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Je dostupný v 59 jazykoch" > <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-59" 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">59 jazykov</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/Asimptoot" title="Asimptoot – afrikánčina" lang="af" hreflang="af" data-title="Asimptoot" data-language-autonym="Afrikaans" data-language-local-name="afrikánčina" class="interlanguage-link-target"><span>Afrikaans</span></a></li><li class="interlanguage-link interwiki-an mw-list-item"><a href="https://an.wikipedia.org/wiki/Asimptota" title="Asimptota – aragónčina" lang="an" hreflang="an" data-title="Asimptota" data-language-autonym="Aragonés" data-language-local-name="aragónčina" class="interlanguage-link-target"><span>Aragonés</span></a></li><li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D8%AE%D8%B7_%D9%85%D9%82%D8%A7%D8%B1%D8%A8" title="خط مقارب – arabčina" lang="ar" hreflang="ar" data-title="خط مقارب" data-language-autonym="العربية" data-language-local-name="arabčina" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-az mw-list-item"><a href="https://az.wikipedia.org/wiki/Asimptot" title="Asimptot – azerbajdžančina" lang="az" hreflang="az" data-title="Asimptot" data-language-autonym="Azərbaycanca" data-language-local-name="azerbajdžančina" class="interlanguage-link-target"><span>Azərbaycanca</span></a></li><li class="interlanguage-link interwiki-be mw-list-item"><a href="https://be.wikipedia.org/wiki/%D0%90%D1%81%D1%96%D0%BC%D0%BF%D1%82%D0%BE%D1%82%D0%B0" title="Асімптота – bieloruština" lang="be" hreflang="be" data-title="Асімптота" data-language-autonym="Беларуская" data-language-local-name="bieloruština" 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%90%D1%81%D0%B8%D0%BC%D0%BF%D1%82%D0%BE%D1%82%D0%B0" title="Асимптота – bulharčina" lang="bg" hreflang="bg" data-title="Асимптота" data-language-autonym="Български" data-language-local-name="bulharčina" class="interlanguage-link-target"><span>Български</span></a></li><li class="interlanguage-link interwiki-bn mw-list-item"><a href="https://bn.wikipedia.org/wiki/%E0%A6%85%E0%A6%B8%E0%A7%80%E0%A6%AE%E0%A6%B8%E0%A7%80%E0%A6%AE%E0%A6%BE_%E0%A6%B0%E0%A7%87%E0%A6%96%E0%A6%BE" title="অসীমসীমা রেখা – bengálčina" lang="bn" hreflang="bn" data-title="অসীমসীমা রেখা" data-language-autonym="বাংলা" data-language-local-name="bengálčina" class="interlanguage-link-target"><span>বাংলা</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/As%C3%ADmptota" title="Asímptota – katalánčina" lang="ca" hreflang="ca" data-title="Asímptota" data-language-autonym="Català" data-language-local-name="katalánčina" 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/%D9%84%DB%8E%D9%86%DB%95%DA%A9%DB%95%D9%88%D8%AA" title="لێنەکەوت – kurdčina (sorání)" lang="ckb" hreflang="ckb" data-title="لێنەکەوت" data-language-autonym="کوردی" data-language-local-name="kurdčina (sorání)" class="interlanguage-link-target"><span>کوردی</span></a></li><li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/Asymptota" title="Asymptota – čeština" lang="cs" hreflang="cs" data-title="Asymptota" data-language-autonym="Čeština" data-language-local-name="čeština" class="interlanguage-link-target"><span>Čeština</span></a></li><li class="interlanguage-link interwiki-cv mw-list-item"><a href="https://cv.wikipedia.org/wiki/%D0%90%D1%81%D0%B8%D0%BC%D0%BF%D1%82%D0%BE%D1%82%D0%B0" title="Асимптота – čuvaština" lang="cv" hreflang="cv" data-title="Асимптота" data-language-autonym="Чӑвашла" data-language-local-name="čuvaština" class="interlanguage-link-target"><span>Чӑвашла</span></a></li><li class="interlanguage-link interwiki-da mw-list-item"><a href="https://da.wikipedia.org/wiki/Asymptote" title="Asymptote – dánčina" lang="da" hreflang="da" data-title="Asymptote" data-language-autonym="Dansk" data-language-local-name="dánčina" class="interlanguage-link-target"><span>Dansk</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Asymptote" title="Asymptote – nemčina" lang="de" hreflang="de" data-title="Asymptote" data-language-autonym="Deutsch" data-language-local-name="nemčina" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-el mw-list-item"><a href="https://el.wikipedia.org/wiki/%CE%91%CF%83%CF%8D%CE%BC%CF%80%CF%84%CF%89%CF%84%CE%B7_%CF%84%CE%B7%CF%82_%CF%83%CF%85%CE%BD%CE%AC%CF%81%CF%84%CE%B7%CF%83%CE%B7%CF%82" title="Ασύμπτωτη της συνάρτησης – gréčtina" lang="el" hreflang="el" data-title="Ασύμπτωτη της συνάρτησης" data-language-autonym="Ελληνικά" data-language-local-name="gréčtina" 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/Asymptote" title="Asymptote – angličtina" lang="en" hreflang="en" data-title="Asymptote" 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/Asimptoto" title="Asimptoto – esperanto" lang="eo" hreflang="eo" data-title="Asimptoto" 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/As%C3%ADntota" title="Asíntota – španielčina" lang="es" hreflang="es" data-title="Asíntota" data-language-autonym="Español" data-language-local-name="španielčina" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-et mw-list-item"><a href="https://et.wikipedia.org/wiki/As%C3%BCmptoot" title="Asümptoot – estónčina" lang="et" hreflang="et" data-title="Asümptoot" data-language-autonym="Eesti" data-language-local-name="estónčina" class="interlanguage-link-target"><span>Eesti</span></a></li><li class="interlanguage-link interwiki-eu mw-list-item"><a href="https://eu.wikipedia.org/wiki/Asintota" title="Asintota – baskičtina" lang="eu" hreflang="eu" data-title="Asintota" 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/%D9%85%D8%AC%D8%A7%D9%86%D8%A8" title="مجانب – perzština" lang="fa" hreflang="fa" data-title="مجانب" data-language-autonym="فارسی" data-language-local-name="perzština" 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/Asymptootti" title="Asymptootti – fínčina" lang="fi" hreflang="fi" data-title="Asymptootti" data-language-autonym="Suomi" data-language-local-name="fínčina" 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/Asymptote" title="Asymptote – francúzština" lang="fr" hreflang="fr" data-title="Asymptote" data-language-autonym="Français" data-language-local-name="francúzština" 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/Asamt%C3%B3it" title="Asamtóit – írčina" lang="ga" hreflang="ga" data-title="Asamtóit" data-language-autonym="Gaeilge" data-language-local-name="írčina" class="interlanguage-link-target"><span>Gaeilge</span></a></li><li class="interlanguage-link interwiki-gl mw-list-item"><a href="https://gl.wikipedia.org/wiki/As%C3%ADntota" title="Asíntota – galícijčina" lang="gl" hreflang="gl" data-title="Asíntota" data-language-autonym="Galego" data-language-local-name="galícijčina" class="interlanguage-link-target"><span>Galego</span></a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/wiki/%D7%90%D7%A1%D7%99%D7%9E%D7%A4%D7%98%D7%95%D7%98%D7%94" title="אסימפטוטה – hebrejčina" lang="he" hreflang="he" data-title="אסימפטוטה" data-language-autonym="עברית" data-language-local-name="hebrejčina" 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%85%E0%A4%A8%E0%A4%82%E0%A4%A4%E0%A4%B8%E0%A5%8D%E0%A4%AA%E0%A4%B0%E0%A5%8D%E0%A4%B6%E0%A5%80" title="अनंतस्पर्शी – hindčina" lang="hi" hreflang="hi" data-title="अनंतस्पर्शी" data-language-autonym="हिन्दी" data-language-local-name="hindčina" class="interlanguage-link-target"><span>हिन्दी</span></a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/Aszimptota" title="Aszimptota – maďarčina" lang="hu" hreflang="hu" data-title="Aszimptota" data-language-autonym="Magyar" data-language-local-name="maďarčina" 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/%D4%B1%D5%BD%D5%AB%D5%B4%D5%BA%D5%BF%D5%B8%D5%BF" title="Ասիմպտոտ – arménčina" lang="hy" hreflang="hy" data-title="Ասիմպտոտ" data-language-autonym="Հայերեն" data-language-local-name="arménčina" 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/Asimtot" title="Asimtot – indonézština" lang="id" hreflang="id" data-title="Asimtot" data-language-autonym="Bahasa Indonesia" data-language-local-name="indonézština" 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/Asimptoto" title="Asimptoto – ido" lang="io" hreflang="io" data-title="Asimptoto" 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/A%C3%B0fella" title="Aðfella – islandčina" lang="is" hreflang="is" data-title="Aðfella" data-language-autonym="Íslenska" data-language-local-name="islandčina" 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/Asintoto" title="Asintoto – taliančina" lang="it" hreflang="it" data-title="Asintoto" data-language-autonym="Italiano" data-language-local-name="taliančina" 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%BC%B8%E8%BF%91%E7%B7%9A" title="漸近線 – japončina" lang="ja" hreflang="ja" data-title="漸近線" data-language-autonym="日本語" data-language-local-name="japončina" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-kk mw-list-item"><a href="https://kk.wikipedia.org/wiki/%D0%90%D1%81%D0%B8%D0%BC%D0%BF%D1%82%D0%BE%D1%82%D0%B0" title="Асимптота – kazaština" lang="kk" hreflang="kk" data-title="Асимптота" data-language-autonym="Қазақша" data-language-local-name="kazaština" class="interlanguage-link-target"><span>Қазақша</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EC%A0%90%EA%B7%BC%EC%84%A0" title="점근선 – kórejčina" lang="ko" hreflang="ko" data-title="점근선" data-language-autonym="한국어" data-language-local-name="kórejčina" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-ky mw-list-item"><a href="https://ky.wikipedia.org/wiki/%D0%90%D1%81%D0%B8%D0%BC%D0%BF%D1%82%D0%BE%D1%82%D0%B0" title="Асимптота – kirgizština" lang="ky" hreflang="ky" data-title="Асимптота" data-language-autonym="Кыргызча" data-language-local-name="kirgizština" class="interlanguage-link-target"><span>Кыргызча</span></a></li><li class="interlanguage-link interwiki-lmo mw-list-item"><a href="https://lmo.wikipedia.org/wiki/Asintot" title="Asintot – lombardčina" lang="lmo" hreflang="lmo" data-title="Asintot" data-language-autonym="Lombard" data-language-local-name="lombardčina" 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/Asimptot%C4%97" title="Asimptotė – litovčina" lang="lt" hreflang="lt" data-title="Asimptotė" data-language-autonym="Lietuvių" data-language-local-name="litovčina" 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/Asimptota" title="Asimptota – lotyština" lang="lv" hreflang="lv" data-title="Asimptota" 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%90%D1%81%D0%B8%D0%BC%D0%BF%D1%82%D0%BE%D1%82%D0%B0" title="Асимптота – macedónčina" lang="mk" hreflang="mk" data-title="Асимптота" data-language-autonym="Македонски" data-language-local-name="macedónčina" class="interlanguage-link-target"><span>Македонски</span></a></li><li class="interlanguage-link interwiki-ml mw-list-item"><a href="https://ml.wikipedia.org/wiki/%E0%B4%85%E0%B4%A8%E0%B4%A8%E0%B5%8D%E0%B4%A4%E0%B4%A4%E0%B4%BE%E0%B4%B8%E0%B5%8D%E0%B4%AA%E0%B5%BC%E0%B4%B6%E0%B4%95%E0%B4%82" title="അനന്തതാസ്പർശകം – malajálamčina" lang="ml" hreflang="ml" data-title="അനന്തതാസ്പർശകം" data-language-autonym="മലയാളം" data-language-local-name="malajálamčina" class="interlanguage-link-target"><span>മലയാളം</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Asymptoot" title="Asymptoot – holandčina" lang="nl" hreflang="nl" data-title="Asymptoot" data-language-autonym="Nederlands" data-language-local-name="holandčina" 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/Asymptote" title="Asymptote – nórčina (nynorsk)" lang="nn" hreflang="nn" data-title="Asymptote" data-language-autonym="Norsk nynorsk" data-language-local-name="nórčina (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/Asymptote" title="Asymptote – nórčina (bokmal)" lang="nb" hreflang="nb" data-title="Asymptote" data-language-autonym="Norsk bokmål" data-language-local-name="nórčina (bokmal)" 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/Asymptota" title="Asymptota – poľština" lang="pl" hreflang="pl" data-title="Asymptota" data-language-autonym="Polski" data-language-local-name="poľština" 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/Assintota" title="Assintota – portugalčina" lang="pt" hreflang="pt" data-title="Assintota" data-language-autonym="Português" data-language-local-name="portugalčina" 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/Asimptot%C4%83" title="Asimptotă – rumunčina" lang="ro" hreflang="ro" data-title="Asimptotă" data-language-autonym="Română" data-language-local-name="rumunčina" 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%90%D1%81%D0%B8%D0%BC%D0%BF%D1%82%D0%BE%D1%82%D0%B0" title="Асимптота – ruština" lang="ru" hreflang="ru" data-title="Асимптота" data-language-autonym="Русский" data-language-local-name="ruština" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-sl mw-list-item"><a href="https://sl.wikipedia.org/wiki/Asimptota" title="Asimptota – slovinčina" lang="sl" hreflang="sl" data-title="Asimptota" data-language-autonym="Slovenščina" data-language-local-name="slovinčina" class="interlanguage-link-target"><span>Slovenščina</span></a></li><li class="interlanguage-link interwiki-sr mw-list-item"><a href="https://sr.wikipedia.org/wiki/%D0%90%D1%81%D0%B8%D0%BC%D0%BF%D1%82%D0%BE%D1%82%D0%B0" title="Асимптота – srbčina" lang="sr" hreflang="sr" data-title="Асимптота" data-language-autonym="Српски / srpski" data-language-local-name="srbčina" 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/Asymptot" title="Asymptot – švédčina" lang="sv" hreflang="sv" data-title="Asymptot" data-language-autonym="Svenska" data-language-local-name="švédčina" 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%85%E0%AE%A3%E0%AF%81%E0%AE%95%E0%AF%81%E0%AE%95%E0%AF%8B%E0%AE%9F%E0%AF%81" title="அணுகுகோடு – tamilčina" lang="ta" hreflang="ta" data-title="அணுகுகோடு" data-language-autonym="தமிழ்" data-language-local-name="tamilčina" class="interlanguage-link-target"><span>தமிழ்</span></a></li><li class="interlanguage-link interwiki-tl mw-list-item"><a href="https://tl.wikipedia.org/wiki/Asymptote" title="Asymptote – tagalčina" lang="tl" hreflang="tl" data-title="Asymptote" data-language-autonym="Tagalog" data-language-local-name="tagalčina" class="interlanguage-link-target"><span>Tagalog</span></a></li><li class="interlanguage-link interwiki-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/Asimptot" title="Asimptot – turečtina" lang="tr" hreflang="tr" data-title="Asimptot" 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%90%D1%81%D0%B8%D0%BC%D0%BF%D1%82%D0%BE%D1%82%D0%B0" title="Асимптота – ukrajinčina" lang="uk" hreflang="uk" data-title="Асимптота" data-language-autonym="Українська" data-language-local-name="ukrajinčina" class="interlanguage-link-target"><span>Українська</span></a></li><li class="interlanguage-link interwiki-uz mw-list-item"><a href="https://uz.wikipedia.org/wiki/Asimptota" title="Asimptota – uzbečtina" lang="uz" hreflang="uz" data-title="Asimptota" 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-wuu mw-list-item"><a href="https://wuu.wikipedia.org/wiki/%E6%B8%90%E8%BF%91%E7%BA%BF" title="渐近线 – čínština (wu)" lang="wuu" hreflang="wuu" data-title="渐近线" data-language-autonym="吴语" data-language-local-name="čínština (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%B8%90%E8%BF%91%E7%BA%BF" title="渐近线 – čínština" lang="zh" hreflang="zh" data-title="渐近线" 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%BC%B8%E8%BF%91%E7%B7%9A" title="漸近線 – kantončina" lang="yue" hreflang="yue" data-title="漸近線" data-language-autonym="粵語" data-language-local-name="kantončina" class="interlanguage-link-target"><span>粵語</span></a></li> </ul> <div class="after-portlet after-portlet-lang"><span class="wb-langlinks-edit 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lang="sk" dir="ltr"><p><b>Asymptota</b> je <a href="/wiki/Priamka" title="Priamka">priamka</a>, ktorá opisuje správanie sa krivky. S narastajúcimi hodnotami súradníc sa vzdialenosť asymptoty a krivky zmenšuje. Prebieha tu limitný proces približovania sa hodnôt a vzdialeností asymptoty a krivky.<br /> Platí teda <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\to -\infty }{\left(f{\left(x\right)}-kx-q\right)}=0\vee \lim _{x\to \infty }{\left(f{\left(x\right)}-kx-q\right)}=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>x</mi> <mo stretchy="false">→</mo> <mo>−</mo> <mi mathvariant="normal">∞</mi> </mrow> </munder> <mrow class="MJX-TeXAtom-ORD"> <mrow> <mo>(</mo> <mrow> <mi>f</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> </mrow> <mo>−</mo> <mi>k</mi> <mi>x</mi> <mo>−</mo> <mi>q</mi> </mrow> <mo>)</mo> </mrow> </mrow> <mo>=</mo> <mn>0</mn> <mo>∨</mo> <munder> <mo movablelimits="true" form="prefix">lim</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>x</mi> <mo stretchy="false">→</mo> <mi mathvariant="normal">∞</mi> </mrow> </munder> <mrow class="MJX-TeXAtom-ORD"> <mrow> <mo>(</mo> <mrow> <mi>f</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> </mrow> <mo>−</mo> <mi>k</mi> <mi>x</mi> <mo>−</mo> <mi>q</mi> </mrow> <mo>)</mo> </mrow> </mrow> <mo>=</mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \lim _{x\to -\infty }{\left(f{\left(x\right)}-kx-q\right)}=0\vee \lim _{x\to \infty }{\left(f{\left(x\right)}-kx-q\right)}=0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6e293086240d768feda31fc343e590614b94205d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:52.646ex; height:4.009ex;" alt="{\displaystyle \lim _{x\to -\infty }{\left(f{\left(x\right)}-kx-q\right)}=0\vee \lim _{x\to \infty }{\left(f{\left(x\right)}-kx-q\right)}=0}" /></span> </p> <div class="mw-heading mw-heading2"><h2 id="Asymptoty_so_smernicou">Asymptoty so smernicou</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Asymptota&veaction=edit&section=1" title="Upraviť sekciu: Asymptoty so smernicou" class="mw-editsection-visualeditor"><span>upraviť</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Asymptota&action=edit&section=1" title="Editovat zdrojový kód sekce Asymptoty so smernicou"><span>upraviť zdroj</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Asymptota so smernicou je priamka <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 \,\!\tau (x)=kx+q}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mspace width="thinmathspace"></mspace> <mspace width="negativethinmathspace"></mspace> <mi>τ</mi> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mi>k</mi> <mi>x</mi> <mo>+</mo> <mi>q</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \,\!\tau (x)=kx+q}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1286705931b66b93439708a11e8991cdf781fd45" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:13.89ex; height:2.843ex;" alt="{\displaystyle \,\!\tau (x)=kx+q}" /></span>, ktorá zviera s osou <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"> <mspace width="thinmathspace"></mspace> <mspace width="negativethinmathspace"></mspace> <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/aab0904dba72ba55b837cec95acde0d80d8988b8" 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> uhol <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 \,\!\phi }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mspace width="thinmathspace"></mspace> <mspace width="negativethinmathspace"></mspace> <mi>ϕ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \,\!\phi }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a53894ae6e1efd0e272291abea516a222ace8a4c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.385ex; height:2.509ex;" alt="{\displaystyle \,\!\phi }" /></span> určený smernicou <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 \,\!k=\tan \phi }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mspace width="thinmathspace"></mspace> <mspace width="negativethinmathspace"></mspace> <mi>k</mi> <mo>=</mo> <mi>tan</mi> <mo>⁡</mo> <mi>ϕ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \,\!k=\tan \phi }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e165e621cdf84e431f1e8bafbe3bb6c184e639b1" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:9.442ex; height:2.509ex;" alt="{\displaystyle \,\!k=\tan \phi }" /></span><br /> Priamka <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 y=kx+q}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>y</mi> <mo>=</mo> <mi>k</mi> <mi>x</mi> <mo>+</mo> <mi>q</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle y=kx+q}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/84978478136543320e4d1fdd92fac179ba9ccd2c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:10.705ex; height:2.509ex;" alt="{\displaystyle y=kx+q}" /></span> je asymptotou grafu funkcie práve vtedy keď <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(k=\lim _{x\to -\infty }{\frac {f(x)}{x}}\wedge q=\lim _{x\to -\infty }(f(x)-kx)\right)\vee \left(k=\lim _{x\to \infty }{\frac {f(x)}{x}}\wedge q=\lim _{x\to \infty }(f(x)-kx)\right)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow> <mo>(</mo> <mrow> <mi>k</mi> <mo>=</mo> <munder> <mo movablelimits="true" form="prefix">lim</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>x</mi> <mo stretchy="false">→</mo> <mo>−</mo> <mi mathvariant="normal">∞</mi> </mrow> </munder> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>f</mi> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> </mrow> <mi>x</mi> </mfrac> </mrow> <mo>∧</mo> <mi>q</mi> <mo>=</mo> <munder> <mo movablelimits="true" form="prefix">lim</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>x</mi> <mo stretchy="false">→</mo> <mo>−</mo> <mi mathvariant="normal">∞</mi> </mrow> </munder> <mo stretchy="false">(</mo> <mi>f</mi> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> <mo>−</mo> <mi>k</mi> <mi>x</mi> <mo stretchy="false">)</mo> </mrow> <mo>)</mo> </mrow> <mo>∨</mo> <mrow> <mo>(</mo> <mrow> <mi>k</mi> <mo>=</mo> <munder> <mo movablelimits="true" form="prefix">lim</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>x</mi> <mo stretchy="false">→</mo> <mi mathvariant="normal">∞</mi> </mrow> </munder> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>f</mi> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> </mrow> <mi>x</mi> </mfrac> </mrow> <mo>∧</mo> <mi>q</mi> <mo>=</mo> <munder> <mo movablelimits="true" form="prefix">lim</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>x</mi> <mo stretchy="false">→</mo> <mi mathvariant="normal">∞</mi> </mrow> </munder> <mo stretchy="false">(</mo> <mi>f</mi> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> <mo>−</mo> <mi>k</mi> <mi>x</mi> <mo stretchy="false">)</mo> </mrow> <mo>)</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \left(k=\lim _{x\to -\infty }{\frac {f(x)}{x}}\wedge q=\lim _{x\to -\infty }(f(x)-kx)\right)\vee \left(k=\lim _{x\to \infty }{\frac {f(x)}{x}}\wedge q=\lim _{x\to \infty }(f(x)-kx)\right)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2ebc27e34d5ad8ecbe293756ac4ae202095b0205" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:85.507ex; height:6.343ex;" alt="{\displaystyle \left(k=\lim _{x\to -\infty }{\frac {f(x)}{x}}\wedge q=\lim _{x\to -\infty }(f(x)-kx)\right)\vee \left(k=\lim _{x\to \infty }{\frac {f(x)}{x}}\wedge q=\lim _{x\to \infty }(f(x)-kx)\right)}" /></span><br /> </p> <div class="mw-heading mw-heading2"><h2 id="Asymptoty_bez_smernice">Asymptoty bez smernice</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Asymptota&veaction=edit&section=2" title="Upraviť sekciu: Asymptoty bez smernice" class="mw-editsection-visualeditor"><span>upraviť</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Asymptota&action=edit&section=2" title="Editovat zdrojový kód sekce Asymptoty bez smernice"><span>upraviť zdroj</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Nech <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}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>f</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle f}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/132e57acb643253e7810ee9702d9581f159a1c61" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.279ex; height:2.509ex;" alt="{\displaystyle f}" /></span> je funkcia (grafom je krivka) 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 \lim _{x\to x_{0}^{+}}{f{\left(x\right)}}=\infty \vee \lim _{x\to x_{0}^{-}}{f{\left(x\right)}}=\infty \vee \lim _{x\to x_{0}^{+}}{f{\left(x\right)}}=-\infty \vee \lim _{x\to x_{0}^{-}}{f{\left(x\right)}}=-\infty }"> <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> <msubsup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>+</mo> </mrow> </msubsup> </mrow> </munder> <mrow class="MJX-TeXAtom-ORD"> <mi>f</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> </mrow> </mrow> <mo>=</mo> <mi mathvariant="normal">∞</mi> <mo>∨</mo> <munder> <mo movablelimits="true" form="prefix">lim</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>x</mi> <mo stretchy="false">→</mo> <msubsup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> </mrow> </msubsup> </mrow> </munder> <mrow class="MJX-TeXAtom-ORD"> <mi>f</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> </mrow> </mrow> <mo>=</mo> <mi mathvariant="normal">∞</mi> <mo>∨</mo> <munder> <mo movablelimits="true" form="prefix">lim</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>x</mi> <mo stretchy="false">→</mo> <msubsup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>+</mo> </mrow> </msubsup> </mrow> </munder> <mrow class="MJX-TeXAtom-ORD"> <mi>f</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> </mrow> </mrow> <mo>=</mo> <mo>−</mo> <mi mathvariant="normal">∞</mi> <mo>∨</mo> <munder> <mo movablelimits="true" form="prefix">lim</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>x</mi> <mo stretchy="false">→</mo> <msubsup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> </mrow> </msubsup> </mrow> </munder> <mrow class="MJX-TeXAtom-ORD"> <mi>f</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> </mrow> </mrow> <mo>=</mo> <mo>−</mo> <mi mathvariant="normal">∞</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \lim _{x\to x_{0}^{+}}{f{\left(x\right)}}=\infty \vee \lim _{x\to x_{0}^{-}}{f{\left(x\right)}}=\infty \vee \lim _{x\to x_{0}^{+}}{f{\left(x\right)}}=-\infty \vee \lim _{x\to x_{0}^{-}}{f{\left(x\right)}}=-\infty }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/113c8338ee52755a04b9b77b8ff0c4235f537e70" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.005ex; width:71.175ex; height:5.009ex;" alt="{\displaystyle \lim _{x\to x_{0}^{+}}{f{\left(x\right)}}=\infty \vee \lim _{x\to x_{0}^{-}}{f{\left(x\right)}}=\infty \vee \lim _{x\to x_{0}^{+}}{f{\left(x\right)}}=-\infty \vee \lim _{x\to x_{0}^{-}}{f{\left(x\right)}}=-\infty }" /></span>.<br /> Asymptotou bez smernice je potom priamka <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=x_{0}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>x</mi> <mo>=</mo> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle x=x_{0}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/04e899fc6eba0b387b91f070adc7bc4fe5a706cb" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:6.812ex; height:2.009ex;" alt="{\displaystyle x=x_{0}}" /></span>. </p> <div class="mw-heading mw-heading2"><h2 id="Externé_odkazy"><span id="Extern.C3.A9_odkazy"></span>Externé odkazy</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Asymptota&veaction=edit&section=3" title="Upraviť sekciu: Externé odkazy" class="mw-editsection-visualeditor"><span>upraviť</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Asymptota&action=edit&section=3" title="Editovat zdrojový kód sekce Externé odkazy"><span>upraviť zdroj</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a rel="nofollow" class="external text" href="https://www.math.muni.cz/~pribylova/asympt.pdf">Asymptoty grafu funkce</a></li> <li><a rel="nofollow" class="external text" href="https://fhi.euba.sk/www_write/files/katedry/kma/2017_18/veda_a_vyskum/odborne_prace_2018/fecenko_18.pdf">Polynomické asymptoty</a></li></ul> <div class="metadata plainlinks stub" style="float:none; 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