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 86: 11

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.\quad$ Nearing $x=-2$ from the left, the graph falls without bound. $\displaystyle \lim_{x\rightarrow-2^{-}}h(x)=-\infty$. $ b.\quad$ Nearing $x=-2$ from the right, the graph falls without bound. $\displaystyle \lim_{x\rightarrow-2^{+}}h(x)=-\infty$. $ c.\quad$ Neither one-sided limit exists, but both are $-\infty.$ We write: $\displaystyle \lim_{x\rightarrow-2}h(x)=-\infty$. $ d.\quad$ Nearing $x=3$ from the left, the graph rises without bound. $\displaystyle \lim_{x\rightarrow 3^{-}}h(x)=\infty$. $ e.\quad$ Nearing $x=3$ from the right, the graph falls without bound. $\displaystyle \lim_{x\rightarrow 3^{+}}h(x)=-\infty$. $ f.\quad$ Neither one-sided limit exists, one is $+\infty$, the other $-\infty.$ We write: $\displaystyle \lim_{x\rightarrow 3}h(x)$ does not exist.
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