Calculus (3rd Edition)

Published by W. H. Freeman
ISBN 10: 1464125260
ISBN 13: 978-1-46412-526-3

Chapter 2 - Limits - 2.7 Limits at Infinity - Exercises - Page 82: 4


$f(x)=2\tan^{-1} x+\pi-2$ $g(x)=2\tan^{-1} (-x)+\pi-2$

Work Step by Step

Let's consider the functions $f(x)$ and $g(x)$: $f(x)=2\tan^{-1} x+\pi-2$ $g(x)=2\tan^{-1} (-x)+\pi-2$ We have: $\displaystyle\lim_{x\rightarrow-\infty} f(x)=-2$ $\displaystyle\lim_{x\rightarrow\infty} f(x)=4$ $\displaystyle\lim_{x\rightarrow -\infty} g(x)=4$ $\displaystyle\lim_{x\rightarrow\infty} g(x)=-2$ Therefore: $\displaystyle\lim_{x\rightarrow \infty} f(x)\not=\displaystyle\lim_{x\rightarrow \infty} g(x)$
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