University Calculus: Early Transcendentals (3rd Edition)

Published by Pearson
ISBN 10: 0321999584
ISBN 13: 978-0-32199-958-0

Chapter 2 - Section 2.6 - Limits Involving Infinity; Asymptotes of Graphs - Exercises - Page 108: 72

Answer

The graph of $y=f(x)$ is sketched below.
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Work Step by Step

The graph of the function $y=f(x)$ is sketched below. - $f$ passed the point $(2,1)$, $\lim_{x\to0^+}f(x)=\infty$ and $\lim_{x\to\infty}f(x)=0$. So here we would draw one line first approaching $\infty$ as $x\to0^+$, passing $(2,1)$ and finally approaching $0$ as $x\to\infty$. - $f$ passed the point $(-1,0)$, $\lim_{x\to0^-}f(x)=-\infty$ and $\lim_{x\to-\infty}f(x)=1$. Here we would draw the second line first approaching $-\infty$ as $x\to0^-$, passing $(-1,0)$ and finally approaching $1$ as $x\to-\infty$.
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