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<!DOCTYPE html><html lang="en"><head><meta charSet="utf-8"/><meta name="viewport" content="width=device-width"/><meta name="description" content="Solution for (e) Show that v(x, t) = u(x, t) — uɛ(x, t) is solution of a homogeneous problem (with a different initial condition) and solve it using the method…"/><link rel="canonical" href="https://www.bartleby.com/questions-and-answers/e-show-that-vx-t-ux-t-ux-t-is-solution-of-a-homogeneous-problem-with-a-different-initial-condition-a/0d7ed346-3e61-48a0-8236-b42a96af6267"/><title>Answered: (e) Show that v(x, t) = u(x, t) — uɛ(x,… | bartleby</title><script type="application/ld+json">{ "@context": "https://schema.org", "@type": [ "QAPage", "WebPage" ], "mainEntityOfPage": { "@type": "WebPage", "@id": "https://www.bartleby.com/questions-and-answers/e-show-that-vx-t-ux-t-ux-t-is-solution-of-a-homogeneous-problem-with-a-different-initial-condition-a/0d7ed346-3e61-48a0-8236-b42a96af6267" }, "name": "I wrote out the question as requested and tried to re-upload the 2 questions I'm interested in. I need the solution to e and f after we find the value of Cn for that question based on your solution before. I hope this clears things up.Consider the following heat equation on a rod (which includes heat loss through the lateral side and fixed heat flow on the boundary): ∂u/∂t = ∂2u/∂x2 − 9u, 0 < x < 1, t > 0,subject to the boundary conditionsux(0, t) = 3, ux(1, t) = 18, t > 0,and the initial conditionu(x, 0) = 0, 0 < x < 1.(a) Find the equilibrium solution uE(x) for this problem by solving a certain boundary value problem on (0, 1).(b) Use integration by parts and the given boundary conditions that uE(x) satisfies to computeA0 = 1∫0 u′′E (x) dxEnter A0. (Do not use the explicit formula for uE(x) obtained in part (a).)(c) Use integration by parts and the given boundary conditions that uE(x) satisfies to show that1∫0 u′′E (x) cos(nπx) dx = An + B*n^2 1∫0 uE(x) cos(nπx) dx, n ≥ 1, (1)for some constants B and An. (Do not use the explicit formula for uE(x) obtained in part (a).) Enter the values of B and An (in that order) into the answer box below, separated with a comma.(d) Use the differential equation that uE(x) satisfies together with the results obtained in (b) and (c) to deduce the Fourier cosine series representation for uE(x) on (0, 1) which is of the form a0/2 + ∞Σn =1 an cos(nπx).Enter the values of a0 and an (in that order) into the answer box below, separated with a comma.(e) Show that v(x, t) = u(x, t) − uE(x, t) is solution of a homogeneous problem (with a different initial condition) and solve it using the method of separation of variables and the superposition principle. The solution has the formv(x, t) = G0(t) + ∞Σn =1 Gn(t) cos(nπx)Enter the functions G0(t) and Gn(t) (in that order) into the answer box below, separated with a comma.(f) The solution u(x, t) of the original problem, written as a cosine Fourier series with coefficients that are functions of t, has the formu(x, t) = H0(t) + ∞Σn =1 Hn(t) cos(nπx)Enter the functions H0(t) and Hn(t) (in that order) into the answer box below, separated with a comma. (e) Show that v(x, t)=u(x, t) — uɛ(x, t) is solution of a homogeneous problem (with a different initial condition)and solve it using the method of separation of variables and the superposition principle. The solution has theformv(x,t) = Go(t) + Σ Gn(t) cos(nлx)n=1Enter the functions Go (t) and Gn(t) (in that order) into the answer box below, separated with a comma.(f) The solution u(x, t) of the original problem, written as a cosine Fourier series with coefficients that arefunctions of t, has the form8u(x,t) = H₁(t) + Σ H₂(t) cos(nлx)n=1Enter the functions Ho(t) and H₂(t) (in that order) into the answer box below, separated with a comma.", "description": "I wrote out the question as requested and tried to re-upload the 2 questions I'm interested in. I need the solution to e and f after we find the value of Cn for that question based on your solution before. I hope this clears things up.Consider the following heat equation on a rod (which includes heat loss through the lateral side and fixed heat flow on the boundary): ∂u/∂t = ∂2u/∂x2 − 9u, 0 < x < 1, t > 0,subject to the boundary conditionsux(0, t) = 3, ux(1, t) = 18, t > 0,and the initial conditionu(x, 0) = 0, 0 < x < 1.(a) Find the equilibrium solution uE(x) for this problem by solving a certain boundary value problem on (0, 1).(b) Use integration by parts and the given boundary conditions that uE(x) satisfies to computeA0 = 1∫0 u′′E (x) dxEnter A0. (Do not use the explicit formula for uE(x) obtained in part (a).)(c) Use integration by parts and the given boundary conditions that uE(x) satisfies to show that1∫0 u′′E (x) cos(nπx) dx = An + B*n^2 1∫0 uE(x) cos(nπx) dx, n ≥ 1, (1)for some constants B and An. (Do not use the explicit formula for uE(x) obtained in part (a).) Enter the values of B and An (in that order) into the answer box below, separated with a comma.(d) Use the differential equation that uE(x) satisfies together with the results obtained in (b) and (c) to deduce the Fourier cosine series representation for uE(x) on (0, 1) which is of the form a0/2 + ∞Σn =1 an cos(nπx).Enter the values of a0 and an (in that order) into the answer box below, separated with a comma.(e) Show that v(x, t) = u(x, t) − uE(x, t) is solution of a homogeneous problem (with a different initial condition) and solve it using the method of separation of variables and the superposition principle. The solution has the formv(x, t) = G0(t) + ∞Σn =1 Gn(t) cos(nπx)Enter the functions G0(t) and Gn(t) (in that order) into the answer box below, separated with a comma.(f) The solution u(x, t) of the original problem, written as a cosine Fourier series with coefficients that are functions of t, has the formu(x, t) = H0(t) + ∞Σn =1 Hn(t) cos(nπx)Enter the functions H0(t) and Hn(t) (in that order) into the answer box below, separated with a comma. (e) Show that v(x, t)=u(x, t) — uɛ(x, t) is solution of a homogeneous problem (with a different initial condition)and solve it using the method of separation of variables and the superposition principle. The solution has theformv(x,t) = Go(t) + Σ Gn(t) cos(nлx)n=1Enter the functions Go (t) and Gn(t) (in that order) into the answer box below, separated with a comma.(f) The solution u(x, t) of the original problem, written as a cosine Fourier series with coefficients that arefunctions of t, has the form8u(x,t) = H₁(t) + Σ H₂(t) cos(nлx)n=1Enter the functions Ho(t) and H₂(t) (in that order) into the answer box below, separated with a comma.", "inLanguage": "en", "headline": "I wrote out the question as requested and tried to re-upload the 2 questions I'm interested in. I need the solution to e and f after we find the value of Cn for that question based on your solution before. I hope this clears things up.Consider the following heat equation on a rod (which includes heat loss through the lateral side and fixed heat flow on the boundary): ∂u/∂t = ∂2u/∂x2 − 9u, 0 < x < 1, t > 0,subject to the boundary conditionsux(0, t) = 3, ux(1, t) = 18, t > 0,and the initial conditionu(x, 0) = 0, 0 < x < 1.(a) Find the equilibrium solution uE(x) for this problem by solving a certain boundary value problem on (0, 1).(b) Use integration by parts and the given boundary conditions that uE(x) satisfies to computeA0 = 1∫0 u′′E (x) dxEnter A0. (Do not use the explicit formula for uE(x) obtained in part (a).)(c) Use integration by parts and the given boundary conditions that uE(x) satisfies to show that1∫0 u′′E (x) cos(nπx) dx = An + B*n^2 1∫0 uE(x) cos(nπx) dx, n ≥ 1, (1)for some constants B and An. (Do not use the explicit formula for uE(x) obtained in part (a).) Enter the values of B and An (in that order) into the answer box below, separated with a comma.(d) Use the differential equation that uE(x) satisfies together with the results obtained in (b) and (c) to deduce the Fourier cosine series representation for uE(x) on (0, 1) which is of the form a0/2 + ∞Σn =1 an cos(nπx).Enter the values of a0 and an (in that order) into the answer box below, separated with a comma.(e) Show that v(x, t) = u(x, t) − uE(x, t) is solution of a homogeneous problem (with a different initial condition) and solve it using the method of separation of variables and the superposition principle. The solution has the formv(x, t) = G0(t) + ∞Σn =1 Gn(t) cos(nπx)Enter the functions G0(t) and Gn(t) (in that order) into the answer box below, separated with a comma.(f) The solution u(x, t) of the original problem, written as a cosine Fourier series with coefficients that are functions of t, has the formu(x, t) = H0(t) + ∞Σn =1 Hn(t) cos(nπx)Enter the functions H0(t) and Hn(t) (in that order) into the answer box below, separated with a comma. (e) Show that v(x, t)=u(x, t) — uɛ(x, t) is solution of a homogeneous problem (with a different initial condition)and solve it using the method of separation of variables and the superposition principle. The solution has theformv(x,t) = Go(t) + Σ Gn(t) cos(nлx)n=1Enter the functions Go (t) and Gn(t) (in that order) into the answer box below, separated with a comma.(f) The solution u(x, t) of the original problem, written as a cosine Fourier series with coefficients that arefunctions of t, has the form8u(x,t) = H₁(t) + Σ H₂(t) cos(nлx)n=1Enter the functions Ho(t) and H₂(t) (in that order) into the answer box below, separated with a comma.", "datePublished": "2024-11-16", "dateModified": "2024-11-16", "isAccessibleForFree": "False", "hasPart": { "@type": "WebPageElement", "isAccessibleForFree": "False", "cssSelector": ".paywall" }, "mainEntity": { "@type": "Question", "name": "I wrote out the question as requested and tried to re-upload the 2 questions I'm interested in. I need the solution to e and f after we find the value of Cn for that question based on your solution before. I hope this clears things up.Consider the following heat equation on a rod (which includes heat loss through the lateral side and fixed heat flow on the boundary): ∂u/∂t = ∂2u/∂x2 − 9u, 0 < x < 1, t > 0,subject to the boundary conditionsux(0, t) = 3, ux(1, t) = 18, t > 0,and the initial conditionu(x, 0) = 0, 0 < x < 1.(a) Find the equilibrium solution uE(x) for this problem by solving a certain boundary value problem on (0, 1).(b) Use integration by parts and the given boundary conditions that uE(x) satisfies to computeA0 = 1∫0 u′′E (x) dxEnter A0. (Do not use the explicit formula for uE(x) obtained in part (a).)(c) Use integration by parts and the given boundary conditions that uE(x) satisfies to show that1∫0 u′′E (x) cos(nπx) dx = An + B*n^2 1∫0 uE(x) cos(nπx) dx, n ≥ 1, (1)for some constants B and An. (Do not use the explicit formula for uE(x) obtained in part (a).) Enter the values of B and An (in that order) into the answer box below, separated with a comma.(d) Use the differential equation that uE(x) satisfies together with the results obtained in (b) and (c) to deduce the Fourier cosine series representation for uE(x) on (0, 1) which is of the form a0/2 + ∞Σn =1 an cos(nπx).Enter the values of a0 and an (in that order) into the answer box below, separated with a comma.(e) Show that v(x, t) = u(x, t) − uE(x, t) is solution of a homogeneous problem (with a different initial condition) and solve it using the method of separation of variables and the superposition principle. The solution has the formv(x, t) = G0(t) + ∞Σn =1 Gn(t) cos(nπx)Enter the functions G0(t) and Gn(t) (in that order) into the answer box below, separated with a comma.(f) The solution u(x, t) of the original problem, written as a cosine Fourier series with coefficients that are functions of t, has the formu(x, t) = H0(t) + ∞Σn =1 Hn(t) cos(nπx)Enter the functions H0(t) and Hn(t) (in that order) into the answer box below, separated with a comma. (e) Show that v(x, t)=u(x, t) — uɛ(x, t) is solution of a homogeneous problem (with a different initial condition)and solve it using the method of separation of variables and the superposition principle. The solution has theformv(x,t) = Go(t) + Σ Gn(t) cos(nлx)n=1Enter the functions Go (t) and Gn(t) (in that order) into the answer box below, separated with a comma.(f) The solution u(x, t) of the original problem, written as a cosine Fourier series with coefficients that arefunctions of t, has the form8u(x,t) = H₁(t) + Σ H₂(t) cos(nлx)n=1Enter the functions Ho(t) and H₂(t) (in that order) into the answer box below, separated with a comma.", "text": "I wrote out the question as requested and tried to re-upload the 2 questions I'm interested in. I need the solution to e and f after we find the value of Cn for that question based on your solution before. I hope this clears things up.Consider the following heat equation on a rod (which includes heat loss through the lateral side and fixed heat flow on the boundary): ∂u/∂t = ∂2u/∂x2 − 9u, 0 < x < 1, t > 0,subject to the boundary conditionsux(0, t) = 3, ux(1, t) = 18, t > 0,and the initial conditionu(x, 0) = 0, 0 < x < 1.(a) Find the equilibrium solution uE(x) for this problem by solving a certain boundary value problem on (0, 1).(b) Use integration by parts and the given boundary conditions that uE(x) satisfies to computeA0 = 1∫0 u′′E (x) dxEnter A0. (Do not use the explicit formula for uE(x) obtained in part (a).)(c) Use integration by parts and the given boundary conditions that uE(x) satisfies to show that1∫0 u′′E (x) cos(nπx) dx = An + B*n^2 1∫0 uE(x) cos(nπx) dx, n ≥ 1, (1)for some constants B and An. (Do not use the explicit formula for uE(x) obtained in part (a).) Enter the values of B and An (in that order) into the answer box below, separated with a comma.(d) Use the differential equation that uE(x) satisfies together with the results obtained in (b) and (c) to deduce the Fourier cosine series representation for uE(x) on (0, 1) which is of the form a0/2 + ∞Σn =1 an cos(nπx).Enter the values of a0 and an (in that order) into the answer box below, separated with a comma.(e) Show that v(x, t) = u(x, t) − uE(x, t) is solution of a homogeneous problem (with a different initial condition) and solve it using the method of separation of variables and the superposition principle. The solution has the formv(x, t) = G0(t) + ∞Σn =1 Gn(t) cos(nπx)Enter the functions G0(t) and Gn(t) (in that order) into the answer box below, separated with a comma.(f) The solution u(x, t) of the original problem, written as a cosine Fourier series with coefficients that are functions of t, has the formu(x, t) = H0(t) + ∞Σn =1 Hn(t) cos(nπx)Enter the functions H0(t) and Hn(t) (in that order) into the answer box below, separated with a comma. (e) Show that v(x, t)=u(x, t) — uɛ(x, t) is solution of a homogeneous problem (with a different initial condition)and solve it using the method of separation of variables and the superposition principle. The solution has theformv(x,t) = Go(t) + Σ Gn(t) cos(nлx)n=1Enter the functions Go (t) and Gn(t) (in that order) into the answer box below, separated with a comma.(f) The solution u(x, t) of the original problem, written as a cosine Fourier series with coefficients that arefunctions of t, has the form8u(x,t) = H₁(t) + Σ H₂(t) cos(nлx)n=1Enter the functions Ho(t) and H₂(t) (in that order) into the answer box below, separated with a comma.", "answerCount": 1, "dateCreated": "2024-11-16", "acceptedAnswer": { "@type": "Answer", "text": "Answered: Image /qna-images/answer/0d7ed346-3e61-48a0-8236-b42a96af6267.jpg" }, "url": "https://www.bartleby.com/questions-and-answers/e-show-that-vx-t-ux-t-ux-t-is-solution-of-a-homogeneous-problem-with-a-different-initial-condition-a/0d7ed346-3e61-48a0-8236-b42a96af6267" } }</script><script type="application/ld+json">{ "@context": "http://schema.org", "@type": "BreadcrumbList", "itemListElement": [ { "@type": "ListItem", "position": 1, "item": { "@id": "https://www.bartleby.com/", "name": "Bartleby Textbook Solutions" } }, { "@type": "ListItem", "position": 2, "item": { "@id": "https://www.bartleby.com/subject/math", "name": "Math Q&A and Textbook Solutions" } }, { "@type": "ListItem", "position": 3, "item": { "@id": "https://www.bartleby.com/subject/math/calculus", "name": "Calculus Q&A, Textbooks, and Solutions" } }, { "@type": "ListItem", "position": 4, "item": { "@id": "https://www.bartleby.com/subject/math/calculus/questions-and-answers", "name": "Calculus Q&A Library" } }, { "@type": "ListItem", "position": 5, "item": { "@id": "https://www.bartleby.com/questions-and-answers/e-show-that-vx-t-ux-t-ux-t-is-solution-of-a-homogeneous-problem-with-a-different-initial-condition-a/0d7ed346-3e61-48a0-8236-b42a96af6267", "name": "(e) Show that v(x, t) = u(x, t) — uɛ(x, t) is solution of a homogeneous problem (with a different initial condition) and solve it using the method of separation of variables and the superposition principle. The solution has the form v(x,t) = Go(t) + Σ Gn(t) cos(nлx) n=1 Enter the functions Go (t) and Gn(t) (in that order) into the answer box below, separated with a comma. (f) The solution u(x, t) of the original problem, written as a cosine Fourier series with coefficients that are functions of t, has the form 8 u(x,t) = H₁(t) + Σ H₂(t) cos(nлx) n=1 Enter the functions Ho(t) and H₂(t) (in that order) into the answer box below, separated with a comma." } } ] }</script><link rel="preload" as="image" href="/static/compass_v2/learnbar/search-icon.svg"/><link rel="preload" as="image" href="/static/compass_v2/learnbar/search-icon-white.svg"/><link rel="preload" as="image" href="/static/compass_v2/learnbar/ask.svg"/><link rel="preload" as="image" href="/static/compass_v2/shared-icons/expand-img.svg" media="(min-width: 768px)"/><link rel="preload" as="image" imageSrcSet="/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9ae7b3bf-1b32-4ccc-a45c-3ac065d5afbc%2F0d7ed346-3e61-48a0-8236-b42a96af6267%2Fl9qlog_processed.png&w=16&q=75 16w, 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Click here to start typing your search terms">Homework help starts here!</button></div><div class="flexRow justify-center items-center ml-auto mdl:justify-start"><button class="navBar-button flex-initial mdl:hidden" tabindex="0"><img src="/static/compass_v2/learnbar/search-icon-white.svg" alt="" class="button-left-icon mr-8px"/>Search</button><button class="navBar-button flex-initial" tabindex="0"><img src="/static/compass_v2/learnbar/ask.svg" alt="" class="button-left-icon mr-8px"/>ASK AN EXPERT</button></div></div></div><div class="hidden flex-1 z-[800] bg-white h-0px navbar-transition overflow-hidden p-0px lg:flex"><div class="flex-1 flexRow justify-center items-center max-w-[1168px] w-full m-auto h-0px "><div class="flex-initial text-20px leading-24px font-semibold text-darkBlue-900 max-w-[40%] overflow-hidden text-ellipsis flex-nowrap whitespace-nowrap h-0px ">(e) Show that v(x, t) = u(x, t) — uɛ(x, t) is solution of a homogeneous problem (with a different initial condition) and solve it using the method of separation of variables and the superposition principle. The solution has the form v(x,t) = Go(t) + Σ Gn(t) cos(nлx) n=1 Enter the functions Go (t) and Gn(t) (in that order) into the answer box below, separated with a comma. (f) The solution u(x, t) of the original problem, written as a cosine Fourier series with coefficients that are functions of t, has the form 8 u(x,t) = H₁(t) + Σ H₂(t) cos(nлx) n=1 Enter the functions Ho(t) and H₂(t) (in that order) into the answer box below, separated with a comma.</div></div></div></header></section><main id="AppLayout-Scrollable-Main-Container-ID" class="flex-1 overflow-x-hidden overflow-y-auto relative"><div><div id="QNA-PAGE-CONTENT" class="flex-col items-center bg-page px-8px md:px-16px mdl:px-32px mdl:pb-32px"><div id="QNA-PAGE-TOP-CONTENT" class="flex flex-1 w-full pt-12px bg-page mdl:pt-24px"><div id="QNA-PAGE-BREADCRUMB" class="flex flex-col flex-1 w-full max-w-1188px m-auto"><div id="QNA-PAGE-BREADCRUMB" class="flex flex-col flex-1 w-full m-auto font-sans"><div id="BREADCRUMB-ID" class="flex flex-row flex-initial items-center w-full m-auto font-sans text-blue-600 text-14px"><div class="flex flex-row flex-initial items-center shrink-0"><a href="/subject/math" class="flex-1 cursor-pointer underline" tabindex="0">Math</a><svg stroke="currentColor" fill="currentColor" stroke-width="0" viewBox="0 0 24 24" class="flex-initial text-grey-200 w-24px" height="1em" width="1em" xmlns="http://www.w3.org/2000/svg"><path fill="none" d="M0 0h24v24H0z"></path><path d="M6.41 6L5 7.41 9.58 12 5 16.59 6.41 18l6-6z"></path><path d="M13 6l-1.41 1.41L16.17 12l-4.58 4.59L13 18l6-6z"></path></svg></div><div class="flex flex-row flex-initial items-center shrink-0"><a href="/subject/math/calculus" class="flex-1 cursor-pointer underline" tabindex="0">Calculus</a><svg stroke="currentColor" fill="currentColor" stroke-width="0" viewBox="0 0 24 24" class="flex-initial text-grey-200 w-24px" height="1em" width="1em" xmlns="http://www.w3.org/2000/svg"><path fill="none" d="M0 0h24v24H0z"></path><path d="M6.41 6L5 7.41 9.58 12 5 16.59 6.41 18l6-6z"></path><path d="M13 6l-1.41 1.41L16.17 12l-4.58 4.59L13 18l6-6z"></path></svg></div><span class="flex-initial text-grey-500 whitespace-nowrap text-ellipsis overflow-hidden">(e) Show that v(x, t) = u(x, t) — uɛ(x, t) is solution of a homogeneous problem (with a different initial condition) and solve it using the method of separation of variables and the superposition principle. The solution has the form v(x,t) = Go(t) + Σ Gn(t) cos(nлx) n=1 Enter the functions Go (t) and Gn(t) (in that order) into the answer box below, separated with a comma. (f) The solution u(x, t) of the original problem, written as a cosine Fourier series with coefficients that are functions of t, has the form 8 u(x,t) = H₁(t) + Σ H₂(t) cos(nлx) n=1 Enter the functions Ho(t) and H₂(t) (in that order) into the answer box below, separated with a comma.</span></div><h1 id="QNA-PAGE-H1" class="mt-16px text-24px leading-32px whitespace-nowrap overflow-hidden text-darkBlue-900 bg-page font-semibold text-ellipsis pb-16px">(e) Show that v(x, t) = u(x, t) — uɛ(x, t) is solution of a homogeneous problem (with a different initial condition) and solve it using the method of separation of variables and the superposition principle. The solution has the form v(x,t) = Go(t) + Σ Gn(t) cos(nлx) n=1 Enter the functions Go (t) and Gn(t) (in that order) into the answer box below, separated with a comma. (f) The solution u(x, t) of the original problem, written as a cosine Fourier series with coefficients that are functions of t, has the form 8 u(x,t) = H₁(t) + Σ H₂(t) cos(nлx) n=1 Enter the functions Ho(t) and H₂(t) (in that order) into the answer box below, separated with a comma.</h1></div></div></div><div id="qa_ad_top" class="sm:h-[90px] sm:min-h-[90px] sm:min-w-[728px] sm:max-w-[970px] m-auto h-[50px] min-h-[50px] min-w-[300px] max-w-[320px]"></div><div id="QNA-PAGE-MAIN-CONTENT" class="flexColReverse w-full max-w-1188px py-24px flex-grow-0 mx-auto bg-page lg:flex-row md:py-32px"><div id="QNA-PAGE-MIDDLE-LEFT-RAIL" class="flexCol flex-initial mt-24px overflow-visible lg:w-[318px] lg:mr-32px lg:mt-0px"><div id="TEXTBOOK-MODULE-ID" class="flex-initial flex-col items-center justify-center w-full p-24px rounded-lg border-[1px] border-grey100 bg-white lg:w-[318px] overflow-hidden"><div class="flexRow overflow-hidden w-full "><div class="flexCol flex-initial justify-start items-center p-2px"><a href="https://amzn.to/3ubPPQT" target="_blank" rel="noopener noreferrer" class="flex-initial" tabindex="0"><img width="100%" height="68px" class="object-cover rounded-lg h-68px w-auto m-auto" src="https://www.bartleby.com/isbn_cover_images/9781285463247/9781285463247_smallCoverImage.gif" alt="Linear Algebra: A Modern Introduction" decoding="async" loading="lazy"/><button class="secondaryGhost-button flex-initial h-34px mt-8px">BUY</button></a></div><div class="flex-col w-full flex-wrap text-ellipsis overflow-hidden p-2px ml-5px"><a href="/textbooks/linear-algebra-a-modern-introduction-4th-edition/9781285463247/solutions" target="_blank" rel="noopener noreferrer" class="flex-initial w-full text-darkBlue-900 font-semibold text-16px leading-16px text-ellipsis overflow-hidden whitespace-nowrap" tabindex="0">Linear Algebra: A Modern Introduction</a><div class="flex-initial w-full text-14px text-grey-500 text-ellipsis overflow-hidden pt-0x">4th Edition</div><div class="flex-initial w-full text-ellipsis overflow-hidden"><span class="text-14px leading-5 text-grey-900 font-semibold">ISBN:</span><span class="text-14px leading-5 text-grey-900 font-normal ml-4px">9781285463247</span></div><div class="flex-initial w-full text-ellipsis overflow-hidden"><span class="text-14px leading-5 text-grey-900 font-semibold">Author:</span><span class="text-14px leading-5 text-grey-900 font-semibold ml-4px">David Poole</span></div><div class="flex-initial w-full text-ellipsis overflow-hidden"><span class="text-14px leading-5 text-grey-900 font-semibold">Publisher:</span><span class="text-14px leading-5 text-grey-900 font-normal ml-4px">David Poole</span></div></div></div><div class="flexCol w-full mt-24px"><div class="flex-initial flexRow w-full"><div class="flex-1"><div class="relative w-full overflow-hidden"><select class="relative text-grey-900 text-14px leading-20px font-semibold w-full h-48px pr-100px pl-16px text-ellipsis appearance-none bg-white rounded border-[1px] border-grey300" aria-label="problem list"><option value="0">1 Vectors</option><option value="1">2 Systems Of Linear Equations</option><option value="2">3 Matrices</option><option value="3" selected="">4 Eigenvalues And Eigenvectors</option><option value="4">5 Orthogonality</option><option value="5">6 Vector Spaces</option><option value="6">7 Distance And Approximation</option></select><div style="width:-56px" class="absolute left-16px top-12px pr-8px pointer-events-none bg-white text-ellipsis overflow-hidden whitespace-nowrap"><span class="text-grey-900 text-14px leading-20px font-semibold">Chapter4: </span><span class="text-grey-900 text-14px leading-20px">Eigenvalues And Eigenvectors</span></div><div class="absolute text-blue-600 top-12px right-12px pointer-events-none "><svg stroke="currentColor" fill="currentColor" stroke-width="0" viewBox="0 0 24 24" style="width:24px;height:24px" height="1em" width="1em" xmlns="http://www.w3.org/2000/svg"><path fill="none" d="M0 0h24v24H0z"></path><path d="M16.59 8.59L12 13.17 7.41 8.59 6 10l6 6 6-6z"></path></svg></div></div></div><div class="flex-initial w-16px"></div><div class="flex-1"><div class="relative w-full overflow-hidden"><select class="relative text-grey-900 text-14px leading-20px font-semibold w-full h-48px pr-100px pl-16px text-ellipsis appearance-none bg-white rounded border-[1px] border-grey300" aria-label="problem list"><option value="3-0">4.1 Introduction To Eigenvalues And Eigenvectors</option><option value="3-1">4.2 Determinants</option><option value="3-2">4.3 Eigenvalues And Eigenvectors Of N X N Matrices</option><option value="3-3">4.4 Similarity And Diagonalization</option><option value="3-4">4.5 Iterative Methods For Computing Eigenvalues</option><option value="3-5" selected="">4.6 Applications And The Perron-frobenius Theorem</option><option value="3-6">Chapter Questions</option></select><div style="width:-56px" class="absolute left-16px top-12px pr-8px pointer-events-none bg-white text-ellipsis overflow-hidden whitespace-nowrap"><span class="text-grey-900 text-14px leading-20px font-semibold">Section4.6: </span><span class="text-grey-900 text-14px leading-20px">Applications And The Perron-frobenius Theorem</span></div><div class="absolute text-blue-600 top-12px right-12px pointer-events-none "><svg stroke="currentColor" fill="currentColor" stroke-width="0" viewBox="0 0 24 24" style="width:24px;height:24px" height="1em" width="1em" xmlns="http://www.w3.org/2000/svg"><path fill="none" d="M0 0h24v24H0z"></path><path d="M16.59 8.59L12 13.17 7.41 8.59 6 10l6 6 6-6z"></path></svg></div></div></div></div><div class="flex-initial flexRow w-full mt-16px"><div class="relative w-full overflow-hidden"><select class="relative text-grey-900 text-14px leading-20px font-semibold w-full h-48px pr-100px pl-16px text-ellipsis appearance-none bg-white rounded border-[1px] border-grey300" aria-label="problem list"><option value="0">Problem 1EQ </option><option value="1">Problem 2EQ </option><option value="2">Problem 3EQ </option><option value="3">Problem 4EQ </option><option value="4">Problem 5EQ </option><option value="5">Problem 6EQ </option><option value="6">Problem 7EQ </option><option value="7">Problem 8EQ </option><option value="8">Problem 9EQ </option><option value="9">Problem 10EQ </option><option value="10">Problem 11EQ </option><option value="11">Problem 12EQ </option><option value="12">Problem 13EQ </option><option value="13">Problem 14EQ </option><option value="14">Problem 15EQ </option><option value="15">Problem 16EQ </option><option value="16">Problem 17EQ </option><option value="17">Problem 18EQ </option><option value="18">Problem 19EQ </option><option value="19">Problem 20EQ </option><option value="20">Problem 21EQ </option><option value="21">Problem 22EQ </option><option value="22">Problem 23EQ </option><option value="23">Problem 24EQ </option><option value="24">Problem 25EQ </option><option value="25">Problem 26EQ </option><option value="26">Problem 27EQ </option><option value="27">Problem 28EQ </option><option value="28">Problem 29EQ </option><option value="29">Problem 30EQ </option><option value="30">Problem 31EQ </option><option value="31">Problem 32EQ </option><option value="32">Problem 33EQ </option><option value="33">Problem 34EQ </option><option value="34">Problem 35EQ </option><option value="35">Problem 36EQ </option><option value="36">Problem 37EQ </option><option value="37">Problem 38EQ </option><option value="38">Problem 39EQ </option><option value="39">Problem 40EQ </option><option value="40">Problem 41EQ </option><option value="41">Problem 42EQ </option><option value="42">Problem 43EQ </option><option value="43">Problem 44EQ </option><option value="44">Problem 45EQ </option><option value="45">Problem 46EQ </option><option value="46">Problem 47EQ </option><option value="47">Problem 48EQ </option><option value="48">Problem 49EQ </option><option value="49">Problem 50EQ </option><option value="50">Problem 51EQ </option><option value="51">Problem 52EQ </option><option value="52">Problem 53EQ </option><option value="53">Problem 54EQ </option><option value="54">Problem 55EQ </option><option value="55">Problem 56EQ </option><option value="56">Problem 57EQ </option><option value="57">Problem 58EQ </option><option value="58">Problem 59EQ </option><option value="59">Problem 60EQ </option><option value="60">Problem 61EQ </option><option value="61">Problem 62EQ </option><option value="62">Problem 63EQ </option><option value="63">Problem 64EQ </option><option value="64">Problem 65EQ </option><option value="65">Problem 66EQ </option><option value="66">Problem 67EQ </option><option value="67">Problem 68EQ </option><option value="68" selected="">Problem 69EQ: Let x=x(t) be a twice-differentiable function and consider the second order differential equation...</option><option value="69">Problem 70EQ </option><option value="70">Problem 71EQ </option><option value="71">Problem 72EQ </option><option value="72">Problem 73EQ </option><option value="73">Problem 74EQ </option><option value="74">Problem 75EQ </option><option value="75">Problem 76EQ </option><option value="76">Problem 77EQ </option><option value="77">Problem 78EQ </option><option value="78">Problem 79EQ </option><option value="79">Problem 80EQ </option><option value="80">Problem 81EQ </option><option value="81">Problem 82EQ </option><option value="82">Problem 83EQ </option><option value="83">Problem 84EQ </option><option value="84">Problem 85EQ </option><option value="85">Problem 86EQ </option><option value="86">Problem 87EQ </option><option value="87">Problem 88EQ </option><option value="88">Problem 89EQ </option><option value="89">Problem 90EQ </option><option value="90">Problem 91EQ </option><option value="91">Problem 92EQ </option></select><div style="width:-56px" class="absolute left-16px top-12px pr-8px pointer-events-none bg-white text-ellipsis overflow-hidden whitespace-nowrap"><span class="text-grey-900 text-14px leading-20px font-semibold">Problem 69EQ: </span><span class="text-grey-900 text-14px leading-20px">Let x=x(t) be a twice-differentiable function and consider the second order differential equation...</span></div><div class="absolute text-blue-600 top-12px right-12px pointer-events-none "><svg stroke="currentColor" fill="currentColor" stroke-width="0" viewBox="0 0 24 24" style="width:24px;height:24px" height="1em" width="1em" xmlns="http://www.w3.org/2000/svg"><path fill="none" d="M0 0h24v24H0V0z"></path><path d="M4 10.5c-.83 0-1.5.67-1.5 1.5s.67 1.5 1.5 1.5 1.5-.67 1.5-1.5-.67-1.5-1.5-1.5zm0-6c-.83 0-1.5.67-1.5 1.5S3.17 7.5 4 7.5 5.5 6.83 5.5 6 4.83 4.5 4 4.5zm0 12c-.83 0-1.5.68-1.5 1.5s.68 1.5 1.5 1.5 1.5-.68 1.5-1.5-.67-1.5-1.5-1.5zM7 19h14v-2H7v2zm0-6h14v-2H7v2zm0-8v2h14V5H7z"></path></svg></div></div></div></div><div class="flex-initial flex-row text-end w-full mt-16px"><a href="/subject/math/algebra/textbook-answers" class="standalone-link 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(i) Compute the…</p><p class="flex-1 m-0 text-shark text-14px leading-20px -tracking-0.1px w-[100%] break-words line-clamp-2">A: </p></div></a><a href="/questions-and-answers/consider-the-circle-c-of-unit-radius.-as-an-equation-c-is-given-by-x-y-1.-find-all-tangent-lines-to-/ef40dfb8-d484-4398-858c-d74e1799346c" class="flex-1 w-full no-underline mx-2px mt-2px mb-24px" tabindex="0"><div class="w-full lg:max-w-[255px]"><p class="text-grey-500 flex-1 m-0 text-16px font-semibold leading-24px -tracking-0.1px pb-6px w-[100%] break-words line-clamp-2">Q: please help thank you a lot. also please don't use chat gpt because that answer is wrong</p><p class="flex-1 m-0 text-shark text-14px leading-20px -tracking-0.1px w-[100%] break-words line-clamp-2">A: Step 1:Method 1 Step 2:Method 2 Step 3: Step 4:</p></div></a><a href="/questions-and-answers/pt-1-1-152-pt-t-.-t-12-.-2t-2tt-152-.-5t-1-12-211-152-tt-12-51-21-1-11-1-71-2-y-6e2x-dy-dx-62e2x-12e/98e17122-dd9d-48d5-8eb6-0a6d9b0ffaa1" class="flex-1 w-full no-underline mx-2px mt-2px mb-24px" tabindex="0"><div class="w-full lg:max-w-[255px]"><p class="text-grey-500 flex-1 m-0 text-16px font-semibold leading-24px -tracking-0.1px pb-6px w-[100%] break-words line-clamp-2">Q: Explain step by step of how they got to the answer for both problems</p><p class="flex-1 m-0 text-shark text-14px leading-20px -tracking-0.1px w-[100%] break-words line-clamp-2">A: </p></div></a><a href="/questions-and-answers/with-explanation-q-prove-that-l-5n1-and-steps-of-solution/760f3d21-3443-4ba0-8b54-98a13b5453dd" class="flex-1 w-full no-underline mx-2px mt-2px mb-24px" tabindex="0"><div class="w-full lg:max-w-[255px]"><p class="text-grey-500 flex-1 m-0 text-16px font-semibold leading-24px -tracking-0.1px pb-6px w-[100%] break-words line-clamp-2">Q: मा With explanation Q / Prove that L{ {"} = "! 5n+1 and steps of solution?</p><p class="flex-1 m-0 text-shark text-14px leading-20px -tracking-0.1px w-[100%] break-words line-clamp-2">A: </p></div></a><a href="/questions-and-answers/q1-9-points-let-zx-y-and-wx-y-be-smooth-functions-that-satisfy-the-equations-ww-xyz-4-0-zwxyw10-and-/98117767-6e6c-4fbe-a9dc-b2ddc0dbf0c4" class="flex-1 w-full no-underline mx-2px mt-2px mb-24px" tabindex="0"><div class="w-full lg:max-w-[255px]"><p class="text-grey-500 flex-1 m-0 text-16px font-semibold leading-24px -tracking-0.1px pb-6px w-[100%] break-words line-clamp-2">Q: Q1 (9 points) Let z(x, y) and w(x, y) be smooth functions that satisfy the equations w+w³ + x²yz + 4…</p><p class="flex-1 m-0 text-shark text-14px leading-20px -tracking-0.1px w-[100%] break-words line-clamp-2">A: Step 1: Set up The question:Analyze the question and observe what is given to you and what you need…</p></div></a><a href="/questions-and-answers/18.-find-the-intercepts-of-the-plane-x-y-z-5-4-3-s-1-0-1-t-1-4-2./f26995ff-bd62-4447-b22d-1af81ce50d25" class="flex-1 w-full no-underline mx-2px mt-2px mb-24px" tabindex="0"><div class="w-full lg:max-w-[255px]"><p class="text-grey-500 flex-1 m-0 text-16px font-semibold leading-24px -tracking-0.1px pb-6px w-[100%] break-words line-clamp-2">Q: Pls help ASAP. Pls show all work and steps. Pls circle the final answer.</p><p class="flex-1 m-0 text-shark text-14px leading-20px -tracking-0.1px w-[100%] break-words line-clamp-2">A: Here is the step-by-step explanation:The equation of the plane is given…</p></div></a><a href="/questions-and-answers/graded-exercise-5-1-3.-a-6-ft-man-walks-away-from-a-9-ft-lamppost-at-a-rate-of-ftsec.-if-the-light-a/eb5f6d51-f758-4236-80e3-a57906e04775" class="flex-1 w-full no-underline mx-2px mt-2px mb-24px" tabindex="0"><div class="w-full lg:max-w-[255px]"><p class="text-grey-500 flex-1 m-0 text-16px font-semibold leading-24px -tracking-0.1px pb-6px w-[100%] break-words line-clamp-2">Q: GRADED EXERCISE 5: 1 3. A 6-ft man walks away from a 9-ft lamppost at a rate of ft/sec. If the light…</p><p class="flex-1 m-0 text-shark text-14px leading-20px -tracking-0.1px w-[100%] break-words line-clamp-2">A: Problem 3: Related Rates ProblemWe are given:A 6 ft tall man walks away from a 9 ft tall lamppost at…</p></div></a><a href="/questions-and-answers/17.-the-line-42-2-s-5-3-1-se-r-crosses-the-xz-plane-and-the-yz-plane-at-points-a-as-b-respectively.-/b12fe077-2a06-4ede-a8d7-2aface8021c2" class="flex-1 w-full no-underline mx-2px mt-2px mb-24px" tabindex="0"><div class="w-full lg:max-w-[255px]"><p class="text-grey-500 flex-1 m-0 text-16px font-semibold leading-24px -tracking-0.1px pb-6px w-[100%] break-words line-clamp-2">Q: Pls help ASAP. Pls show all work and steps. Pls circle the final answer.</p><p class="flex-1 m-0 text-shark text-14px leading-20px -tracking-0.1px w-[100%] break-words line-clamp-2">A: Steps and explanations are as follows:In case of any doubt, please let me know. Thank you.</p></div></a><a href="/questions-and-answers/1.-a-graphing-calculator-is-required-for-this-question.-you-are-permitted-to-use-your-calculator-to-/45c63827-ba91-4c25-9eaf-d171442444e0" class="flex-1 w-full no-underline mx-2px mt-2px mb-24px" tabindex="0"><div class="w-full lg:max-w-[255px]"><p class="text-grey-500 flex-1 m-0 text-16px font-semibold leading-24px -tracking-0.1px pb-6px w-[100%] break-words line-clamp-2">Q: 1. A GRAPHING CALCULATOR IS REQUIRED FOR THIS QUESTION. You are permitted to use your calculator to…</p><p class="flex-1 m-0 text-shark text-14px leading-20px -tracking-0.1px w-[100%] break-words line-clamp-2">A: Here is the calculation for the answer in Part (d) using Desmos graphing calculator. To find x,…</p></div></a><a href="/questions-and-answers/7.-determine-the-value-of-m-will-make-the-planes-new-shequel-2x-my-3z-1-0-and-p2-2mx-3y-2z-4-0-6-a.-/a6d0780e-9876-44a1-bae9-fe8845836b12" class="flex-1 w-full no-underline mx-2px mt-2px mb-24px" tabindex="0"><div class="w-full lg:max-w-[255px]"><p class="text-grey-500 flex-1 m-0 text-16px font-semibold leading-24px -tracking-0.1px pb-6px w-[100%] break-words line-clamp-2">Q: Pls help ASAP. Pls show all work and steps. Pls circle the final answer.</p><p class="flex-1 m-0 text-shark text-14px leading-20px -tracking-0.1px w-[100%] break-words line-clamp-2">A: 1. Assuming they are asking for the value of m for which both planes will be perpendicular:To make…</p></div></a><a href="/questions-and-answers/5t-7t-rt-31-1-rt-31-1-10t-7-5t-7t33t-13-31-132-31-1-101-7-95t-7t3t-1-31-16-31-110t-7-95t-71-31-14-30/f40d27b8-1680-4449-ad72-f2d189a7fa73" class="flex-1 w-full no-underline mx-2px mt-2px mb-24px" tabindex="0"><div class="w-full lg:max-w-[255px]"><p class="text-grey-500 flex-1 m-0 text-16px font-semibold leading-24px -tracking-0.1px pb-6px w-[100%] break-words line-clamp-2">Q: Help solve step by step</p><p class="flex-1 m-0 text-shark text-14px leading-20px -tracking-0.1px w-[100%] break-words line-clamp-2">A: Step 1: Identify the derivative rules that applyConstant Rule: (where c = constant, ex: 10)d/dx (c)…</p></div></a><a href="/questions-and-answers/consider-the-following-heat-equation-on-a-rod-which-includes-heat-loss-through-the-lateral-side-and-/457d5f8b-f55e-4c47-839b-420898ae2a2f" class="flex-1 w-full no-underline mx-2px mt-2px mb-24px" tabindex="0"><div class="w-full lg:max-w-[255px]"><p class="text-grey-500 flex-1 m-0 text-16px font-semibold leading-24px -tracking-0.1px pb-6px w-[100%] break-words line-clamp-2">Q: Consider the following heat equation on a rod (which includes heat loss through the lateral side and…</p><p class="flex-1 m-0 text-shark text-14px leading-20px -tracking-0.1px w-[100%] break-words line-clamp-2">A: If doubt then aks. Please like.</p></div></a><a href="/questions-and-answers/24-1.3.-241/a03313e0-7b8a-491d-a04c-172aa15b86be" class="flex-1 w-full no-underline mx-2px mt-2px mb-24px" tabindex="0"><div class="w-full lg:max-w-[255px]"><p class="text-grey-500 flex-1 m-0 text-16px font-semibold leading-24px -tracking-0.1px pb-6px w-[100%] break-words line-clamp-2">Q: Look at the figure:The radius r measures 10cm and the radius R measures 20cm. The height h1 measures…</p><p class="flex-1 m-0 text-shark text-14px leading-20px -tracking-0.1px w-[100%] break-words line-clamp-2">A: (c) If the height of the cylinder were to change from 25cm to 25.2cm and all other measurements…</p></div></a><a href="/questions-and-answers/13.-find-the-equation-of-the-tangent-to-the-following-functions-at-the-indicated-point.-a-fx-x-3x6-a/a9d6b522-ef33-4ef0-af1e-dd115908c7a9" class="flex-1 w-full no-underline mx-2px mt-2px mb-24px" tabindex="0"><div class="w-full lg:max-w-[255px]"><p class="text-grey-500 flex-1 m-0 text-16px font-semibold leading-24px -tracking-0.1px pb-6px w-[100%] break-words line-clamp-2">Q: Please help on all asked questions, Pls show all work and steps, and circle the final answer.</p><p class="flex-1 m-0 text-shark text-14px leading-20px -tracking-0.1px w-[100%] break-words line-clamp-2">A: Step 1:13. a) The provided function is:f(x)=x2−3x+6 ..........(1)It is needed to obtain the…</p></div></a><a href="/questions-and-answers/classify-each-of-the-following-first-order-differential-equations-x-1-y-x-y-x-u-xy-32-14-dz-2y-dy-0-/367b7e47-1875-4039-ac10-736269e4bc0d" class="flex-1 w-full no-underline mx-2px mt-2px mb-24px" tabindex="0"><div class="w-full lg:max-w-[255px]"><p class="text-grey-500 flex-1 m-0 text-16px font-semibold leading-24px -tracking-0.1px pb-6px w-[100%] break-words line-clamp-2">Q: Classify each of the following first order differential equations (x + 1) y' + (x + y)² = x² У xy…</p><p class="flex-1 m-0 text-shark text-14px leading-20px -tracking-0.1px w-[100%] break-words line-clamp-2">A: Explanation:</p></div></a><a href="/questions-and-answers/in-this-question-we-will-consider-the-function-a-use-asymptotics-as-in-the-first-week-of-class-to-ma/7620e6bf-bc29-4e06-85a0-6d0755c7ca1b" class="flex-1 w-full no-underline mx-2px mt-2px mb-24px" tabindex="0"><div class="w-full lg:max-w-[255px]"><p class="text-grey-500 flex-1 m-0 text-16px font-semibold leading-24px -tracking-0.1px pb-6px w-[100%] break-words line-clamp-2">Q: solve part e</p><p class="flex-1 m-0 text-shark text-14px leading-20px -tracking-0.1px w-[100%] break-words line-clamp-2">A: Step 1:</p></div></a><a href="/questions-and-answers/in-exercises-33-38-find-the-value-of-fog-at-the-given-value-of-x.-x-x-1-u-1-u-gx-x-33.-fu-u-1-3-34.-/84831e5e-41d3-4150-9c6c-303936265658" class="flex-1 w-full no-underline mx-2px mt-2px mb-24px" tabindex="0"><div class="w-full lg:max-w-[255px]"><p class="text-grey-500 flex-1 m-0 text-16px font-semibold leading-24px -tracking-0.1px pb-6px w-[100%] break-words line-clamp-2">Q: In Exercises 33-38, find the value of (fog)' at the given value of x. √√√x, x = 1 u³ + 1, u = g(x) =…</p><p class="flex-1 m-0 text-shark text-14px leading-20px -tracking-0.1px w-[100%] break-words line-clamp-2">A: We are given two functions, f(u) and g(x), and we are asked to find the derivative of the composite…</p></div></a><a href="/questions-and-answers/4.-find-if-any-the-horizontal-asymptotes-of-the-following-functions-and-use-that-information-to-matc/abbb095b-fdb3-4664-99fb-b534d12eead9" class="flex-1 w-full no-underline mx-2px mt-2px mb-24px" tabindex="0"><div class="w-full lg:max-w-[255px]"><p class="text-grey-500 flex-1 m-0 text-16px font-semibold leading-24px -tracking-0.1px pb-6px w-[100%] break-words line-clamp-2">Q: 4. Find, if any, the horizontal asymptotes of the following functions and use that information to…</p><p class="flex-1 m-0 text-shark text-14px leading-20px -tracking-0.1px w-[100%] break-words line-clamp-2">A: (a)f(x)=x4+3x2+7x+10(x+1)4 Degree of the numerator: 4 (after expansion)Degree of the denominator:…</p></div></a><a href="/questions-and-answers/consider-the-following-heat-equation-on-a-rod-which-includes-heat-loss-through-the-lateral-side-and-/00faa39d-77d1-4183-84c5-f0f27d083011" class="flex-1 w-full no-underline mx-2px mt-2px mb-24px" tabindex="0"><div class="w-full lg:max-w-[255px]"><p class="text-grey-500 flex-1 m-0 text-16px font-semibold leading-24px -tracking-0.1px pb-6px w-[100%] break-words line-clamp-2">Q: Could section E and F be solved explicitly please?</p><p class="flex-1 m-0 text-shark text-14px leading-20px -tracking-0.1px w-[100%] break-words line-clamp-2">A: </p></div></a><a href="/questions-and-answers/a-12percent-interest-compounded-annually-b-11percent-interest-compounded-monthly-c-10percent-interes/0acd2c38-bb43-40f2-aed9-261804e22bc0" class="flex-1 w-full no-underline mx-2px mt-2px mb-24px" tabindex="0"><div class="w-full lg:max-w-[255px]"><p class="text-grey-500 flex-1 m-0 text-16px font-semibold leading-24px -tracking-0.1px pb-6px w-[100%] break-words line-clamp-2">Q: question says to rank in order the following options</p><p class="flex-1 m-0 text-shark text-14px leading-20px -tracking-0.1px w-[100%] break-words line-clamp-2">A: The effective annual rate (EAR) represents how much interest you earn in a year after compounding.…</p></div></a><a href="/questions-and-answers/find-the-general-and-particular-solution.-y6y-10y2220x-y0-2-y0-2/0183b442-b78f-40a3-983a-b28fde102362" class="flex-1 w-full no-underline mx-2px mt-2px mb-24px" tabindex="0"><div class="w-full lg:max-w-[255px]"><p class="text-grey-500 flex-1 m-0 text-16px font-semibold leading-24px -tracking-0.1px pb-6px w-[100%] break-words line-clamp-2">Q: Find the general and particular solution. y"+6y' + 10y=22+20x, y(0) = 2, y'(0) = -2</p><p class="flex-1 m-0 text-shark text-14px leading-20px -tracking-0.1px w-[100%] break-words line-clamp-2">A: Approach to solving the question: Solution for Differential EquationConsider the differential…</p></div></a><a href="/questions-and-answers/let-c-be-the-curve-consisting-of-the-three-line-segments-from-00-to-1-1-from-1-1-to-1-1-and-from-1-1/6200e566-8cac-4a4c-a501-344166e0625a" class="flex-1 w-full no-underline mx-2px mt-2px mb-24px" tabindex="0"><div class="w-full lg:max-w-[255px]"><p class="text-grey-500 flex-1 m-0 text-16px font-semibold leading-24px -tracking-0.1px pb-6px w-[100%] break-words line-clamp-2">Q: Let C be the curve consisting of the three line segments from (0, 0) to (1, 1), from (1, 1) to (1,…</p><p class="flex-1 m-0 text-shark text-14px leading-20px -tracking-0.1px w-[100%] break-words line-clamp-2">A: Step 1:</p></div></a><a href="/questions-and-answers/the-solution-of-the-initial-value-problem.-s-t-y-4-y-ty-4y-4-y1-4-t4-is-s-u-t4-7-2t4-5t4-1-y-t8-1-ln/a901f485-c2ec-438e-a239-a8ade9fd4597" class="flex-1 w-full no-underline mx-2px mt-2px mb-24px" tabindex="0"><div class="w-full lg:max-w-[255px]"><p class="text-grey-500 flex-1 m-0 text-16px font-semibold leading-24px -tracking-0.1px pb-6px w-[100%] break-words line-clamp-2">Q: The solution of the initial value problem. = S t y + 4 y √ty 4y = 4 โy(1) = 4 t4 is S У t4 +7 2t4…</p><p class="flex-1 m-0 text-shark text-14px leading-20px -tracking-0.1px w-[100%] break-words line-clamp-2">A: Step 1: Step 2:Step 3: Step 4:</p></div></a><a href="/questions-and-answers/1-1-0-19-13-c-lim-x-3-x-3-x-3-a-113-b-1-d-lim-2h-1-h-1-h-1-a-009-b-infinity-c-1-19-d-113-d-0/f2672bb3-d5a6-4249-b33d-35c48e24460b" class="flex-1 w-full no-underline mx-2px mt-2px mb-24px" tabindex="0"><div class="w-full lg:max-w-[255px]"><p class="text-grey-500 flex-1 m-0 text-16px font-semibold leading-24px -tracking-0.1px pb-6px w-[100%] break-words line-clamp-2">Q: Please help on all asked questions, Pls show all work and steps, and circle the final answer.</p><p class="flex-1 m-0 text-shark text-14px leading-20px -tracking-0.1px w-[100%] break-words line-clamp-2">A: Step 1: Step 2: Step 3: Step 4:</p></div></a><a href="/questions-and-answers/use-rref-method-to-solve-the-linear-system-x1-3x2-9-2x1-x2-8.-we-must-show-the-elementary-row-operat/bb19fb93-0de3-49c0-afe2-2e8fcf3a4b51" class="flex-1 w-full no-underline mx-2px mt-2px mb-24px" tabindex="0"><div class="w-full lg:max-w-[255px]"><p class="text-grey-500 flex-1 m-0 text-16px font-semibold leading-24px -tracking-0.1px pb-6px w-[100%] break-words line-clamp-2">Q: Use RREF method to solve the linear system x1 + 3x2 = 9, 2x1 + x2 8. We must show the elementary row…</p><p class="flex-1 m-0 text-shark text-14px leading-20px -tracking-0.1px w-[100%] break-words line-clamp-2">A: </p></div></a><a href="/questions-and-answers/find-x-for-x2-2/c8e43830-d8ae-4c56-afbf-ddb3fb02a7ad" class="flex-1 w-full no-underline mx-2px mt-2px mb-24px" tabindex="0"><div class="w-full lg:max-w-[255px]"><p class="text-grey-500 flex-1 m-0 text-16px font-semibold leading-24px -tracking-0.1px pb-6px w-[100%] break-words line-clamp-2">Q: find x for √x+2=-2</p><p class="flex-1 m-0 text-shark text-14px leading-20px -tracking-0.1px w-[100%] break-words line-clamp-2">A: There is no solution to the equation x+2=−2,because the square root of a number is always…</p></div></a><a href="/questions-and-answers/differentiate-the-function.-v-x-v-enhanced-feedback-1-2-3/d2d77d63-51bf-4399-862f-c931cb670145" class="flex-1 w-full no-underline mx-2px mt-2px mb-24px" tabindex="0"><div class="w-full lg:max-w-[255px]"><p class="text-grey-500 flex-1 m-0 text-16px font-semibold leading-24px -tracking-0.1px pb-6px w-[100%] break-words line-clamp-2">Q: Differentiate the function. v = (√x+· v' = Enhanced Feedback 1 2 3</p><p class="flex-1 m-0 text-shark text-14px leading-20px -tracking-0.1px w-[100%] break-words line-clamp-2">A: Step 1: Given function v=(x+3x1)2. We have to find v'. (differentiation of the function v) Step…</p></div></a><a href="/questions-and-answers/find-the-limit.-hint-use-polar-coordinates.-x2y2-lim-xy00-xy2-find-all-first-and-second-order-partia/3fdf73f5-70c3-488d-98ae-966cd890bce4" class="flex-1 w-full no-underline mx-2px mt-2px mb-24px" tabindex="0"><div class="w-full lg:max-w-[255px]"><p class="text-grey-500 flex-1 m-0 text-16px font-semibold leading-24px -tracking-0.1px pb-6px w-[100%] break-words line-clamp-2">Q: Find the limit. Hint use Polar Coordinates. x2y2 lim (x,y)+(0,0) x²+y2</p><p class="flex-1 m-0 text-shark text-14px leading-20px -tracking-0.1px w-[100%] break-words line-clamp-2">A: First, we need to find the first order partial derivatives of the function f(x,y) = x*y^(-2) +…</p></div></a><a href="/questions-and-answers/a-ladder-23-feet-long-leans-against-a-wall-and-the-foot-of-the-ladder-is-sliding-away-at-a-constant-/f55543c1-01b6-4022-ac3a-ac6600631e3c" class="flex-1 w-full no-underline mx-2px mt-2px mb-24px" tabindex="0"><div class="w-full lg:max-w-[255px]"><p class="text-grey-500 flex-1 m-0 text-16px font-semibold leading-24px -tracking-0.1px pb-6px w-[100%] break-words line-clamp-2">Q: A ladder 23 feet long leans against a wall and the foot of the ladder is sliding away at a constant…</p><p class="flex-1 m-0 text-shark text-14px leading-20px -tracking-0.1px w-[100%] break-words line-clamp-2">A: if doubt arises please mention in the comments.</p></div></a><a href="/questions-and-answers/b-ving-after-july.-2-c-what-kind-of-time-will-lation-5-5-a-bank-advertises-that-it-compounds-continu/a78e1e4e-f61e-4e52-9b7b-39a900d4cddb" class="flex-1 w-full no-underline mx-2px mt-2px mb-24px" tabindex="0"><div class="w-full lg:max-w-[255px]"><p class="text-grey-500 flex-1 m-0 text-16px font-semibold leading-24px -tracking-0.1px pb-6px w-[100%] break-words line-clamp-2">Q: b) Ving after July). (2) c) what kind of time will: lation (5) 5) A bank advertises that it…</p><p class="flex-1 m-0 text-shark text-14px leading-20px -tracking-0.1px w-[100%] break-words line-clamp-2">A: Because the bank employs continuous compounding, your money will increase steadily over time. We…</p></div></a><a href="/questions-and-answers/6-for-the-graph-provided-answer-the-following-a-for-which-x-is-the-function-discontinuous-what-is-th/02f06d40-56e4-4dca-a988-9d9c30bb05bc" class="flex-1 w-full no-underline mx-2px mt-2px mb-24px" tabindex="0"><div class="w-full lg:max-w-[255px]"><p class="text-grey-500 flex-1 m-0 text-16px font-semibold leading-24px -tracking-0.1px pb-6px w-[100%] break-words line-clamp-2">Q: 6) For the graph provided answer the following: a) For which x is the function discontinuous? What…</p><p class="flex-1 m-0 text-shark text-14px leading-20px -tracking-0.1px w-[100%] break-words line-clamp-2">A: (a)The function is discontinuous at x=Reason-5The limx→−5f(x) does not exist since its left-hand…</p></div></a><a href="/questions-and-answers/diego-deposited-a-certain-sum-of-money-in-a-bank-4-years-ago.-the-bank-had-been-paying-interest-at-t/ecad4ecc-71e7-480d-abfc-078188f3f996" class="flex-1 w-full no-underline mx-2px mt-2px mb-24px" tabindex="0"><div class="w-full lg:max-w-[255px]"><p class="text-grey-500 flex-1 m-0 text-16px font-semibold leading-24px -tracking-0.1px pb-6px w-[100%] break-words line-clamp-2">Q: Diego deposited a certain sum of money in a bank 4 years ago. The bank had been paying interest at…</p><p class="flex-1 m-0 text-shark text-14px leading-20px -tracking-0.1px w-[100%] break-words line-clamp-2">A: Step 1:For the compounded continuously, the formula for the amount at time t is given by…</p></div></a><a href="/questions-and-answers/course-name-calculus-with-analytical-geometry-1-course-code-math-132-do-not-use-artificial-intellige/528c6715-d869-4cf2-9064-17c76ad16160" class="flex-1 w-full no-underline mx-2px mt-2px mb-24px" tabindex="0"><div class="w-full lg:max-w-[255px]"><p class="text-grey-500 flex-1 m-0 text-16px font-semibold leading-24px -tracking-0.1px pb-6px w-[100%] break-words line-clamp-2">Q: Do not use AI apps for solving these maths . To solve by handwriting</p><p class="flex-1 m-0 text-shark text-14px leading-20px -tracking-0.1px w-[100%] break-words line-clamp-2">A: We are asked to find the limit of the function (x-2)^-16 as x approaches 2 using L'Hopital's Rule.…</p></div></a><a href="/questions-and-answers/problem-1.-discrete-stochastic-integrals-for-general-martingales.-n0-let-mn-be-a-martingale-with-res/9eb11759-f171-4a0b-a65d-81744bca2af7" class="flex-1 w-full no-underline mx-2px mt-2px mb-24px" tabindex="0"><div class="w-full lg:max-w-[255px]"><p class="text-grey-500 flex-1 m-0 text-16px font-semibold leading-24px -tracking-0.1px pb-6px w-[100%] break-words line-clamp-2">Q: Problem 1. Discrete stochastic integrals for general martingales. n=0 Let (Mn) be a martingale with…</p><p class="flex-1 m-0 text-shark text-14px leading-20px -tracking-0.1px w-[100%] break-words line-clamp-2">A: Part (a): Prove that E[In]=0The process (In) is defined as:In=∑k=1nZk(Mk−Mk−1)Since (Mn) is…</p></div></a><a href="/questions-and-answers/8.-consider-the-function-x-x-8x-18x-27-and-in-factored-form-fx-x-1x-3-a-determine-the-x-and-y-interc/7396f302-08b7-4a73-b792-50312cfc678f" class="flex-1 w-full no-underline mx-2px mt-2px mb-24px" tabindex="0"><div class="w-full lg:max-w-[255px]"><p class="text-grey-500 flex-1 m-0 text-16px font-semibold leading-24px -tracking-0.1px pb-6px w-[100%] break-words line-clamp-2">Q: pls draw the graph by showing and incorporating everything.</p><p class="flex-1 m-0 text-shark text-14px leading-20px -tracking-0.1px w-[100%] break-words line-clamp-2">A: f)</p></div></a><a href="/questions-and-answers/2-find-the-value-of-b-in-the-definite-integral-below.-l-tanx-dr-2/6f8d8a07-431a-41b5-83f4-79557b7e36b6" class="flex-1 w-full no-underline mx-2px mt-2px mb-24px" tabindex="0"><div class="w-full lg:max-w-[255px]"><p class="text-grey-500 flex-1 m-0 text-16px font-semibold leading-24px -tracking-0.1px pb-6px w-[100%] break-words line-clamp-2">Q: 2) Find the value of b in the definite integral below. L tan(x) dr = 2</p><p class="flex-1 m-0 text-shark text-14px leading-20px -tracking-0.1px w-[100%] break-words line-clamp-2">A: </p></div></a><a href="/questions-and-answers/instruction-course-name-calculus-with-analytical-geometry-1-course-code-math-132-1.-solution-must-ha/ac2efcb0-bf9a-4e8a-9933-7be6fd20bdce" class="flex-1 w-full no-underline mx-2px mt-2px mb-24px" tabindex="0"><div class="w-full lg:max-w-[255px]"><p class="text-grey-500 flex-1 m-0 text-16px font-semibold leading-24px -tracking-0.1px pb-6px w-[100%] break-words line-clamp-2">Q: Instruction: Course Name: Calculus with Analytical Geometry-1 Course Code: MATH 132 1. Solution must…</p><p class="flex-1 m-0 text-shark text-14px leading-20px -tracking-0.1px w-[100%] break-words line-clamp-2">A: </p></div></a><a href="/questions-and-answers/43.-in-parts-a-c-find-the-limit-by-making-the-indicated-substitution.-1-1-a-lim-x-sin-t-8x-x-x-b-lim/13504673-d604-4429-bf7d-994fee343a88" class="flex-1 w-full no-underline mx-2px mt-2px mb-24px" tabindex="0"><div class="w-full lg:max-w-[255px]"><p class="text-grey-500 flex-1 m-0 text-16px font-semibold leading-24px -tracking-0.1px pb-6px w-[100%] break-words line-clamp-2">Q: #5, 43 a and b Hello! Please , can you help me with the attached Calculus problem seen in the…</p><p class="flex-1 m-0 text-shark text-14px leading-20px -tracking-0.1px w-[100%] break-words line-clamp-2">A: Let's solve these limits using the indicated substitution (t=x1). a)(limx→∞xsin(x1)) Substitute…</p></div></a><a href="/questions-and-answers/which-of-the-following-is-a-solution-of-the-initial-value-problem-s-1-sy-lny-dx-x-dy-0-ye-e-hint-int/12e1a97c-bd92-4513-968c-8bc492c18bd6" class="flex-1 w-full no-underline mx-2px mt-2px mb-24px" tabindex="0"><div class="w-full lg:max-w-[255px]"><p class="text-grey-500 flex-1 m-0 text-16px font-semibold leading-24px -tracking-0.1px pb-6px w-[100%] break-words line-clamp-2">Q: Which of the following is a solution of the initial value problem S 1 Sy ln(y) dx + x dy = 0 \y(e) =…</p><p class="flex-1 m-0 text-shark text-14px leading-20px -tracking-0.1px w-[100%] break-words line-clamp-2">A: Step 1: Step 2: Step 3: Step 4:</p></div></a><a href="/questions-and-answers/6.-if-f4-3-and-f4-5-find-g4-where-gx-xfx./b8ce1ea8-10ec-488d-9075-b13e2d3f62a7" class="flex-1 w-full no-underline mx-2px mt-2px mb-24px" tabindex="0"><div class="w-full lg:max-w-[255px]"><p class="text-grey-500 flex-1 m-0 text-16px font-semibold leading-24px -tracking-0.1px pb-6px w-[100%] break-words line-clamp-2">Q: Please help on all asked questions. Please show all work and steps. Pls circle the final answer.</p><p class="flex-1 m-0 text-shark text-14px leading-20px -tracking-0.1px w-[100%] break-words line-clamp-2">A: </p></div></a><a href="/questions-and-answers/find-the-radius-of-convergence-r-of-the-series.-x5-5-inn-n-2-r-5-find-the-interval-i-of-convergence-/e211fe8d-36c4-4d32-bf4a-dfc163e81632" class="flex-1 w-full no-underline mx-2px mt-2px mb-24px" tabindex="0"><div class="w-full lg:max-w-[255px]"><p class="text-grey-500 flex-1 m-0 text-16px font-semibold leading-24px -tracking-0.1px pb-6px w-[100%] break-words line-clamp-2">Q: Please help me with these questions. I am having trouble understanding what to do. I keep getting…</p><p class="flex-1 m-0 text-shark text-14px leading-20px -tracking-0.1px w-[100%] break-words line-clamp-2">A: Part (a):</p></div></a><a href="/questions-and-answers/0-5.-x-x-sin-dx-s-x3-3x-sin-x-x2-2-cos-6x-4-sin-x-8-cos-x-16-sin-nix/93117b08-0722-4d84-9d68-900f611dcc2d" class="flex-1 w-full no-underline mx-2px mt-2px mb-24px" tabindex="0"><div class="w-full lg:max-w-[255px]"><p class="text-grey-500 flex-1 m-0 text-16px font-semibold leading-24px -tracking-0.1px pb-6px w-[100%] break-words line-clamp-2">Q: 0 5. χ √√ x³ sin dx = S: x3 3x² sin x X2 -2 cos 6x -4 sin X 8 cos x 16 sin NIX</p><p class="flex-1 m-0 text-shark text-14px leading-20px -tracking-0.1px w-[100%] break-words line-clamp-2">A: If you have any problem let me know in comment section thank you.</p></div></a><a href="/questions-and-answers/15.-lim-x0-2-x-_-3-sinx-3-x-x/73fbb3e8-e068-48c3-9aff-0d099815b641" class="flex-1 w-full no-underline mx-2px mt-2px mb-24px" tabindex="0"><div class="w-full lg:max-w-[255px]"><p class="text-grey-500 flex-1 m-0 text-16px font-semibold leading-24px -tracking-0.1px pb-6px w-[100%] break-words line-clamp-2">Q: #5, 15 Please help me solve this problem in the attached image. Thank you. The instruction for the…</p><p class="flex-1 m-0 text-shark text-14px leading-20px -tracking-0.1px w-[100%] break-words line-clamp-2">A: </p></div></a><a href="/questions-and-answers/1.-s-x1-x-5-dx/a37fb278-ae7e-44a1-b275-cb93375ae90d" class="flex-1 w-full no-underline mx-2px mt-2px mb-24px" tabindex="0"><div class="w-full lg:max-w-[255px]"><p class="text-grey-500 flex-1 m-0 text-16px font-semibold leading-24px -tracking-0.1px pb-6px w-[100%] break-words line-clamp-2">Q: 1. S x+1 √x-5 dx</p><p class="flex-1 m-0 text-shark text-14px leading-20px -tracking-0.1px w-[100%] break-words line-clamp-2">A: Step 1: Step 2: Step 3: Step 4:</p></div></a><a href="/questions-and-answers/use-integration-by-parts-to-find-the-indefinite-integral.-1.-x-cos-x-dx-fx-2.-xe-dx-xex-dx-math-iz-a/cd033a0e-e20e-4cbb-9b23-9c3910d6587c" class="flex-1 w-full no-underline mx-2px mt-2px mb-24px" tabindex="0"><div class="w-full lg:max-w-[255px]"><p class="text-grey-500 flex-1 m-0 text-16px font-semibold leading-24px -tracking-0.1px pb-6px w-[100%] break-words line-clamp-2">Q: Answer all parts and show work pls</p><p class="flex-1 m-0 text-shark text-14px leading-20px -tracking-0.1px w-[100%] break-words line-clamp-2">A: If you have any problem let me know in the comment section thank you.</p></div></a><a href="/questions-and-answers/4.-i-let-f-r2-r-be-defined-by-fx1-x2-2x-8x1x24x1.-find-all-local-minima-of-f-on-r.-20-marks-ii-does-/670ba45a-5246-49f8-8827-0ee152ae211d" class="flex-1 w-full no-underline mx-2px mt-2px mb-24px" tabindex="0"><div class="w-full lg:max-w-[255px]"><p class="text-grey-500 flex-1 m-0 text-16px font-semibold leading-24px -tracking-0.1px pb-6px w-[100%] break-words line-clamp-2">Q: 4. (i) Let f R2 → R be defined by f(x1, x2) = 2x 8x1x2+4x+1. Find all local minima of ƒ on R². [20…</p><p class="flex-1 m-0 text-shark text-14px leading-20px -tracking-0.1px w-[100%] break-words line-clamp-2">A: Step 1: Step 2: Step 3: Step 4:</p></div></a><a href="/questions-and-answers/x-c.instructure.comcourses1512external_toolsretrievedisplayfull_widthandurlhttpspercent3apercent2fpe/809df3a4-fef7-4981-af50-2d6389a16afd" class="flex-1 w-full no-underline mx-2px mt-2px mb-24px" tabindex="0"><div class="w-full lg:max-w-[255px]"><p class="text-grey-500 flex-1 m-0 text-16px font-semibold leading-24px -tracking-0.1px pb-6px w-[100%] break-words line-clamp-2">Q: X +…</p><p class="flex-1 m-0 text-shark text-14px leading-20px -tracking-0.1px w-[100%] break-words line-clamp-2">A: a.It is given that there are 200 students in the class and 35% are science majors. Hence number of…</p></div></a></div></div></div></div><div id="qa_ad_sidebar" class="mt-[1rem] mx-auto mb-0 min-h-[250px] max-h-[600px] w-[300px] max-md:hidden"></div></div><div id="QNA-PAGE-MIDDLE-MAIN" class="flexCol"><div class="flex flex-col-reverse sm:flex-row sm:justify-between sm:items-center"><div class="flex flex-initial border-l-[2px] border-solid border-yellow700"><div aria-level="2" role="heading" data-section-name="Question" class="flex-initial text-20px font-semibold font-sans text-darkBlue-900 ml-8px md:text-24px">Question</div></div></div><div class="flexCol flex-initial border-[1px] mt-24px p-24px rounded-lg border-solid border-ghost bg-white"><div class="font-sans text-16px text-black leading-24px mb-24px"><p>I wrote out the question as requested and tried to re-upload the 2 questions I'm interested in. I need the solution to e and f after we find the value of Cn for that question based on your solution before. I hope this clears things up.</p> <p>Consider the following heat equation on a rod (which includes heat loss through the lateral side and fixed heat flow on the boundary):</p> <p> ∂u/∂t = ∂2u/∂x2 − 9u, 0 < x < 1, t > 0,</p> <p>subject to the boundary conditions</p> <p>ux(0, t) = 3, ux(1, t) = 18, t > 0,</p> <p>and the initial condition</p> <p>u(x, 0) = 0, 0 < x < 1.</p> <p>(a) Find the equilibrium solution uE(x) for this problem by solving a certain boundary value problem on (0, 1).<br />(b) Use integration by parts and the given boundary conditions that uE(x) satisfies to compute</p> <p>A0 = 1∫0 u′′E (x) dx</p> <p>Enter A0. (Do not use the explicit formula for uE(x) obtained in part (a).)</p> <p><br />(c) Use integration by parts and the given boundary conditions that uE(x) satisfies to show that<br />1∫0 u′′E (x) cos(nπx) dx = An + B*n^2 1∫0 uE(x) cos(nπx) dx, n ≥ 1, (1)</p> <p>for some constants B and An. (Do not use the explicit formula for uE(x) obtained in part (a).) Enter the values of B and An (in that order) into the answer box below, separated with a comma.</p> <p><br />(d) Use the differential equation that uE(x) satisfies together with the results obtained in (b) and (c) to deduce the Fourier cosine series representation for uE(x) on (0, 1) which is of the form</p> <p> a0/2 + ∞Σn =1 an cos(nπx).</p> <p>Enter the values of a0 and an (in that order) into the answer box below, separated with a comma.</p> <p><br />(e) Show that v(x, t) = u(x, t) − uE(x, t) is solution of a homogeneous problem (with a different initial condition) and solve it using the method of separation of variables and the superposition principle. The solution has the form</p> <p>v(x, t) = G0(t) + ∞Σn =1 Gn(t) cos(nπx)</p> <p>Enter the functions G0(t) and Gn(t) (in that order) into the answer box below, separated with a comma.</p> <p><br />(f) The solution u(x, t) of the original problem, written as a cosine Fourier series with coefficients that are functions of t, has the form</p> <p>u(x, t) = H0(t) + ∞Σn =1 Hn(t) cos(nπx)</p> <p>Enter the functions H0(t) and Hn(t) (in that order) into the answer box below, separated with a comma. </p></div><figure class=""><div class="relative"><img alt="(e) Show that v(x, t) = u(x, t) — uɛ(x, t) is solution of a homogeneous problem (with a different initial condition) and solve it using the method of separation of variables and the superposition principle. The solution has the form v(x,t) = Go(t) + Σ Gn(t) cos(nлx) n=1 Enter the functions Go (t) and Gn(t) (in that order) into the answer box below, separated with a comma. (f) The solution u(x, t) of the original problem, written as a cosine Fourier series with coefficients that are functions of t, has the form 8 u(x,t) = H₁(t) + Σ H₂(t) cos(nлx) n=1 Enter the functions Ho(t) and H₂(t) (in that order) into the answer box below, separated with a comma." fetchpriority="high" width="1200" height="351" decoding="async" data-nimg="1" style="color:transparent;max-width:100%;height:auto;max-height:540px;aspect-ratio:1200 / 351" sizes="(min-width: 1320px) 788px, (min-width: 1040px) calc(88.08vw - 357px), (min-width: 860px) calc(100vw - 131px), calc(97.04vw - 74px)" srcSet="/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9ae7b3bf-1b32-4ccc-a45c-3ac065d5afbc%2F0d7ed346-3e61-48a0-8236-b42a96af6267%2Fl9qlog_processed.png&w=16&q=75 16w, /v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9ae7b3bf-1b32-4ccc-a45c-3ac065d5afbc%2F0d7ed346-3e61-48a0-8236-b42a96af6267%2Fl9qlog_processed.png&w=32&q=75 32w, /v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9ae7b3bf-1b32-4ccc-a45c-3ac065d5afbc%2F0d7ed346-3e61-48a0-8236-b42a96af6267%2Fl9qlog_processed.png&w=48&q=75 48w, /v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9ae7b3bf-1b32-4ccc-a45c-3ac065d5afbc%2F0d7ed346-3e61-48a0-8236-b42a96af6267%2Fl9qlog_processed.png&w=64&q=75 64w, /v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9ae7b3bf-1b32-4ccc-a45c-3ac065d5afbc%2F0d7ed346-3e61-48a0-8236-b42a96af6267%2Fl9qlog_processed.png&w=96&q=75 96w, /v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9ae7b3bf-1b32-4ccc-a45c-3ac065d5afbc%2F0d7ed346-3e61-48a0-8236-b42a96af6267%2Fl9qlog_processed.png&w=128&q=75 128w, /v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9ae7b3bf-1b32-4ccc-a45c-3ac065d5afbc%2F0d7ed346-3e61-48a0-8236-b42a96af6267%2Fl9qlog_processed.png&w=256&q=75 256w, /v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9ae7b3bf-1b32-4ccc-a45c-3ac065d5afbc%2F0d7ed346-3e61-48a0-8236-b42a96af6267%2Fl9qlog_processed.png&w=384&q=75 384w, /v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9ae7b3bf-1b32-4ccc-a45c-3ac065d5afbc%2F0d7ed346-3e61-48a0-8236-b42a96af6267%2Fl9qlog_processed.png&w=640&q=75 640w, /v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9ae7b3bf-1b32-4ccc-a45c-3ac065d5afbc%2F0d7ed346-3e61-48a0-8236-b42a96af6267%2Fl9qlog_processed.png&w=750&q=75 750w, /v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9ae7b3bf-1b32-4ccc-a45c-3ac065d5afbc%2F0d7ed346-3e61-48a0-8236-b42a96af6267%2Fl9qlog_processed.png&w=828&q=75 828w, /v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9ae7b3bf-1b32-4ccc-a45c-3ac065d5afbc%2F0d7ed346-3e61-48a0-8236-b42a96af6267%2Fl9qlog_processed.png&w=1080&q=75 1080w, /v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9ae7b3bf-1b32-4ccc-a45c-3ac065d5afbc%2F0d7ed346-3e61-48a0-8236-b42a96af6267%2Fl9qlog_processed.png&w=1200&q=75 1200w, /v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9ae7b3bf-1b32-4ccc-a45c-3ac065d5afbc%2F0d7ed346-3e61-48a0-8236-b42a96af6267%2Fl9qlog_processed.png&w=1920&q=75 1920w, /v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9ae7b3bf-1b32-4ccc-a45c-3ac065d5afbc%2F0d7ed346-3e61-48a0-8236-b42a96af6267%2Fl9qlog_processed.png&w=2048&q=75 2048w, /v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9ae7b3bf-1b32-4ccc-a45c-3ac065d5afbc%2F0d7ed346-3e61-48a0-8236-b42a96af6267%2Fl9qlog_processed.png&w=3840&q=75 3840w" src="/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9ae7b3bf-1b32-4ccc-a45c-3ac065d5afbc%2F0d7ed346-3e61-48a0-8236-b42a96af6267%2Fl9qlog_processed.png&w=3840&q=75"/></div><div class="w-full mt-16px bg-cometB/30 p-8px"><span class="font-semibold text-darkBlue-900 text-12px leading-24px mr-8px">Transcribed Image Text:</span><span class=" text-darkBlue-900 text-12px leading-16px my-16px mx-0px">(e) Show that v(x, t) = u(x, t) — uɛ(x, t) is solution of a homogeneous problem (with a different initial condition) and solve it using the method of separation of variables and the superposition principle. The solution has the form v(x,t) = Go(t) + Σ Gn(t) cos(nлx) n=1 Enter the functions Go (t) and Gn(t) (in that order) into the answer box below, separated with a comma. (f) The solution u(x, t) of the original problem, written as a cosine Fourier series with coefficients that are functions of t, has the form 8 u(x,t) = H₁(t) + Σ H₂(t) cos(nлx) n=1 Enter the functions Ho(t) and H₂(t) (in that order) into the answer box below, separated with a comma.</span></div></figure></div><div class="flex flex-initial items-center mt-24px border-l-[2px] border-solid border-yellow700"><div aria-level="2" role="heading" data-section-name="Expert Solution" class="flex-initial text-20px font-semibold font-sans text-darkBlue-900 ml-8px md:text-24px">Expert Solution</div><img class="w-24px h-24px ml-16px" src="/static/compass_v2/shared-icons/check-mark.png" alt="" decoding="async" width="24" height="24"/></div><div id="Expert-Solution" class="paywall"></div><div id="solution-summary-v2-wrapper" class="hidden relative flexCol flex-initial border-[1px] mt-24px p-24px rounded-lg border-solid border-ghost bg-white"><div class="relative"><div style="height:350px" 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I need the solution to e and f after we find the value of Cn for that question based on your solution before. I hope this clears things up.\u003c/p\u003e\n\u003cp\u003eConsider the following heat equation on a rod (which includes heat loss through the lateral side and fixed heat flow on the boundary):\u003c/p\u003e\n\u003cp\u003e ∂u/∂t = ∂2u/∂x2 − 9u, 0 \u0026lt; x \u0026lt; 1, t \u0026gt; 0,\u003c/p\u003e\n\u003cp\u003esubject to the boundary conditions\u003c/p\u003e\n\u003cp\u003eux(0, t) = 3, ux(1, t) = 18, t \u0026gt; 0,\u003c/p\u003e\n\u003cp\u003eand the initial condition\u003c/p\u003e\n\u003cp\u003eu(x, 0) = 0, 0 \u0026lt; x \u0026lt; 1.\u003c/p\u003e\n\u003cp\u003e(a) Find the equilibrium solution uE(x) for this problem by solving a certain boundary value problem on (0, 1).\u003cbr /\u003e(b) Use integration by parts and the given boundary conditions that uE(x) satisfies to compute\u003c/p\u003e\n\u003cp\u003eA0 = 1∫0 u′′E (x) dx\u003c/p\u003e\n\u003cp\u003eEnter A0. (Do not use the explicit formula for uE(x) obtained in part (a).)\u003c/p\u003e\n\u003cp\u003e\u003cbr /\u003e(c) Use integration by parts and the given boundary conditions that uE(x) satisfies to show that\u003cbr /\u003e1∫0 u′′E (x) cos(nπx) dx = An + B*n^2 1∫0 uE(x) cos(nπx) dx, n ≥ 1, (1)\u003c/p\u003e\n\u003cp\u003efor some constants B and An. (Do not use the explicit formula for uE(x) obtained in part (a).) Enter the values of B and An (in that order) into the answer box below, separated with a comma.\u003c/p\u003e\n\u003cp\u003e\u003cbr /\u003e(d) Use the differential equation that uE(x) satisfies together with the results obtained in (b) and (c) to deduce the Fourier cosine series representation for uE(x) on (0, 1) which is of the form\u003c/p\u003e\n\u003cp\u003e a0/2 + ∞Σn =1 an cos(nπx).\u003c/p\u003e\n\u003cp\u003eEnter the values of a0 and an (in that order) into the answer box below, separated with a comma.\u003c/p\u003e\n\u003cp\u003e\u003cbr /\u003e(e) Show that v(x, t) = u(x, t) − uE(x, t) is solution of a homogeneous problem (with a different initial condition) and solve it using the method of separation of variables and the superposition principle. The solution has the form\u003c/p\u003e\n\u003cp\u003ev(x, t) = G0(t) + ∞Σn =1 Gn(t) cos(nπx)\u003c/p\u003e\n\u003cp\u003eEnter the functions G0(t) and Gn(t) (in that order) into the answer box below, separated with a comma.\u003c/p\u003e\n\u003cp\u003e\u003cbr /\u003e(f) The solution u(x, t) of the original problem, written as a cosine Fourier series with coefficients that are functions of t, has the form\u003c/p\u003e\n\u003cp\u003eu(x, t) = H0(t) + ∞Σn =1 Hn(t) cos(nπx)\u003c/p\u003e\n\u003cp\u003eEnter the functions H0(t) and Hn(t) (in that order) into the answer box below, separated with a comma. \u003c/p\u003e","status":"Answered","images":[{"id":"5234b4e0-97d9-4228-8eef-0b5fe20169cc","ocr":"(e) Show that v(x, t)\n=\nu(x, t) — uɛ(x, t) is solution of a homogeneous problem (with a different initial condition)\nand solve it using the method of separation of variables and the superposition principle. The solution has the\nform\nv(x,t) = Go(t) + Σ Gn(t) cos(nлx)\nn=1\nEnter the functions Go (t) and Gn(t) (in that order) into the answer box below, separated with a comma.\n(f) The solution u(x, t) of the original problem, written as a cosine Fourier series with coefficients that are\nfunctions of t, has the form\n8\nu(x,t) = H₁(t) + Σ H₂(t) cos(nлx)\nn=1\nEnter the functions Ho(t) and H₂(t) (in that order) into the answer box below, separated with a comma.","smallImageUrl":"https://content.bartleby.com/qna-images/question/9ae7b3bf-1b32-4ccc-a45c-3ac065d5afbc/0d7ed346-3e61-48a0-8236-b42a96af6267/l9qlog_thumbnail.png","imageUrl":"https://content.bartleby.com/qna-images/question/9ae7b3bf-1b32-4ccc-a45c-3ac065d5afbc/0d7ed346-3e61-48a0-8236-b42a96af6267/l9qlog_processed.png","width":1200,"height":351}],"subjects":[{"id":"d0016c54-4459-11e8-a2ac-0eefbb92016e","title":"Math","shortName":"math","smallImage":"https://isbn-assets.bnedcompass.com/subject_images/math/math.svg","subSubject":{"id":"d0240865-4459-11e8-a2ac-0eefbb92016e","title":"Calculus","shortName":"calculus","smallImage":"https://isbn-assets.bnedcompass.com/subject_images/math/calculus.svg"}},{"id":"d0240865-4459-11e8-a2ac-0eefbb92016e","title":"Calculus","shortName":"calculus","smallImage":"https://isbn-assets.bnedcompass.com/subject_images/math/calculus.svg"}],"sampleQuestion":false,"createdDate":"2024-11-16T06:28:59.000Z","questionSource":"User","topics":[],"selectedText":null,"topicTaxonomy":[],"answeredDate":"2024-11-16T07:20:35.000Z","hasMicroExplainers":false,"microExplainersData":[],"computed":{"subject":{"id":"d0240865-4459-11e8-a2ac-0eefbb92016e","title":"Calculus","shortName":"calculus","smallImage":"https://isbn-assets.bnedcompass.com/subject_images/math/calculus.svg"},"childSubjectTitle":"Calculus"}},"answer":{"id":"4a48edb2-b194-4294-b043-f0b19c6c6a8e","status":"Accepted","questionId":"0d7ed346-3e61-48a0-8236-b42a96af6267","createdDate":"2024-11-16T07:20:35.000Z","steps":[],"rejectionMessage":null,"imagesProcessed":1,"primaryRejectionReason":null,"secondaryRejectionReason":null,"numberOfAnswerSteps":0,"schemaAnswerSteps":"Answered: Image /qna-images/answer/0d7ed346-3e61-48a0-8236-b42a96af6267.jpg","previewAnswer":true,"hasMicroExplainers":false,"certified":false,"hasVideo":false},"isOwned":false,"isRestricted":false,"exactMatch":null,"parentQuestion":null,"isBlocked":false,"followUpQuestions":[],"defaultTopicAdded":false,"inReview":false,"isUnlocked":false,"practicePacks":[],"solutionSummaryDetails":{"imagesCount":8,"stepsCount":2,"hasVideo":false,"isPopular":false,"aiSummary":null},"isAiResponse":false,"isAiResponseAccepted":null,"answerSource":"COURSE_HERO","fullAnswerDisplayed":false,"isGoogleBot":false},"qnaStats":{"numberOfUpVotes":0,"numberOfDownVotes":0,"numberOfStars":null,"shouldShowRating":false,"pageViews":null},"followUpQuestions":[],"liveChatSupport":{"isLiveChatEnabled":true,"id":"d0240865-4459-11e8-a2ac-0eefbb92016e","title":"Calculus","shortName":"calculus","waitQueueTooLong":false},"shouldHideFollowUpForCurrentSubject":false,"questionHeaderText":"(e) Show that v(x, t) = u(x, t) — uɛ(x, t) is solution of a homogeneous problem (with a different initial condition) and solve it using the method of separation of variables and the superposition principle. The solution has the form v(x,t) = Go(t) + Σ Gn(t) cos(nлx) n=1 Enter the functions Go (t) and Gn(t) (in that order) into the answer box below, separated with a comma. (f) The solution u(x, t) of the original problem, written as a cosine Fourier series with coefficients that are functions of t, has the form 8 u(x,t) = H₁(t) + Σ H₂(t) cos(nлx) n=1 Enter the functions Ho(t) and H₂(t) (in that order) into the answer box below, separated with a comma.","acceptedAnswerText":"","isBookshelved":false,"bookmarks":[],"questionText":"(e) Show that v(x, t) = u(x, t) — uɛ(x, t) is solution of a homogeneous problem (with a different initial condition) and solve it using the method of separation of variables and the superposition principle. The solution has the form v(x,t) = Go(t) + Σ Gn(t) cos(nлx) n=1 Enter the functions Go (t) and Gn(t) (in that order) into the answer box below, separated with a comma. (f) The solution u(x, t) of the original problem, written as a cosine Fourier series with coefficients that are functions of t, has the form 8 u(x,t) = H₁(t) + Σ H₂(t) cos(nлx) n=1 Enter the functions Ho(t) and H₂(t) (in that order) into the answer box below, separated with a comma.","qnaQuestionXmlSchemaData":{"@context":"https://schema.org","@type":["QAPage","WebPage"],"mainEntityOfPage":{"@type":"WebPage","@id":"https://www.bartleby.com/questions-and-answers/e-show-that-vx-t-ux-t-ux-t-is-solution-of-a-homogeneous-problem-with-a-different-initial-condition-a/0d7ed346-3e61-48a0-8236-b42a96af6267"},"name":"I wrote out the question as requested and tried to re-upload the 2 questions I'm interested in. I need the solution to e and f after we find the value of Cn for that question based on your solution before. I hope this clears things up.Consider the following heat equation on a rod (which includes heat loss through the lateral side and fixed heat flow on the boundary): ∂u/∂t = ∂2u/∂x2 − 9u, 0 \u0026lt; x \u0026lt; 1, t \u0026gt; 0,subject to the boundary conditionsux(0, t) = 3, ux(1, t) = 18, t \u0026gt; 0,and the initial conditionu(x, 0) = 0, 0 \u0026lt; x \u0026lt; 1.(a) Find the equilibrium solution uE(x) for this problem by solving a certain boundary value problem on (0, 1).(b) Use integration by parts and the given boundary conditions that uE(x) satisfies to computeA0 = 1∫0 u′′E (x) dxEnter A0. (Do not use the explicit formula for uE(x) obtained in part (a).)(c) Use integration by parts and the given boundary conditions that uE(x) satisfies to show that1∫0 u′′E (x) cos(nπx) dx = An + B*n^2 1∫0 uE(x) cos(nπx) dx, n ≥ 1, (1)for some constants B and An. (Do not use the explicit formula for uE(x) obtained in part (a).) Enter the values of B and An (in that order) into the answer box below, separated with a comma.(d) Use the differential equation that uE(x) satisfies together with the results obtained in (b) and (c) to deduce the Fourier cosine series representation for uE(x) on (0, 1) which is of the form a0/2 + ∞Σn =1 an cos(nπx).Enter the values of a0 and an (in that order) into the answer box below, separated with a comma.(e) Show that v(x, t) = u(x, t) − uE(x, t) is solution of a homogeneous problem (with a different initial condition) and solve it using the method of separation of variables and the superposition principle. The solution has the formv(x, t) = G0(t) + ∞Σn =1 Gn(t) cos(nπx)Enter the functions G0(t) and Gn(t) (in that order) into the answer box below, separated with a comma.(f) The solution u(x, t) of the original problem, written as a cosine Fourier series with coefficients that are functions of t, has the formu(x, t) = H0(t) + ∞Σn =1 Hn(t) cos(nπx)Enter the functions H0(t) and Hn(t) (in that order) into the answer box below, separated with a comma. (e) Show that v(x, t)=u(x, t) — uɛ(x, t) is solution of a homogeneous problem (with a different initial condition)and solve it using the method of separation of variables and the superposition principle. The solution has theformv(x,t) = Go(t) + Σ Gn(t) cos(nлx)n=1Enter the functions Go (t) and Gn(t) (in that order) into the answer box below, separated with a comma.(f) The solution u(x, t) of the original problem, written as a cosine Fourier series with coefficients that arefunctions of t, has the form8u(x,t) = H₁(t) + Σ H₂(t) cos(nлx)n=1Enter the functions Ho(t) and H₂(t) (in that order) into the answer box below, separated with a comma.","description":"I wrote out the question as requested and tried to re-upload the 2 questions I'm interested in. I need the solution to e and f after we find the value of Cn for that question based on your solution before. I hope this clears things up.Consider the following heat equation on a rod (which includes heat loss through the lateral side and fixed heat flow on the boundary): ∂u/∂t = ∂2u/∂x2 − 9u, 0 \u0026lt; x \u0026lt; 1, t \u0026gt; 0,subject to the boundary conditionsux(0, t) = 3, ux(1, t) = 18, t \u0026gt; 0,and the initial conditionu(x, 0) = 0, 0 \u0026lt; x \u0026lt; 1.(a) Find the equilibrium solution uE(x) for this problem by solving a certain boundary value problem on (0, 1).(b) Use integration by parts and the given boundary conditions that uE(x) satisfies to computeA0 = 1∫0 u′′E (x) dxEnter A0. (Do not use the explicit formula for uE(x) obtained in part (a).)(c) Use integration by parts and the given boundary conditions that uE(x) satisfies to show that1∫0 u′′E (x) cos(nπx) dx = An + B*n^2 1∫0 uE(x) cos(nπx) dx, n ≥ 1, (1)for some constants B and An. (Do not use the explicit formula for uE(x) obtained in part (a).) Enter the values of B and An (in that order) into the answer box below, separated with a comma.(d) Use the differential equation that uE(x) satisfies together with the results obtained in (b) and (c) to deduce the Fourier cosine series representation for uE(x) on (0, 1) which is of the form a0/2 + ∞Σn =1 an cos(nπx).Enter the values of a0 and an (in that order) into the answer box below, separated with a comma.(e) Show that v(x, t) = u(x, t) − uE(x, t) is solution of a homogeneous problem (with a different initial condition) and solve it using the method of separation of variables and the superposition principle. The solution has the formv(x, t) = G0(t) + ∞Σn =1 Gn(t) cos(nπx)Enter the functions G0(t) and Gn(t) (in that order) into the answer box below, separated with a comma.(f) The solution u(x, t) of the original problem, written as a cosine Fourier series with coefficients that are functions of t, has the formu(x, t) = H0(t) + ∞Σn =1 Hn(t) cos(nπx)Enter the functions H0(t) and Hn(t) (in that order) into the answer box below, separated with a comma. (e) Show that v(x, t)=u(x, t) — uɛ(x, t) is solution of a homogeneous problem (with a different initial condition)and solve it using the method of separation of variables and the superposition principle. The solution has theformv(x,t) = Go(t) + Σ Gn(t) cos(nлx)n=1Enter the functions Go (t) and Gn(t) (in that order) into the answer box below, separated with a comma.(f) The solution u(x, t) of the original problem, written as a cosine Fourier series with coefficients that arefunctions of t, has the form8u(x,t) = H₁(t) + Σ H₂(t) cos(nлx)n=1Enter the functions Ho(t) and H₂(t) (in that order) into the answer box below, separated with a comma.","inLanguage":"en","headline":"I wrote out the question as requested and tried to re-upload the 2 questions I'm interested in. I need the solution to e and f after we find the value of Cn for that question based on your solution before. I hope this clears things up.Consider the following heat equation on a rod (which includes heat loss through the lateral side and fixed heat flow on the boundary): ∂u/∂t = ∂2u/∂x2 − 9u, 0 \u0026lt; x \u0026lt; 1, t \u0026gt; 0,subject to the boundary conditionsux(0, t) = 3, ux(1, t) = 18, t \u0026gt; 0,and the initial conditionu(x, 0) = 0, 0 \u0026lt; x \u0026lt; 1.(a) Find the equilibrium solution uE(x) for this problem by solving a certain boundary value problem on (0, 1).(b) Use integration by parts and the given boundary conditions that uE(x) satisfies to computeA0 = 1∫0 u′′E (x) dxEnter A0. (Do not use the explicit formula for uE(x) obtained in part (a).)(c) Use integration by parts and the given boundary conditions that uE(x) satisfies to show that1∫0 u′′E (x) cos(nπx) dx = An + B*n^2 1∫0 uE(x) cos(nπx) dx, n ≥ 1, (1)for some constants B and An. (Do not use the explicit formula for uE(x) obtained in part (a).) Enter the values of B and An (in that order) into the answer box below, separated with a comma.(d) Use the differential equation that uE(x) satisfies together with the results obtained in (b) and (c) to deduce the Fourier cosine series representation for uE(x) on (0, 1) which is of the form a0/2 + ∞Σn =1 an cos(nπx).Enter the values of a0 and an (in that order) into the answer box below, separated with a comma.(e) Show that v(x, t) = u(x, t) − uE(x, t) is solution of a homogeneous problem (with a different initial condition) and solve it using the method of separation of variables and the superposition principle. The solution has the formv(x, t) = G0(t) + ∞Σn =1 Gn(t) cos(nπx)Enter the functions G0(t) and Gn(t) (in that order) into the answer box below, separated with a comma.(f) The solution u(x, t) of the original problem, written as a cosine Fourier series with coefficients that are functions of t, has the formu(x, t) = H0(t) + ∞Σn =1 Hn(t) cos(nπx)Enter the functions H0(t) and Hn(t) (in that order) into the answer box below, separated with a comma. (e) Show that v(x, t)=u(x, t) — uɛ(x, t) is solution of a homogeneous problem (with a different initial condition)and solve it using the method of separation of variables and the superposition principle. The solution has theformv(x,t) = Go(t) + Σ Gn(t) cos(nлx)n=1Enter the functions Go (t) and Gn(t) (in that order) into the answer box below, separated with a comma.(f) The solution u(x, t) of the original problem, written as a cosine Fourier series with coefficients that arefunctions of t, has the form8u(x,t) = H₁(t) + Σ H₂(t) cos(nлx)n=1Enter the functions Ho(t) and H₂(t) (in that order) into the answer box below, separated with a comma.","datePublished":"2024-11-16","dateModified":"2024-11-16","isAccessibleForFree":"False","hasPart":{"@type":"WebPageElement","isAccessibleForFree":"False","cssSelector":".paywall"},"mainEntity":{"@type":"Question","name":"I wrote out the question as requested and tried to re-upload the 2 questions I'm interested in. I need the solution to e and f after we find the value of Cn for that question based on your solution before. I hope this clears things up.Consider the following heat equation on a rod (which includes heat loss through the lateral side and fixed heat flow on the boundary): ∂u/∂t = ∂2u/∂x2 − 9u, 0 \u0026lt; x \u0026lt; 1, t \u0026gt; 0,subject to the boundary conditionsux(0, t) = 3, ux(1, t) = 18, t \u0026gt; 0,and the initial conditionu(x, 0) = 0, 0 \u0026lt; x \u0026lt; 1.(a) Find the equilibrium solution uE(x) for this problem by solving a certain boundary value problem on (0, 1).(b) Use integration by parts and the given boundary conditions that uE(x) satisfies to computeA0 = 1∫0 u′′E (x) dxEnter A0. (Do not use the explicit formula for uE(x) obtained in part (a).)(c) Use integration by parts and the given boundary conditions that uE(x) satisfies to show that1∫0 u′′E (x) cos(nπx) dx = An + B*n^2 1∫0 uE(x) cos(nπx) dx, n ≥ 1, (1)for some constants B and An. (Do not use the explicit formula for uE(x) obtained in part (a).) Enter the values of B and An (in that order) into the answer box below, separated with a comma.(d) Use the differential equation that uE(x) satisfies together with the results obtained in (b) and (c) to deduce the Fourier cosine series representation for uE(x) on (0, 1) which is of the form a0/2 + ∞Σn =1 an cos(nπx).Enter the values of a0 and an (in that order) into the answer box below, separated with a comma.(e) Show that v(x, t) = u(x, t) − uE(x, t) is solution of a homogeneous problem (with a different initial condition) and solve it using the method of separation of variables and the superposition principle. The solution has the formv(x, t) = G0(t) + ∞Σn =1 Gn(t) cos(nπx)Enter the functions G0(t) and Gn(t) (in that order) into the answer box below, separated with a comma.(f) The solution u(x, t) of the original problem, written as a cosine Fourier series with coefficients that are functions of t, has the formu(x, t) = H0(t) + ∞Σn =1 Hn(t) cos(nπx)Enter the functions H0(t) and Hn(t) (in that order) into the answer box below, separated with a comma. (e) Show that v(x, t)=u(x, t) — uɛ(x, t) is solution of a homogeneous problem (with a different initial condition)and solve it using the method of separation of variables and the superposition principle. The solution has theformv(x,t) = Go(t) + Σ Gn(t) cos(nлx)n=1Enter the functions Go (t) and Gn(t) (in that order) into the answer box below, separated with a comma.(f) The solution u(x, t) of the original problem, written as a cosine Fourier series with coefficients that arefunctions of t, has the form8u(x,t) = H₁(t) + Σ H₂(t) cos(nлx)n=1Enter the functions Ho(t) and H₂(t) (in that order) into the answer box below, separated with a comma.","text":"I wrote out the question as requested and tried to re-upload the 2 questions I'm interested in. I need the solution to e and f after we find the value of Cn for that question based on your solution before. I hope this clears things up.Consider the following heat equation on a rod (which includes heat loss through the lateral side and fixed heat flow on the boundary): ∂u/∂t = ∂2u/∂x2 − 9u, 0 \u0026lt; x \u0026lt; 1, t \u0026gt; 0,subject to the boundary conditionsux(0, t) = 3, ux(1, t) = 18, t \u0026gt; 0,and the initial conditionu(x, 0) = 0, 0 \u0026lt; x \u0026lt; 1.(a) Find the equilibrium solution uE(x) for this problem by solving a certain boundary value problem on (0, 1).(b) Use integration by parts and the given boundary conditions that uE(x) satisfies to computeA0 = 1∫0 u′′E (x) dxEnter A0. (Do not use the explicit formula for uE(x) obtained in part (a).)(c) Use integration by parts and the given boundary conditions that uE(x) satisfies to show that1∫0 u′′E (x) cos(nπx) dx = An + B*n^2 1∫0 uE(x) cos(nπx) dx, n ≥ 1, (1)for some constants B and An. (Do not use the explicit formula for uE(x) obtained in part (a).) Enter the values of B and An (in that order) into the answer box below, separated with a comma.(d) Use the differential equation that uE(x) satisfies together with the results obtained in (b) and (c) to deduce the Fourier cosine series representation for uE(x) on (0, 1) which is of the form a0/2 + ∞Σn =1 an cos(nπx).Enter the values of a0 and an (in that order) into the answer box below, separated with a comma.(e) Show that v(x, t) = u(x, t) − uE(x, t) is solution of a homogeneous problem (with a different initial condition) and solve it using the method of separation of variables and the superposition principle. The solution has the formv(x, t) = G0(t) + ∞Σn =1 Gn(t) cos(nπx)Enter the functions G0(t) and Gn(t) (in that order) into the answer box below, separated with a comma.(f) The solution u(x, t) of the original problem, written as a cosine Fourier series with coefficients that are functions of t, has the formu(x, t) = H0(t) + ∞Σn =1 Hn(t) cos(nπx)Enter the functions H0(t) and Hn(t) (in that order) into the answer box below, separated with a comma. (e) Show that v(x, t)=u(x, t) — uɛ(x, t) is solution of a homogeneous problem (with a different initial condition)and solve it using the method of separation of variables and the superposition principle. The solution has theformv(x,t) = Go(t) + Σ Gn(t) cos(nлx)n=1Enter the functions Go (t) and Gn(t) (in that order) into the answer box below, separated with a comma.(f) The solution u(x, t) of the original problem, written as a cosine Fourier series with coefficients that arefunctions of t, has the form8u(x,t) = H₁(t) + Σ H₂(t) cos(nлx)n=1Enter the functions Ho(t) and H₂(t) (in that order) into the answer box below, separated with a comma.","answerCount":1,"dateCreated":"2024-11-16","acceptedAnswer":{"@type":"Answer","text":"Answered: Image /qna-images/answer/0d7ed346-3e61-48a0-8236-b42a96af6267.jpg"},"url":"https://www.bartleby.com/questions-and-answers/e-show-that-vx-t-ux-t-ux-t-is-solution-of-a-homogeneous-problem-with-a-different-initial-condition-a/0d7ed346-3e61-48a0-8236-b42a96af6267"}},"breadcrumbXmlSchemaData":{"@context":"http://schema.org","@type":"BreadcrumbList","itemListElement":[{"@type":"ListItem","position":1,"item":{"@id":"https://www.bartleby.com/","name":"Bartleby Textbook Solutions"}},{"@type":"ListItem","position":2,"item":{"@id":"https://www.bartleby.com/subject/math","name":"Math Q\u0026A and Textbook Solutions"}},{"@type":"ListItem","position":3,"item":{"@id":"https://www.bartleby.com/subject/math/calculus","name":"Calculus Q\u0026A, Textbooks, and Solutions"}},{"@type":"ListItem","position":4,"item":{"@id":"https://www.bartleby.com/subject/math/calculus/questions-and-answers","name":"Calculus Q\u0026A Library"}},{"@type":"ListItem","position":5,"item":{"@id":"https://www.bartleby.com/questions-and-answers/e-show-that-vx-t-ux-t-ux-t-is-solution-of-a-homogeneous-problem-with-a-different-initial-condition-a/0d7ed346-3e61-48a0-8236-b42a96af6267","name":"(e) Show that v(x, t) = u(x, t) — uɛ(x, t) is solution of a homogeneous problem (with a different initial condition) and solve it using the method of separation of variables and the superposition principle. The solution has the form v(x,t) = Go(t) + Σ Gn(t) cos(nлx) n=1 Enter the functions Go (t) and Gn(t) (in that order) into the answer box below, separated with a comma. (f) The solution u(x, t) of the original problem, written as a cosine Fourier series with coefficients that are functions of t, has the form 8 u(x,t) = H₁(t) + Σ H₂(t) cos(nлx) n=1 Enter the functions Ho(t) and H₂(t) (in that order) into the answer box below, separated with a comma."}}]},"solutionVideoXmlSchemaData":null,"topicVideoXmlSchemaData":null,"qnaBreadcrumbProps":{"breadcrumbWithH1Props":{"h1Text":"(e) Show that v(x, t) = u(x, t) — uɛ(x, t) is solution of a homogeneous problem (with a different initial condition) and solve it using the method of separation of variables and the superposition principle. The solution has the form v(x,t) = Go(t) + Σ Gn(t) cos(nлx) n=1 Enter the functions Go (t) and Gn(t) (in that order) into the answer box below, separated with a comma. (f) The solution u(x, t) of the original problem, written as a cosine Fourier series with coefficients that are functions of t, has the form 8 u(x,t) = H₁(t) + Σ H₂(t) cos(nлx) n=1 Enter the functions Ho(t) and H₂(t) (in that order) into the answer box below, separated with a comma.","breadcrumbProps":{"parts":[{"name":"Math","linkProps":{"href":"/subject/math","isExternal":true},"shouldShrinkSlowly":true,"onClickGtmEvent":{"event":"Clicked on Q\u0026A Solution Breadcrumb","location":{"name":"Q\u0026A Solution Page"}}},{"name":"Calculus","linkProps":{"href":"/subject/math/calculus","isExternal":true},"shouldShrinkSlowly":true,"onClickGtmEvent":{"event":"Clicked on Q\u0026A Solution Breadcrumb","location":{"name":"Q\u0026A Solution Page"}}},{"name":"(e) Show that v(x, t) = u(x, t) — uɛ(x, t) is solution of a homogeneous problem (with a different initial condition) and solve it using the method of separation of variables and the superposition principle. The solution has the form v(x,t) = Go(t) + Σ Gn(t) cos(nлx) n=1 Enter the functions Go (t) and Gn(t) (in that order) into the answer box below, separated with a comma. (f) The solution u(x, t) of the original problem, written as a cosine Fourier series with coefficients that are functions of t, has the form 8 u(x,t) = H₁(t) + Σ H₂(t) cos(nлx) n=1 Enter the functions Ho(t) and H₂(t) (in that order) into the answer box below, separated with a comma.","shouldShrinkSlowly":false}]}}},"qnaSample":{"id":"0001183d-8c9b-44b2-a8b7-072b245cc489","url":"/questions-and-answers/1-determine-the-area-of-the-region-bounded-by-the-graph-of-the-function-and-the-tangent-line-to-the-/0001183d-8c9b-44b2-a8b7-072b245cc489","slug":"1-determine-the-area-of-the-region-bounded-by-the-graph-of-the-function-and-the-tangent-line-to-the-"},"sampleQnaIHrefAndAs":"/questions-and-answers/1-determine-the-area-of-the-region-bounded-by-the-graph-of-the-function-and-the-tangent-line-to-the-/0001183d-8c9b-44b2-a8b7-072b245cc489#undefined","knowledgeBoosterProps":{"knowledgeBoosterIntroData":{"iconSrc":"/static/compass_v2/subjects/math/calculus.svg","subjectCopy":"calculus"},"ceLinks":[],"recommendedTextbooksData":{"popularTextBooks":[{"subject":"Algebra","isbn13":"9781285463247","author":"David Poole","publisher":"Cengage Learning","bookTitle":"Linear Algebra: A Modern Introduction","smallImage":"https://www.bartleby.com/isbn_cover_images/9781285463247/9781285463247_smallCoverImage.gif","textbookLinkProps":{"href":"/textbooks/linear-algebra-a-modern-introduction-4th-edition/9781285463247/solutions"}}],"seeMoreTextBooksHref":"/search?scope=Textbooks\u0026q=Calculus\u0026subject=Calculus\u0026page=1"},"hasSimilarQuestions":true,"hasConceptExplainers":false,"hasPopularTextbooks":true,"dcsRecommendations":[{"questionUrl":{"href":"/solution-answer/chapter-46-problem-69eq-linear-algebra-a-modern-introduction-4th-edition/9781285463247/let-xxt-be-a-twice-differentiable-function-and-consider-the-second-order-differential-equation/bea81a49-561f-4f50-a38c-2e5d5215c5db"},"questioText":"Let x=x(t) be a twice-differentiable function and consider the second order differential equation x+ax+bx=0(11) Show that the change of variables y = x' and z = x allows Equation (11) to be written as a system of two linear differential equations in y and z. 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(f) The solution u(x, t) of the original problem, written as a cosine Fourier series with coefficients that are functions of t, has the form 8 u(x,t) = H₁(t) + Σ H₂(t) cos(nлx) n=1 Enter the functions Ho(t) and H₂(t) (in that order) into the answer box below, separated with a comma."},"followUpQuestionProps":[],"qnaVideoProps":{"video":null,"topicVideo":null,"questionId":"0d7ed346-3e61-48a0-8236-b42a96af6267","qnaHref":{"href":"/account/registration"}},"textbookModuleProps":{"bookInfoProps":{"shouldShowAbbreviatedView":true,"isbn13":"9781285463247","title":"Linear Algebra: A Modern Introduction","authors":"David Poole","publisher":"David Poole","edition":"4th 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83EQ","href":"/solution-answer/chapter-46-problem-83eq-linear-algebra-a-modern-introduction-4th-edition/9781285463247/ebb6d29e-e0b0-43fd-8225-38ff9988886b","value":"82","children":[]},{"text":"","textPrefix":" 84EQ","href":"/solution-answer/chapter-46-problem-84eq-linear-algebra-a-modern-introduction-4th-edition/9781285463247/9d061543-8fcf-47af-bc05-24a6f80b0559","value":"83","children":[]},{"text":"","textPrefix":" 85EQ","href":"/solution-answer/chapter-46-problem-85eq-linear-algebra-a-modern-introduction-4th-edition/9781285463247/ce6051b5-ae17-4939-9ac9-cd8a23648fd7","value":"84","children":[]},{"text":"","textPrefix":" 86EQ","href":"/solution-answer/chapter-46-problem-86eq-linear-algebra-a-modern-introduction-4th-edition/9781285463247/760309b4-7629-400b-b9c3-e1d961f2f7f8","value":"85","children":[]},{"text":"","textPrefix":" 87EQ","href":"/solution-answer/chapter-46-problem-87eq-linear-algebra-a-modern-introduction-4th-edition/9781285463247/1366c3d0-bdb8-40aa-9d39-bf8b81c030d9","value":"86","children":[]},{"text":"","textPrefix":" 88EQ","href":"/solution-answer/chapter-46-problem-88eq-linear-algebra-a-modern-introduction-4th-edition/9781285463247/7e7077cc-5e88-4cd6-adb0-3fe10f1e4f35","value":"87","children":[]},{"text":"","textPrefix":" 89EQ","href":"/solution-answer/chapter-46-problem-89eq-linear-algebra-a-modern-introduction-4th-edition/9781285463247/b232728b-4643-42fb-bba9-fec521d4102b","value":"88","children":[]},{"text":"","textPrefix":" 90EQ","href":"/solution-answer/chapter-46-problem-90eq-linear-algebra-a-modern-introduction-4th-edition/9781285463247/c24299a7-9270-4bdf-8f57-ae4db66ae598","value":"89","children":[]},{"text":"","textPrefix":" 91EQ","href":"/solution-answer/chapter-46-problem-91eq-linear-algebra-a-modern-introduction-4th-edition/9781285463247/f91df7be-29cb-4c58-af02-cecd6485f996","value":"90","children":[]},{"text":"","textPrefix":" 92EQ","href":"/solution-answer/chapter-46-problem-92eq-linear-algebra-a-modern-introduction-4th-edition/9781285463247/c4434e22-e923-4c91-974c-ab07c580bb15","value":"91","children":[]}],"defaultChildValue":"0"}},"similarTextnooksHref":"/subject/math/algebra/textbook-answers","qnaZippiesProps":{"headerProps":{"title":"Related questions","iconUrl":"/static/compass_v2/leftrail/relatedQuestions.svg","iconWidth":"12px","iconHeight":"14px","iconAlt":"","iconBackgroundColor":"#D8199E","buttonAriaProps":{"aria-label":"open related questions","aria-controls":"related-question-panel","id":"related-question-left-rail"}},"zippies":[{"question":"For each surface below, give a parameterization r(u, v); be sure to use rectangular bounds (u, v) ∈…","answer":"1. Upside-Down ConeFor the cone with height 3, tip at the origin, and circular base of radius…","href":"/questions-and-answers/for-each-surface-below-give-a-parameterization-ru-v-be-sure-to-use-rectangular-bounds-u-v-euro-a-b-x/006d8bc0-4c32-4524-8342-d66ab1ecce20"},{"question":"SITUATION NO. 02 P14-P1S\nGiven the following field notes for a differential leveling\nAll units are…","answer":"","href":"/questions-and-answers/situation-no.-02-p14-p1s-given-the-following-field-notes-for-a-differential-leveling-all-units-are-i/8f1b5988-8093-44c2-867d-41e7ece794b4"},{"question":"solve it","answer":"1. For which values of x is f(x) continuous? f(x) is continuous for x in the interval (-1, ∞) 2.…","href":"/questions-and-answers/in-this-question-well-gather-information-for-sketching-the-function-1.-for-which-values-of-a-is-fx-c/482e679a-44b9-4595-b81e-54f3275a456d"},{"question":"2. Consider the function f : R2 R defined by\nf(x) = ||x||³,\nwhere ||x|| = √√x² + x².\n(i) Compute the…","answer":"","href":"/questions-and-answers/2.-consider-the-function-f-r2-r-defined-by-fx-ororxoror-where-ororxoror-x-x.-i-compute-the-gradient-/b6b6b732-a600-48e2-a284-b2e1074af05d"},{"question":"please help thank you a lot. also please don't use chat gpt because that answer is wrong","answer":"Step 1:Method 1 Step 2:Method 2 Step 3: Step 4:","href":"/questions-and-answers/consider-the-circle-c-of-unit-radius.-as-an-equation-c-is-given-by-x-y-1.-find-all-tangent-lines-to-/ef40dfb8-d484-4398-858c-d74e1799346c"},{"question":"Explain step by step of how they got to the answer for both problems","answer":"","href":"/questions-and-answers/pt-1-1-152-pt-t-.-t-12-.-2t-2tt-152-.-5t-1-12-211-152-tt-12-51-21-1-11-1-71-2-y-6e2x-dy-dx-62e2x-12e/98e17122-dd9d-48d5-8eb6-0a6d9b0ffaa1"},{"question":"मा\nWith explanation\nQ / Prove that L{ {\"} = \"!\n5n+1\nand steps of solution?","answer":"","href":"/questions-and-answers/with-explanation-q-prove-that-l-5n1-and-steps-of-solution/760f3d21-3443-4ba0-8b54-98a13b5453dd"},{"question":"Q1 (9 points)\nLet z(x, y) and w(x, y) be smooth functions that satisfy the equations\nw+w³ + x²yz + 4…","answer":"Step 1: Set up The question:Analyze the question and observe what is given to you and what you need…","href":"/questions-and-answers/q1-9-points-let-zx-y-and-wx-y-be-smooth-functions-that-satisfy-the-equations-ww-xyz-4-0-zwxyw10-and-/98117767-6e6c-4fbe-a9dc-b2ddc0dbf0c4"},{"question":"Pls help ASAP. Pls show all work and steps. Pls circle the final answer.","answer":"Here is the step-by-step explanation:The equation of the plane is given…","href":"/questions-and-answers/18.-find-the-intercepts-of-the-plane-x-y-z-5-4-3-s-1-0-1-t-1-4-2./f26995ff-bd62-4447-b22d-1af81ce50d25"},{"question":"GRADED EXERCISE 5:\n1\n3. A 6-ft man walks away from a 9-ft lamppost at a rate of\nft/sec. If the light…","answer":"Problem 3: Related Rates ProblemWe are given:A 6 ft tall man walks away from a 9 ft tall lamppost at…","href":"/questions-and-answers/graded-exercise-5-1-3.-a-6-ft-man-walks-away-from-a-9-ft-lamppost-at-a-rate-of-ftsec.-if-the-light-a/eb5f6d51-f758-4236-80e3-a57906e04775"},{"question":"Pls help ASAP. Pls show all work and steps. Pls circle the final answer.","answer":"Steps and explanations are as follows:In case of any doubt, please let me know. Thank you.","href":"/questions-and-answers/17.-the-line-42-2-s-5-3-1-se-r-crosses-the-xz-plane-and-the-yz-plane-at-points-a-as-b-respectively.-/b12fe077-2a06-4ede-a8d7-2aface8021c2"},{"question":"1. A GRAPHING CALCULATOR IS REQUIRED FOR THIS QUESTION.\nYou are permitted to use your calculator to…","answer":"Here is the calculation for the answer in Part (d) using Desmos graphing calculator. To find x,…","href":"/questions-and-answers/1.-a-graphing-calculator-is-required-for-this-question.-you-are-permitted-to-use-your-calculator-to-/45c63827-ba91-4c25-9eaf-d171442444e0"},{"question":"Pls help ASAP. Pls show all work and steps. Pls circle the final answer.","answer":"1. Assuming they are asking for the value of m for which both planes will be perpendicular:To make…","href":"/questions-and-answers/7.-determine-the-value-of-m-will-make-the-planes-new-shequel-2x-my-3z-1-0-and-p2-2mx-3y-2z-4-0-6-a.-/a6d0780e-9876-44a1-bae9-fe8845836b12"},{"question":"Help solve step by step","answer":"Step 1: Identify the derivative rules that applyConstant Rule: (where c = constant, ex: 10)d/dx (c)…","href":"/questions-and-answers/5t-7t-rt-31-1-rt-31-1-10t-7-5t-7t33t-13-31-132-31-1-101-7-95t-7t3t-1-31-16-31-110t-7-95t-71-31-14-30/f40d27b8-1680-4449-ad72-f2d189a7fa73"},{"question":"Consider the following heat equation on a rod (which includes heat loss through the lateral side and…","answer":"If doubt then aks. Please like.","href":"/questions-and-answers/consider-the-following-heat-equation-on-a-rod-which-includes-heat-loss-through-the-lateral-side-and-/457d5f8b-f55e-4c47-839b-420898ae2a2f"},{"question":"Look at the figure:The radius r measures 10cm and the radius R measures 20cm. The height h1 measures…","answer":"(c) If the height of the cylinder were to change from 25cm to 25.2cm and all other measurements…","href":"/questions-and-answers/24-1.3.-241/a03313e0-7b8a-491d-a04c-172aa15b86be"},{"question":"Please help on all asked questions, Pls show all work and steps, and circle the final answer.","answer":"Step 1:13. a) The provided function is:f(x)=x2−3x+6 ..........(1)It is needed to obtain the…","href":"/questions-and-answers/13.-find-the-equation-of-the-tangent-to-the-following-functions-at-the-indicated-point.-a-fx-x-3x6-a/a9d6b522-ef33-4ef0-af1e-dd115908c7a9"},{"question":"Classify each of the following first order differential equations\n(x + 1) y' + (x + y)² = x²\nУ\nxy…","answer":"Explanation:","href":"/questions-and-answers/classify-each-of-the-following-first-order-differential-equations-x-1-y-x-y-x-u-xy-32-14-dz-2y-dy-0-/367b7e47-1875-4039-ac10-736269e4bc0d"},{"question":"solve part e","answer":"Step 1:","href":"/questions-and-answers/in-this-question-we-will-consider-the-function-a-use-asymptotics-as-in-the-first-week-of-class-to-ma/7620e6bf-bc29-4e06-85a0-6d0755c7ca1b"},{"question":"In Exercises 33-38, find the value of (fog)' at the given value of x.\n√√√x, x = 1\nu³ + 1, u = g(x) =…","answer":"We are given two functions, f(u) and g(x), and we are asked to find the derivative of the composite…","href":"/questions-and-answers/in-exercises-33-38-find-the-value-of-fog-at-the-given-value-of-x.-x-x-1-u-1-u-gx-x-33.-fu-u-1-3-34.-/84831e5e-41d3-4150-9c6c-303936265658"},{"question":"4. Find, if any, the horizontal asymptotes of the following functions and use that information\nto…","answer":"(a)f(x)=x4+3x2+7x+10(x+1)4 Degree of the numerator: 4 (after expansion)Degree of the denominator:…","href":"/questions-and-answers/4.-find-if-any-the-horizontal-asymptotes-of-the-following-functions-and-use-that-information-to-matc/abbb095b-fdb3-4664-99fb-b534d12eead9"},{"question":"Could section E and F be solved explicitly please?","answer":"","href":"/questions-and-answers/consider-the-following-heat-equation-on-a-rod-which-includes-heat-loss-through-the-lateral-side-and-/00faa39d-77d1-4183-84c5-f0f27d083011"},{"question":"question says to rank in order the following options","answer":"The effective annual rate (EAR) represents how much interest you earn in a year after compounding.…","href":"/questions-and-answers/a-12percent-interest-compounded-annually-b-11percent-interest-compounded-monthly-c-10percent-interes/0acd2c38-bb43-40f2-aed9-261804e22bc0"},{"question":"Find the general and particular solution.\ny\"+6y' + 10y=22+20x, y(0) = 2, y'(0) = -2","answer":"Approach to solving the question: Solution for Differential EquationConsider the differential…","href":"/questions-and-answers/find-the-general-and-particular-solution.-y6y-10y2220x-y0-2-y0-2/0183b442-b78f-40a3-983a-b28fde102362"},{"question":"Let C be the curve consisting of the three line segments from (0, 0) to (1, 1), from (1, 1) to (1,…","answer":"Step 1:","href":"/questions-and-answers/let-c-be-the-curve-consisting-of-the-three-line-segments-from-00-to-1-1-from-1-1-to-1-1-and-from-1-1/6200e566-8cac-4a4c-a501-344166e0625a"},{"question":"The solution of the initial value problem.\n=\nS t y + 4 y\n√ty 4y = 4\nโy(1) = 4\nt4\nis\nS\nУ\nt4 +7\n2t4…","answer":"Step 1: Step 2:Step 3: Step 4:","href":"/questions-and-answers/the-solution-of-the-initial-value-problem.-s-t-y-4-y-ty-4y-4-y1-4-t4-is-s-u-t4-7-2t4-5t4-1-y-t8-1-ln/a901f485-c2ec-438e-a239-a8ade9fd4597"},{"question":"Please help on all asked questions, Pls show all work and steps, and circle the final answer.","answer":"Step 1: Step 2: Step 3: Step 4:","href":"/questions-and-answers/1-1-0-19-13-c-lim-x-3-x-3-x-3-a-113-b-1-d-lim-2h-1-h-1-h-1-a-009-b-infinity-c-1-19-d-113-d-0/f2672bb3-d5a6-4249-b33d-35c48e24460b"},{"question":"Use RREF method to solve the linear system\nx1\n+ 3x2\n=\n9,\n2x1 + x2\n8.\nWe must show the elementary row…","answer":"","href":"/questions-and-answers/use-rref-method-to-solve-the-linear-system-x1-3x2-9-2x1-x2-8.-we-must-show-the-elementary-row-operat/bb19fb93-0de3-49c0-afe2-2e8fcf3a4b51"},{"question":"find x for\n√x+2=-2","answer":"There is no solution to the equation x+2=−2,because the square root of a number is always…","href":"/questions-and-answers/find-x-for-x2-2/c8e43830-d8ae-4c56-afbf-ddb3fb02a7ad"},{"question":"Differentiate the function.\nv = (√x+·\nv' =\nEnhanced Feedback\n1\n2\n3","answer":"Step 1: Given function v=(x+3x1)2. We have to find v'. (differentiation of the function v) Step…","href":"/questions-and-answers/differentiate-the-function.-v-x-v-enhanced-feedback-1-2-3/d2d77d63-51bf-4399-862f-c931cb670145"},{"question":"Find the limit. Hint use Polar Coordinates.\nx2y2\nlim\n(x,y)+(0,0) x²+y2","answer":"First, we need to find the first order partial derivatives of the function f(x,y) = x*y^(-2) +…","href":"/questions-and-answers/find-the-limit.-hint-use-polar-coordinates.-x2y2-lim-xy00-xy2-find-all-first-and-second-order-partia/3fdf73f5-70c3-488d-98ae-966cd890bce4"},{"question":"A ladder 23 feet long leans against a wall and the foot of the ladder is sliding away at a constant…","answer":"if doubt arises please mention in the comments.","href":"/questions-and-answers/a-ladder-23-feet-long-leans-against-a-wall-and-the-foot-of-the-ladder-is-sliding-away-at-a-constant-/f55543c1-01b6-4022-ac3a-ac6600631e3c"},{"question":"b)\nVing\nafter July). (2)\nc)\nwhat kind of time will:\nlation\n(5)\n5) A bank advertises that it…","answer":"Because the bank employs continuous compounding, your money will increase steadily over time. We…","href":"/questions-and-answers/b-ving-after-july.-2-c-what-kind-of-time-will-lation-5-5-a-bank-advertises-that-it-compounds-continu/a78e1e4e-f61e-4e52-9b7b-39a900d4cddb"},{"question":"6) For the graph provided answer the following:\na)\nFor which x is the function discontinuous? What…","answer":"(a)The function is discontinuous at x=Reason-5The limx→−5f(x) does not exist since its left-hand…","href":"/questions-and-answers/6-for-the-graph-provided-answer-the-following-a-for-which-x-is-the-function-discontinuous-what-is-th/02f06d40-56e4-4dca-a988-9d9c30bb05bc"},{"question":"Diego deposited a certain sum of money in a bank 4 years ago. The bank had been paying interest at…","answer":"Step 1:For the compounded continuously, the formula for the amount at time t is given by…","href":"/questions-and-answers/diego-deposited-a-certain-sum-of-money-in-a-bank-4-years-ago.-the-bank-had-been-paying-interest-at-t/ecad4ecc-71e7-480d-abfc-078188f3f996"},{"question":"Do not use AI apps for solving these maths . To solve by handwriting","answer":"We are asked to find the limit of the function (x-2)^-16 as x approaches 2 using L'Hopital's Rule.…","href":"/questions-and-answers/course-name-calculus-with-analytical-geometry-1-course-code-math-132-do-not-use-artificial-intellige/528c6715-d869-4cf2-9064-17c76ad16160"},{"question":"Problem 1. Discrete stochastic integrals for general martingales.\nn=0\nLet (Mn) be a martingale with…","answer":"Part (a): Prove that E[In]=0The process (In) is defined as:In=∑k=1nZk(Mk−Mk−1)Since (Mn) is…","href":"/questions-and-answers/problem-1.-discrete-stochastic-integrals-for-general-martingales.-n0-let-mn-be-a-martingale-with-res/9eb11759-f171-4a0b-a65d-81744bca2af7"},{"question":"pls draw the graph by showing and incorporating everything.","answer":"f)","href":"/questions-and-answers/8.-consider-the-function-x-x-8x-18x-27-and-in-factored-form-fx-x-1x-3-a-determine-the-x-and-y-interc/7396f302-08b7-4a73-b792-50312cfc678f"},{"question":"2) Find the value of b in the definite integral below.\nL\ntan(x) dr = 2","answer":"","href":"/questions-and-answers/2-find-the-value-of-b-in-the-definite-integral-below.-l-tanx-dr-2/6f8d8a07-431a-41b5-83f4-79557b7e36b6"},{"question":"Instruction:\nCourse Name: Calculus with Analytical Geometry-1\nCourse Code: MATH 132\n1. Solution must…","answer":"","href":"/questions-and-answers/instruction-course-name-calculus-with-analytical-geometry-1-course-code-math-132-1.-solution-must-ha/ac2efcb0-bf9a-4e8a-9933-7be6fd20bdce"},{"question":"#5, 43 a and b\nHello!\nPlease , can you help me with the attached Calculus problem seen in the…","answer":"Let's solve these limits using the indicated substitution (t=x1). a)(limx→∞xsin(x1)) Substitute…","href":"/questions-and-answers/43.-in-parts-a-c-find-the-limit-by-making-the-indicated-substitution.-1-1-a-lim-x-sin-t-8x-x-x-b-lim/13504673-d604-4429-bf7d-994fee343a88"},{"question":"Which of the following is a solution of the initial value problem\nS\n1\nSy ln(y) dx + x dy = 0\n\\y(e) =…","answer":"Step 1: Step 2: Step 3: Step 4:","href":"/questions-and-answers/which-of-the-following-is-a-solution-of-the-initial-value-problem-s-1-sy-lny-dx-x-dy-0-ye-e-hint-int/12e1a97c-bd92-4513-968c-8bc492c18bd6"},{"question":"Please help on all asked questions. Please show all work and steps. Pls circle the final answer.","answer":"","href":"/questions-and-answers/6.-if-f4-3-and-f4-5-find-g4-where-gx-xfx./b8ce1ea8-10ec-488d-9075-b13e2d3f62a7"},{"question":"Please help me with these questions. I am having trouble understanding what to do. I keep getting…","answer":"Part (a):","href":"/questions-and-answers/find-the-radius-of-convergence-r-of-the-series.-x5-5-inn-n-2-r-5-find-the-interval-i-of-convergence-/e211fe8d-36c4-4d32-bf4a-dfc163e81632"},{"question":"0\n5.\nχ\n√√ x³ sin dx =\nS:\nx3\n3x²\nsin\nx\nX2\n-2 cos\n6x\n-4 sin\nX\n8 cos\nx\n16 sin\nNIX","answer":"If you have any problem let me know in comment section thank you.","href":"/questions-and-answers/0-5.-x-x-sin-dx-s-x3-3x-sin-x-x2-2-cos-6x-4-sin-x-8-cos-x-16-sin-nix/93117b08-0722-4d84-9d68-900f611dcc2d"},{"question":"#5, 15\nPlease help me solve this problem in the attached image. Thank you.\nThe instruction for the…","answer":"","href":"/questions-and-answers/15.-lim-x0-2-x-_-3-sinx-3-x-x/73fbb3e8-e068-48c3-9aff-0d099815b641"},{"question":"1. S\nx+1\n√x-5\ndx","answer":"Step 1: Step 2: Step 3: Step 4:","href":"/questions-and-answers/1.-s-x1-x-5-dx/a37fb278-ae7e-44a1-b275-cb93375ae90d"},{"question":"Answer all parts and show work pls","answer":"If you have any problem let me know in the comment section thank you.","href":"/questions-and-answers/use-integration-by-parts-to-find-the-indefinite-integral.-1.-x-cos-x-dx-fx-2.-xe-dx-xex-dx-math-iz-a/cd033a0e-e20e-4cbb-9b23-9c3910d6587c"},{"question":"4. (i) Let f R2 → R be defined by\nf(x1, x2) = 2x 8x1x2+4x+1.\nFind all local minima of ƒ on R².\n[20…","answer":"Step 1: Step 2: Step 3: Step 4:","href":"/questions-and-answers/4.-i-let-f-r2-r-be-defined-by-fx1-x2-2x-8x1x24x1.-find-all-local-minima-of-f-on-r.-20-marks-ii-does-/670ba45a-5246-49f8-8827-0ee152ae211d"},{"question":"X\n+…","answer":"a.It is given that there are 200 students in the class and 35% are science majors. 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