Calculus: Early Transcendentals (2nd Edition)

Published by Pearson
ISBN 10: 0321947347
ISBN 13: 978-0-32194-734-5

Chapter 2 - Limits - 2.4 Infinite Limits - 2.4 Exercises - Page 85: 9

Answer

$ a.\quad\infty$. $ b.\quad\infty$. $ c.\quad\infty$. $ d.\quad\infty$. $ e.\quad-\infty$. $ f.\quad$ does not exist.

Work Step by Step

$a.$ Nearing $x=1$ from the left, the graph rises without bound. $\displaystyle \lim_{x\rightarrow 1^{-}}f(x)=\infty$. $b.$ Nearing $x=1$ from the right, the graph rises without bound. $\displaystyle \lim_{x\rightarrow 1^{+}}f(x)=\infty$. $c.$ Neither one-sided limit exists, but both are $+\infty.$ We write: $\displaystyle \lim_{x\rightarrow 1}f(x)=\infty$. $d.$ Nearing $x=2$ from the left, the graph rises without bound. $\displaystyle \lim_{x\rightarrow 2^{-}}f(x)=\infty$. $e.$ Nearing $x=2$ from the right, the graph falls without bound. $\displaystyle \lim_{x\rightarrow 2^{+}}f(x)=-\infty$. $f.$ Neither one-sided limit exists, one is $+\infty$, the other $-\infty.$ We write: $\displaystyle \lim_{x\rightarrow 1}f(x)$ does not exist.
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.