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MATB41H3 Final: matb41-problems15

Canada

Techniques of the Calculus of Several Variables I

Mathematics

Xiao

University of Toronto Scarborough

Introduction to Anthropology: Becoming Human

The Ancient Mediterranean World

Introduction to Computer Science I

Introduction to Computer Science II

Discrete Mathematics

Introduction to the Theory of Computation

Introduction to Microeconomics

Introduction to Twentieth-Century Literature and Film: 1945 to Today

Introduction to Planet Earth

History and Culture of the Greek World

Introduction to Linguistics

Calculus I for Mathematical Sciences

Linear Algebra II

Reason and Truth

Physics I for the Physical Sciences

An Introduction to Probability

An Introduction to Statistics

Calculus II for Mathematical Sciences

Introduction to Analysis

Introduction to Combinatorics

Linear Algebra I for Mathematical Sciences

<p>Integration by Parts When evaluating <picture><source srcset="https://s3.amazonaws.com/prealliance-textbook-qa.oneclass.com/qa_images/homework_help/question/qa_images/953660155812198/question/0.webp?img=1f7ff259f2a6df128b9e729d1833e659" type="image/webp"><img src="https://s3.amazonaws.com/prealliance-textbook-qa.oneclass.com/qa_images/homework_help/question/qa_images/953660155812198/question/0.png?img=3a7e1701445bd717574a23dc9dcf80d9" data-mlang="latex" data-equation="%7Bint%7Bxsinx%7D%7D%2Cdx"></picture>, explain how letting <picture><source srcset="https://s3.amazonaws.com/prealliance-textbook-qa.oneclass.com/qa_images/homework_help/question/qa_images/953660155812198/question/1.webp?img=0f361784b05d17f67bd1796e62be6582" type="image/webp"><img src="https://s3.amazonaws.com/prealliance-textbook-qa.oneclass.com/qa_images/homework_help/question/qa_images/953660155812198/question/1.png?img=82611abedd790f4874280097b7781286" data-mlang="latex" data-equation="u%3Dsinx"></picture> and <picture><source srcset="https://s3.amazonaws.com/prealliance-textbook-qa.oneclass.com/qa_images/homework_help/question/qa_images/953660155812198/question/2.webp?img=eec46a765eefe1c5a883b92fdebe5d30" type="image/webp"><img src="https://s3.amazonaws.com/prealliance-textbook-qa.oneclass.com/qa_images/homework_help/question/qa_images/953660155812198/question/2.png?img=f13097159c26f2e0cfb34aecbfdefe20" data-mlang="latex" data-equation="dv%3Dx%2Cdx"></picture> makes the solution more difficult to find.</p>

<div style="font-family:'Helvetica Neue', Helvetica, Arial;color:#333333;"> <div> <br> <picture><source srcset="https://prealliance-textbook-qa.oneclass.com/qa_images/homework_help/question/qa_images/79/7945446.webp" type="image/webp"></source><img src="https://prealliance-textbook-qa.oneclass.com/qa_images/homework_help/question/qa_images/79/7945446.png" alt=""></picture> </div> </div> <div id="fm9" class="hidden">Use cylindrical or spherical coordinates, whichever seems more appropriate. (a) Find the volume enclosed by the torus 10 sin(p). (b) Use a computer to draw the torus. </div> <span class="transcribed-text">Show transcribed image text</span> <span class="transcribed-image-text hidden">Use cylindrical or spherical coordinates, whichever seems more appropriate. (a) Find the volume enclosed by the torus 10 sin(p). (b) Use a computer to draw the torus. </span>

<p>Consider the given function:</p>
<p><picture><source srcset="https://s3.amazonaws.com/prealliance-textbook-qa.oneclass.com/qa_images/homework_help/question/qa_images/647754853703299/question/0.webp?img=6222a97b234d586c1acaad2d5b4859ff" type="image/webp"><img src="https://s3.amazonaws.com/prealliance-textbook-qa.oneclass.com/qa_images/homework_help/question/qa_images/647754853703299/question/0.png?img=66d5631c848174779f3217dbbc849620" data-mlang="latex" data-equation="f(x)%20%3D%20%5Cfrac%7Bx%5E2%20%2B5x%20-%2014%7D%7Bx%2B7%7D"></picture>  </p>
<p>a. Find the vertical asymptote(s). If there is more than one vertical asymptote give a list of the <picture><source srcset="https://s3.amazonaws.com/prealliance-textbook-qa.oneclass.com/qa_images/homework_help/question/qa_images/647754853703299/question/1.webp?img=63f6b334eed135be43a78ba4babb59d9" type="image/webp"><img src="https://s3.amazonaws.com/prealliance-textbook-qa.oneclass.com/qa_images/homework_help/question/qa_images/647754853703299/question/1.png?img=3aae8369b94da94389a9cfa7548da04b" data-mlang="latex" data-equation="x"></picture>-values separated by commas. If there is no vertical asymptote, answer none. </p>
<p>b. If this function has a horizontal asymptote, give its <picture><source srcset="https://s3.amazonaws.com/prealliance-textbook-qa.oneclass.com/qa_images/homework_help/question/qa_images/647754853703299/question/2.webp?img=664975b20e44147d938fda1535573424" type="image/webp"><img src="https://s3.amazonaws.com/prealliance-textbook-qa.oneclass.com/qa_images/homework_help/question/qa_images/647754853703299/question/2.png?img=57ef78a115f9838a829d0902ee50c1b1" data-mlang="latex" data-equation="y"></picture>-value. If there is no horizontal asymptote, answer none. </p>
<p>c. Find the <picture><source srcset="https://s3.amazonaws.com/prealliance-textbook-qa.oneclass.com/qa_images/homework_help/question/qa_images/647754853703299/question/3.webp?img=f104bc5b3aa54197c8611a26693497fa" type="image/webp"><img src="https://s3.amazonaws.com/prealliance-textbook-qa.oneclass.com/qa_images/homework_help/question/qa_images/647754853703299/question/3.png?img=97eaf17215f990dd04d04bc49b0125e8" data-mlang="latex" data-equation="x"></picture>-intercept(s). If there is more than one <picture><source srcset="https://s3.amazonaws.com/prealliance-textbook-qa.oneclass.com/qa_images/homework_help/question/qa_images/647754853703299/question/4.webp?img=4ef5ced47b04bc2f6d65d72d44dc2cae" type="image/webp"><img src="https://s3.amazonaws.com/prealliance-textbook-qa.oneclass.com/qa_images/homework_help/question/qa_images/647754853703299/question/4.png?img=1ce1a92d8ecb452b7c16b234994f0890" data-mlang="latex" data-equation="x"></picture>-intercept give a list of the <picture><source srcset="https://s3.amazonaws.com/prealliance-textbook-qa.oneclass.com/qa_images/homework_help/question/qa_images/647754853703299/question/5.webp?img=dbbdb3a5d58fe82d22a6892e65f63b5e" type="image/webp"><img src="https://s3.amazonaws.com/prealliance-textbook-qa.oneclass.com/qa_images/homework_help/question/qa_images/647754853703299/question/5.png?img=507e4aef896f520c32b1651470352d03" data-mlang="latex" data-equation="x"></picture>-values separated by commas. </p>
<p>d. Find the <picture><source srcset="https://s3.amazonaws.com/prealliance-textbook-qa.oneclass.com/qa_images/homework_help/question/qa_images/647754853703299/question/6.webp?img=9ab8457ccc836b6aa9c15a795f57919f" type="image/webp"><img src="https://s3.amazonaws.com/prealliance-textbook-qa.oneclass.com/qa_images/homework_help/question/qa_images/647754853703299/question/6.png?img=ca141d9a23a259861bb943ce16ba013a" data-mlang="latex" data-equation="y"></picture>-intercept. </p>
<p> </p>

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