Calculus 8th Edition

Published by Cengage
ISBN 10: 1285740629
ISBN 13: 978-1-28574-062-1

Chapter 1 - Functions and Limits - 1.6 Calculating Limits Using the Limit Laws - 1.6 Exercises: 62

Answer

SAmple answer: $f(x)=\displaystyle \frac{1}{x},\ g(x)=-\displaystyle \frac{1}{x}$, a=0.

Work Step by Step

Take, for example, $f(x)=\displaystyle \frac{1}{x},\ g(x)=-\displaystyle \frac{1}{x}$, a=0. Approaching 0 from the right , $ f(x)\rightarrow\infty,\ g(x)\rightarrow-\infty$ Approaching 0 from the left , $ f(x)\rightarrow-\infty,\ g(x)\rightarrow\infty$ (the limits $\displaystyle \lim_{x\rightarrow 0}f(x)$ and $\displaystyle \lim_{x\rightarrow 0}g(x)$ do not exist) But, $f(x)+g(x)=0$ and $\displaystyle \lim_{x\rightarrow 0}[f(x)+g(x)] =\displaystyle \lim_{x\rightarrow 0}0=0$ (exists)
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