5357" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:16.844ex; height:3.843ex;" alt="{\displaystyle \lim _{n\rightarrow \infty }\rho (x_{n},x)=0}"></span>. </p> <div class="mw-heading mw-heading2"><h2 id="Limita_v_topologickém_prostoru"><span id="Limita_v_topologick.C3.A9m_prostoru"></span>Limita v topologickém prostoru</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Limita&veaction=edit&section=4" title="Editace sekce: Limita v topologickém prostoru" class="mw-editsection-visualeditor"><span>editovat</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Limita&action=edit&section=4" title="Editovat zdrojový kód sekce Limita v topologickém prostoru"><span>editovat zdroj</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="uvodni-upozorneni hatnote"> Podrobnější informace naleznete v článku <a href="/wiki/Limita_posloupnosti#V_topologických_prostorech" title="Limita posloupnosti">Limita_posloupnosti#V_topologických_prostorech</a>.</div> <p><b>Limita zobrazení</b> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle f:A\to B}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>f</mi> <mo>:</mo> <mi>A</mi> <mo stretchy="false">→</mo> <mi>B</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle f:A\to B}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/20040a52d9391f2fe271f0aaa300bf7887a0c7b1" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:10.337ex; height:2.509ex;" alt="{\displaystyle f:A\to B}"></span> mezi <a href="/wiki/Topologick%C3%BD_prostor" title="Topologický prostor">topologickými prostory</a> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle A}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>A</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7daff47fa58cdfd29dc333def748ff5fa4c923e3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.743ex; height:2.176ex;" alt="{\displaystyle A}"></span> a <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle B}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>B</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle B}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/47136aad860d145f75f3eed3022df827cee94d7a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.764ex; height:2.176ex;" alt="{\displaystyle B}"></span> je v bodě <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle a\in A}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>a</mi> <mo>∈</mo> <mi>A</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle a\in A}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a97387981adb5d65f74518e20b6785a284d7abd5" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:5.814ex; height:2.176ex;" alt="{\displaystyle a\in A}"></span> definována jako <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle b\in B}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>b</mi> <mo>∈</mo> <mi>B</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle b\in B}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/61dbfba9ff608c8700a30596649d98dcc6147d86" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:5.602ex; height:2.176ex;" alt="{\displaystyle b\in B}"></span> takové, že pro každé okolí <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle O(b)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>O</mi> <mo stretchy="false">(</mo> <mi>b</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle O(b)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/617e0fcc33be0730c40d7c458cd4951c60b4d66a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:4.58ex; height:2.843ex;" alt="{\displaystyle O(b)}"></span> bodu <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle b}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>b</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle b}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f11423fbb2e967f986e36804a8ae4271734917c3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:0.998ex; height:2.176ex;" alt="{\displaystyle b}"></span> existuje okolí <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle O(a)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>O</mi> <mo stretchy="false">(</mo> <mi>a</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle O(a)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/dce111d97f41e5f2d88c91079a1572f8d45ee0d5" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:4.812ex; height:2.843ex;" alt="{\displaystyle O(a)}"></span> bodu <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle a}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>a</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle a}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ffd2487510aa438433a2579450ab2b3d557e5edc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.23ex; height:1.676ex;" alt="{\displaystyle a}"></span> takové, že <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle x\in O(a)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>x</mi> <mo>∈</mo> <mi>O</mi> <mo stretchy="false">(</mo> <mi>a</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle x\in O(a)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9fea27b88c8cd2e757daca94cb8f05e1b76e874f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:8.983ex; height:2.843ex;" alt="{\displaystyle x\in O(a)}"></span> implikuje <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle f(x)\in O(b)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>f</mi> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> <mo>∈</mo> <mi>O</mi> <mo stretchy="false">(</mo> <mi>b</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle f(x)\in O(b)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ebac9ca34f5b911ee56856e8dcedb94eeb116307" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:11.838ex; height:2.843ex;" alt="{\displaystyle f(x)\in O(b)}"></span>. </p><p>Dalším zobecněním limity posloupnosti, funkce i zobrazení jsou limity topologických sítí<sup id="cite_ref-1" class="reference"><a href="#cite_note-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup>. Limita zobrazení nebo topologické sítě může být v obecném topologickém prostoru víceznačná. Platí však, že v <a href="/wiki/Hausdorff%C5%AFv_prostor" title="Hausdorffův prostor">Hausdorffově prostoru</a> je tato limita jednoznačná, tj. každé zobrazení či topologická síť má nejvýše jednu limitu. </p> <div class="mw-heading mw-heading2"><h2 id="Nevlastní_limita_v_nevlastním_bodě"><span id="Nevlastn.C3.AD_limita_v_nevlastn.C3.ADm_bod.C4.9B"></span>Nevlastní limita v nevlastním bodě</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Limita&veaction=edit&section=5" title="Editace sekce: Nevlastní limita v nevlastním bodě" class="mw-editsection-visualeditor"><span>editovat</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Limita&action=edit&section=5" title="Editovat zdrojový kód sekce Nevlastní limita v nevlastním bodě"><span>editovat zdroj</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Pokud pro libovolné číslo <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \varepsilon >0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>ε</mi> <mo>></mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \varepsilon >0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e04ec3670b50384a3ce48aca42e7cc5131a06b12" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:5.344ex; height:2.176ex;" alt="{\displaystyle \varepsilon >0}"></span> lze nalézt prvek posloupnosti, počínaje kterým jsou všechny hodnoty posloupnosti větší než <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \varepsilon }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>ε</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \varepsilon }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a30c89172e5b88edbd45d3e2772c7f5e562e5173" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.083ex; height:1.676ex;" alt="{\displaystyle \varepsilon }"></span>, říkáme, že <b>posloupnost roste nade všechny meze</b> neboli že má <b>nevlastní limitu</b> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle +\infty }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>+</mo> <mi mathvariant="normal">∞</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle +\infty }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/bddbb0e4420a7e744cf71bd71216e11b0bf88831" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:4.132ex; height:2.176ex;" alt="{\displaystyle +\infty }"></span>. Obdobně se definuje nevlastní limita <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle -\infty }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>−</mo> <mi mathvariant="normal">∞</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle -\infty }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ca2608c4b5fd3bffc73585f8c67e379b4e99b6f1" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:4.132ex; height:2.176ex;" alt="{\displaystyle -\infty }"></span>. </p><p>Pokud pro libovolné číslo <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \varepsilon >0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>ε</mi> <mo>></mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \varepsilon >0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e04ec3670b50384a3ce48aca42e7cc5131a06b12" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:5.344ex; height:2.176ex;" alt="{\displaystyle \varepsilon >0}"></span> lze nalézt okolí bodu <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle a}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>a</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle a}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ffd2487510aa438433a2579450ab2b3d557e5edc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.23ex; height:1.676ex;" alt="{\displaystyle a}"></span>, ve kterém má funkce hodnotu větší než <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \varepsilon }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>ε</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \varepsilon }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a30c89172e5b88edbd45d3e2772c7f5e562e5173" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.083ex; height:1.676ex;" alt="{\displaystyle \varepsilon }"></span>, říkáme, že v okolí bodu <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle a}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>a</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle a}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ffd2487510aa438433a2579450ab2b3d557e5edc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.23ex; height:1.676ex;" alt="{\displaystyle a}"></span> <b>funkce roste nade všechny meze</b> neboli že má <b>nevlastní limitu</b> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle +\infty }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>+</mo> <mi mathvariant="normal">∞</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle +\infty }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/bddbb0e4420a7e744cf71bd71216e11b0bf88831" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:4.132ex; height:2.176ex;" alt="{\displaystyle +\infty }"></span>. Obdobně se definuje nevlastní limita <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle -\infty }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>−</mo> <mi mathvariant="normal">∞</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle -\infty }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ca2608c4b5fd3bffc73585f8c67e379b4e99b6f1" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:4.132ex; height:2.176ex;" alt="{\displaystyle -\infty }"></span>. </p><p>Limitou tedy může být nejen <a href="/wiki/Re%C3%A1ln%C3%A9_%C4%8D%C3%ADslo" title="Reálné číslo">reálné číslo</a>, ale i <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle +\infty }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>+</mo> <mi mathvariant="normal">∞</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle +\infty }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/bddbb0e4420a7e744cf71bd71216e11b0bf88831" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:4.132ex; height:2.176ex;" alt="{\displaystyle +\infty }"></span> nebo <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle -\infty }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>−</mo> <mi mathvariant="normal">∞</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle -\infty }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ca2608c4b5fd3bffc73585f8c67e379b4e99b6f1" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:4.132ex; height:2.176ex;" alt="{\displaystyle -\infty }"></span> (<a href="/wiki/Roz%C5%A1%C3%AD%C5%99en%C3%A1_re%C3%A1ln%C3%A1_%C4%8D%C3%ADsla" title="Rozšířená reálná čísla">rozšířené reálné číslo</a>). </p><p>Pokud se hodnoty limity neliší od čísla <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle A}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>A</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7daff47fa58cdfd29dc333def748ff5fa4c923e3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.743ex; height:2.176ex;" alt="{\displaystyle A}"></span> o více než libovolné číslo <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \varepsilon >0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>ε</mi> <mo>></mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \varepsilon >0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e04ec3670b50384a3ce48aca42e7cc5131a06b12" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:5.344ex; height:2.176ex;" alt="{\displaystyle \varepsilon >0}"></span>, má funkce v <b>nevlastním bodě</b> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle +\infty }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>+</mo> <mi mathvariant="normal">∞</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle +\infty }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/bddbb0e4420a7e744cf71bd71216e11b0bf88831" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:4.132ex; height:2.176ex;" alt="{\displaystyle +\infty }"></span> <b>vlastní limitu</b> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle A}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>A</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7daff47fa58cdfd29dc333def748ff5fa4c923e3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.743ex; height:2.176ex;" alt="{\displaystyle A}"></span>. Pokud jsou hodnoty limity větší než libovolné číslo <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \varepsilon >0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>ε</mi> <mo>></mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \varepsilon >0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e04ec3670b50384a3ce48aca42e7cc5131a06b12" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:5.344ex; height:2.176ex;" alt="{\displaystyle \varepsilon >0}"></span>, má funkce v <b>nevlastním bodě</b> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle +\infty }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>+</mo> <mi mathvariant="normal">∞</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle +\infty }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/bddbb0e4420a7e744cf71bd71216e11b0bf88831" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:4.132ex; height:2.176ex;" alt="{\displaystyle +\infty }"></span> <b>nevlastní limitu</b> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle +\infty }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>+</mo> <mi mathvariant="normal">∞</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle +\infty }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/bddbb0e4420a7e744cf71bd71216e11b0bf88831" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:4.132ex; height:2.176ex;" alt="{\displaystyle +\infty }"></span>. Obdobným způsobem lze definovat limitu v nevlastním bodě <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle -\infty }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>−</mo> <mi mathvariant="normal">∞</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle -\infty }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ca2608c4b5fd3bffc73585f8c67e379b4e99b6f1" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:4.132ex; height:2.176ex;" alt="{\displaystyle -\infty }"></span>. </p><p>V každém z nevlastních bodů <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle +\infty }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>+</mo> <mi mathvariant="normal">∞</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle +\infty }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/bddbb0e4420a7e744cf71bd71216e11b0bf88831" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:4.132ex; height:2.176ex;" alt="{\displaystyle +\infty }"></span> nebo <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle -\infty }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>−</mo> <mi mathvariant="normal">∞</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle -\infty }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ca2608c4b5fd3bffc73585f8c67e379b4e99b6f1" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:4.132ex; height:2.176ex;" alt="{\displaystyle -\infty }"></span> může mít funkce vlastní limitu, nevlastní limitu nebo limita nemusí existovat. Příkladem funkce, která nemá limitu v žádném z bodů <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle +\infty }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>+</mo> <mi mathvariant="normal">∞</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle +\infty }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/bddbb0e4420a7e744cf71bd71216e11b0bf88831" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:4.132ex; height:2.176ex;" alt="{\displaystyle +\infty }"></span> nebo <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle -\infty }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>−</mo> <mi mathvariant="normal">∞</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle -\infty }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ca2608c4b5fd3bffc73585f8c67e379b4e99b6f1" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:4.132ex; height:2.176ex;" alt="{\displaystyle -\infty }"></span>, je funkce <a href="/wiki/Sinus" title="Sinus">sinus</a>. </p> <div class="mw-heading mw-heading2"><h2 id="Příklady"><span id="P.C5.99.C3.ADklady"></span>Příklady</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Limita&veaction=edit&section=6" title="Editace sekce: Příklady" class="mw-editsection-visualeditor"><span>editovat</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Limita&action=edit&section=6" title="Editovat zdrojový kód sekce Příklady"><span>editovat zdroj</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul class="gallery mw-gallery-traditional"> <li class="gallerybox" style="width: 275px"> <div class="thumb" style="width: 270px; height: 210px;"><span typeof="mw:File"><a href="/wiki/Soubor:Sinc_function_(unnormalized).svg" class="mw-file-description" title="Graf funkce '"`UNIQ--postMath-0000003B-QINU`"'. Je vidět, že tato funkce má limitu 1 v bodě nula."><img alt="Graf funkce '"`UNIQ--postMath-0000003B-QINU`"'. Je vidět, že tato funkce má limitu 1 v bodě nula." src="//upload.wikimedia.org/wikipedia/commons/thumb/4/4e/Sinc_function_%28unnormalized%29.svg/240px-Sinc_function_%28unnormalized%29.svg.png" decoding="async" width="240" height="180" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/4e/Sinc_function_%28unnormalized%29.svg/360px-Sinc_function_%28unnormalized%29.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/4e/Sinc_function_%28unnormalized%29.svg/480px-Sinc_function_%28unnormalized%29.svg.png 2x" data-file-width="1300" data-file-height="975" /></a></span></div> <div class="gallerytext">Graf funkce <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \scriptstyle f(x)={\frac {\sin(x)}{x}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mstyle displaystyle="false" scriptlevel="1"> <mi>f</mi> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>sin</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> </mrow> <mi>x</mi> </mfrac> </mrow> </mstyle> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \scriptstyle f(x)={\frac {\sin(x)}{x}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/021086b7144316ffddcdd738999f4501d5f53a0a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:8.68ex; height:3.343ex;" alt="{\displaystyle \scriptstyle f(x)={\frac {\sin(x)}{x}}}"></span>. Je vidět, že tato funkce má limitu 1 v bodě nula.</div> </li> <li class="gallerybox" style="width: 275px"> <div class="thumb" style="width: 270px; height: 210px;"><span typeof="mw:File"><a href="/wiki/Soubor:Graph_of_function_1_to_minus_1_in_Neighbourhood_of_zero.svg" class="mw-file-description" title="Graf funkce '"`UNIQ--postMath-0000003C-QINU`"'. Je vidět, že tato funkce nemá limitu v bodě nula a má vlastní limity 0 v '"`UNIQ--postMath-0000003D-QINU`"'."><img alt="Graf funkce '"`UNIQ--postMath-0000003C-QINU`"'. Je vidět, že tato funkce nemá limitu v bodě nula a má vlastní limity 0 v '"`UNIQ--postMath-0000003D-QINU`"'." src="//upload.wikimedia.org/wikipedia/commons/thumb/5/59/Graph_of_function_1_to_minus_1_in_Neighbourhood_of_zero.svg/240px-Graph_of_function_1_to_minus_1_in_Neighbourhood_of_zero.svg.png" decoding="async" width="240" height="180" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/5/59/Graph_of_function_1_to_minus_1_in_Neighbourhood_of_zero.svg/360px-Graph_of_function_1_to_minus_1_in_Neighbourhood_of_zero.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/5/59/Graph_of_function_1_to_minus_1_in_Neighbourhood_of_zero.svg/480px-Graph_of_function_1_to_minus_1_in_Neighbourhood_of_zero.svg.png 2x" data-file-width="1300" data-file-height="975" /></a></span></div> <div class="gallerytext">Graf funkce <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \scriptstyle f(x)={\frac {1}{x}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mstyle displaystyle="false" scriptlevel="1"> <mi>f</mi> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mi>x</mi> </mfrac> </mrow> </mstyle> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \scriptstyle f(x)={\frac {1}{x}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/da82b8d5b1c06a6c3caedb4d2c3e56d44b64b2a0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:6.002ex; height:2.843ex;" alt="{\displaystyle \scriptstyle f(x)={\frac {1}{x}}}"></span>. Je vidět, že tato funkce nemá limitu v bodě nula a má vlastní limity 0 v <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \scriptstyle \pm \infty }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mstyle displaystyle="false" scriptlevel="1"> <mo>±</mo> <mi mathvariant="normal">∞</mi> </mstyle> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \scriptstyle \pm \infty }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/bd4415d2118612a537f272c2dbe35c3abc88e0d2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.922ex; height:1.676ex;" alt="{\displaystyle \scriptstyle \pm \infty }"></span>.</div> </li> <li class="gallerybox" style="width: 275px"> <div class="thumb" style="width: 270px; height: 210px;"><span typeof="mw:File"><a href="/wiki/Soubor:1_to_minus_2.svg" class="mw-file-description" title="Graf funkce '"`UNIQ--postMath-0000003E-QINU`"'. Je vidět, že tato funkce má nevlastní limitu '"`UNIQ--postMath-0000003F-QINU`"' v bodě nula a má vlastní limity 0 v '"`UNIQ--postMath-00000040-QINU`"'."><img alt="Graf funkce '"`UNIQ--postMath-0000003E-QINU`"'. Je vidět, že tato funkce má nevlastní limitu '"`UNIQ--postMath-0000003F-QINU`"' v bodě nula a má vlastní limity 0 v '"`UNIQ--postMath-00000040-QINU`"'." src="//upload.wikimedia.org/wikipedia/commons/thumb/9/95/1_to_minus_2.svg/240px-1_to_minus_2.svg.png" decoding="async" width="240" height="180" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/9/95/1_to_minus_2.svg/360px-1_to_minus_2.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/9/95/1_to_minus_2.svg/480px-1_to_minus_2.svg.png 2x" data-file-width="1300" data-file-height="975" /></a></span></div> <div class="gallerytext">Graf funkce <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \scriptstyle f(x)={\frac {1}{x^{2}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mstyle displaystyle="false" scriptlevel="1"> <mi>f</mi> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mfrac> </mrow> </mstyle> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \scriptstyle f(x)={\frac {1}{x^{2}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f2e1b23a236c12d7d99e20c7538c518c6d687e38" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.505ex; width:6.802ex; height:3.509ex;" alt="{\displaystyle \scriptstyle f(x)={\frac {1}{x^{2}}}}"></span>. Je vidět, že tato funkce má nevlastní limitu <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \scriptstyle +\infty \,\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mstyle displaystyle="false" scriptlevel="1"> <mo>+</mo> <mi mathvariant="normal">∞</mi> <mspace width="thinmathspace" /> <mspace width="negativethinmathspace" /> </mstyle> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \scriptstyle +\infty \,\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f73463a90c8ae9199f2585756fcb761c662f66ea" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; margin-right: -0.387ex; width:3.309ex; height:1.509ex;" alt="{\displaystyle \scriptstyle +\infty \,\!}"></span> v bodě nula a má vlastní limity 0 v <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \scriptstyle \pm \infty }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mstyle displaystyle="false" scriptlevel="1"> <mo>±</mo> <mi mathvariant="normal">∞</mi> </mstyle> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \scriptstyle \pm \infty }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/bd4415d2118612a537f272c2dbe35c3abc88e0d2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.922ex; height:1.676ex;" alt="{\displaystyle \scriptstyle \pm \infty }"></span>.</div> </li> </ul> <ul><li>Funkce <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\sin x} \over x\,\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi>sin</mi> <mo>⁡</mo> <mi>x</mi> </mrow> </mstyle> <mrow> <mi>x</mi> <mspace width="thinmathspace" /> <mspace width="negativethinmathspace" /> </mrow> </mfrac> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\sin x} \over x\,\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/86f6023d65c07c16cf952560572e68e6de139a41" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:5.409ex; height:5.176ex;" alt="{\displaystyle {\sin x} \over x\,\!}"></span> není v nule definovaná, ale má v ní limitu 1<sup id="cite_ref-2" class="reference"><a href="#cite_note-2"><span class="cite-bracket">[</span>pozn. 1<span class="cite-bracket">]</span></a></sup> (vlastní limita ve vlastním bodě) a v <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle +\infty \,\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>+</mo> <mi mathvariant="normal">∞</mi> <mspace width="thinmathspace" /> <mspace width="negativethinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle +\infty \,\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/45105754a7eba4fc8d7f142d3fbb72654682e9a9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; margin-right: -0.387ex; width:4.519ex; height:2.176ex;" alt="{\displaystyle +\infty \,\!}"></span> má limitu 0 (vlastní limita v nevlastním bodě).</li> <li>Funkce <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\sin {1 \over x}}\,\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi>sin</mi> <mo>⁡</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mi>x</mi> </mfrac> </mrow> </mrow> <mspace width="thinmathspace" /> <mspace width="negativethinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\sin {1 \over x}}\,\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/cfd80be88ad5fa2994e571268417324acba853a0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; margin-right: -0.387ex; width:5.796ex; height:5.176ex;" alt="{\displaystyle {\sin {1 \over x}}\,\!}"></span> ani <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\sin {1 \over x}} \over x\,\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi>sin</mi> <mo>⁡</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mi>x</mi> </mfrac> </mrow> </mrow> </mstyle> <mrow> <mi>x</mi> <mspace width="thinmathspace" /> <mspace width="negativethinmathspace" /> </mrow> </mfrac> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\sin {1 \over x}} \over x\,\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/85d01b9f0b3dceb5dcafb2fe93fd30ec300bc686" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:6.245ex; height:8.009ex;" alt="{\displaystyle {\sin {1 \over x}} \over x\,\!}"></span> v nule limitu nemají. Totéž platí i o funkcích <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {1 \over x}\,\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mi>x</mi> </mfrac> </mrow> <mspace width="thinmathspace" /> <mspace width="negativethinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {1 \over x}\,\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7bec54138af90467f5014e03856e194d9b68a892" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; margin-right: -0.387ex; width:2.553ex; height:5.176ex;" alt="{\displaystyle {1 \over x}\,\!}"></span> či <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {1 \over x^{3}}\,\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msup> </mfrac> </mrow> <mspace width="thinmathspace" /> <mspace width="negativethinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {1 \over x^{3}}\,\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c00db451c0dcba978086547c734c2cecc2a88730" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.171ex; margin-right: -0.387ex; width:3.607ex; height:5.509ex;" alt="{\displaystyle {1 \over x^{3}}\,\!}"></span>, ovšem ty mají alespoň jednostranné limity: jejich pravostranná limita je <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle +\infty \,\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>+</mo> <mi mathvariant="normal">∞</mi> <mspace width="thinmathspace" /> <mspace width="negativethinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle +\infty \,\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/45105754a7eba4fc8d7f142d3fbb72654682e9a9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; margin-right: -0.387ex; width:4.519ex; height:2.176ex;" alt="{\displaystyle +\infty \,\!}"></span> a levostranná <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle -\infty \,\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>−</mo> <mi mathvariant="normal">∞</mi> <mspace width="thinmathspace" /> <mspace width="negativethinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle -\infty \,\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b6eaccbf63128b80880b52e21549faff45ac5e63" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; margin-right: -0.387ex; width:4.519ex; height:2.176ex;" alt="{\displaystyle -\infty \,\!}"></span>.</li> <li>Funkce <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {1 \over x^{2}}\,\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mfrac> </mrow> <mspace width="thinmathspace" /> <mspace width="negativethinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {1 \over x^{2}}\,\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8deba6405da48e84fd12424fb9a4cbb72de0f541" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.171ex; margin-right: -0.387ex; width:3.607ex; height:5.509ex;" alt="{\displaystyle {1 \over x^{2}}\,\!}"></span> a <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {1 \over x^{4}}\,\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>4</mn> </mrow> </msup> </mfrac> </mrow> <mspace width="thinmathspace" /> <mspace width="negativethinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {1 \over x^{4}}\,\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8b35febbdc0ea351985e81a11a2e0cf2777547cc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.171ex; margin-right: -0.387ex; width:3.607ex; height:5.509ex;" alt="{\displaystyle {1 \over x^{4}}\,\!}"></span> mají v nule limitu <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle +\infty \,\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>+</mo> <mi mathvariant="normal">∞</mi> <mspace width="thinmathspace" /> <mspace width="negativethinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle +\infty \,\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/45105754a7eba4fc8d7f142d3fbb72654682e9a9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; margin-right: -0.387ex; width:4.519ex; height:2.176ex;" alt="{\displaystyle +\infty \,\!}"></span> (nevlastní limita ve vlastním bodě).</li> <li>Funkce <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\sin x}\,\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi>sin</mi> <mo>⁡</mo> <mi>x</mi> </mrow> <mspace width="thinmathspace" /> <mspace width="negativethinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\sin x}\,\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/80bad8f053217f0b6ddb8d16910f62dee445eaa1" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; margin-right: -0.387ex; width:4.96ex; height:2.176ex;" alt="{\displaystyle {\sin x}\,\!}"></span> má v nule limitu 0 a v <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle +\infty \,\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>+</mo> <mi mathvariant="normal">∞</mi> <mspace width="thinmathspace" /> <mspace width="negativethinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle +\infty \,\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/45105754a7eba4fc8d7f142d3fbb72654682e9a9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; margin-right: -0.387ex; width:4.519ex; height:2.176ex;" alt="{\displaystyle +\infty \,\!}"></span> limitu nemá. Obě tato tvrzení platí i o funkci <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {x\cdot \sin x}\,\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi>x</mi> <mo>⋅</mo> <mi>sin</mi> <mo>⁡</mo> <mi>x</mi> </mrow> <mspace width="thinmathspace" /> <mspace width="negativethinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {x\cdot \sin x}\,\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4db5af0a042ddab0a5fde2bcdd7413339ad9add4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; margin-right: -0.387ex; width:7.968ex; height:2.176ex;" alt="{\displaystyle {x\cdot \sin x}\,\!}"></span>.</li> <li>Funkce <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle e^{x}\,\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>e</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>x</mi> </mrow> </msup> <mspace width="thinmathspace" /> <mspace width="negativethinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle e^{x}\,\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c73ed2202d84cada844b32d77e0d71ff31b863ec" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; margin-right: -0.387ex; width:2.643ex; height:2.343ex;" alt="{\displaystyle e^{x}\,\!}"></span> má v <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle -\infty \,\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>−</mo> <mi mathvariant="normal">∞</mi> <mspace width="thinmathspace" /> <mspace width="negativethinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle -\infty \,\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b6eaccbf63128b80880b52e21549faff45ac5e63" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; margin-right: -0.387ex; width:4.519ex; height:2.176ex;" alt="{\displaystyle -\infty \,\!}"></span> limitu 0 (vlastní limita v nevlastním bodě) a v <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle +\infty \,\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>+</mo> <mi mathvariant="normal">∞</mi> <mspace width="thinmathspace" /> <mspace width="negativethinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle +\infty \,\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/45105754a7eba4fc8d7f142d3fbb72654682e9a9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; margin-right: -0.387ex; width:4.519ex; height:2.176ex;" alt="{\displaystyle +\infty \,\!}"></span> limitu <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle +\infty \,\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>+</mo> <mi mathvariant="normal">∞</mi> <mspace width="thinmathspace" /> <mspace width="negativethinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle +\infty \,\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/45105754a7eba4fc8d7f142d3fbb72654682e9a9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; margin-right: -0.387ex; width:4.519ex; height:2.176ex;" alt="{\displaystyle +\infty \,\!}"></span>.</li></ul> <div class="mw-heading mw-heading2"><h2 id="Poznámky"><span id="Pozn.C3.A1mky"></span>Poznámky</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Limita&veaction=edit&section=7" title="Editace sekce: Poznámky" class="mw-editsection-visualeditor"><span>editovat</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Limita&action=edit&section=7" title="Editovat zdrojový kód sekce Poznámky"><span>editovat zdroj</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-references-wrap"><ol class="references"> <li id="cite_note-2"><span class="mw-cite-backlink"><a href="#cite_ref-2">↑</a></span> <span class="reference-text">To lze intuitivně zdůvodnit tak, že funkce <i>sin x</i> má v okolí nuly „velmi podobný“ průběh, jako funkce f(x) = x; proto se jejich poměr blíží k jedné. (<a href="/wiki/L%27Hospitalovo_pravidlo" title="L'Hospitalovo pravidlo">L'Hospitalovo pravidlo</a>)</span> </li> </ol></div> <div class="mw-heading mw-heading2"><h2 id="Reference">Reference</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Limita&veaction=edit&section=8" title="Editace sekce: Reference" class="mw-editsection-visualeditor"><span>editovat</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Limita&action=edit&section=8" title="Editovat zdrojový kód sekce Reference"><span>editovat zdroj</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-references-wrap"><ol class="references"> <li id="cite_note-1"><span class="mw-cite-backlink"><a href="#cite_ref-1">↑</a></span> <span class="reference-text">Michael C. Gemignani, Elementary topology, Courier Dover Publications, 1990 (strana 122, def. 3)</span> </li> </ol></div> <div class="mw-heading mw-heading2"><h2 id="Související_články"><span id="Souvisej.C3.ADc.C3.AD_.C4.8Dl.C3.A1nky"></span>Související články</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Limita&veaction=edit&section=9" title="Editace sekce: Související články" class="mw-editsection-visualeditor"><span>editovat</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Limita&action=edit&section=9" title="Editovat zdrojový kód sekce Související články"><span>editovat zdroj</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Limita_funkce" title="Limita funkce">Limita funkce</a></li> <li><a href="/wiki/Limita_posloupnosti" title="Limita posloupnosti">Limita posloupnosti</a></li> <li><a href="/wiki/Okol%C3%AD_(matematika)" title="Okolí (matematika)">Okolí (matematika)</a></li></ul> <div class="mw-heading mw-heading2"><h2 id="Externí_odkazy"><span id="Extern.C3.AD_odkazy"></span>Externí odkazy</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Limita&veaction=edit&section=10" title="Editace sekce: Externí odkazy" class="mw-editsection-visualeditor"><span>editovat</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Limita&action=edit&section=10" title="Editovat zdrojový kód sekce Externí odkazy"><span>editovat zdroj</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><span class="wd"><span class="sisterproject sisterproject-commons"><span class="sisterproject_image"><span typeof="mw:File"><a href="/wiki/Wikimedia_Commons" title="Wikimedia Commons"><img alt="Logo Wikimedia Commons" src="//upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Commons-logo.svg/12px-Commons-logo.svg.png" decoding="async" width="12" height="16" 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