Calculus 8th Edition

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

Chapter 1 - Functions and Limits - Review - True-False Quiz - Page 95: 21

Answer

True.

Work Step by Step

See sec.1-8, Th.8: If f is continuous at b, and $\displaystyle \lim_{x\rightarrow a}g(x)=b,$ Then $\displaystyle \lim_{x\rightarrow a}f(\mathrm{g}(x))=f(\lim_{x\rightarrow a}\mathrm{g}(x))=f(b)$ ------------ Let $g(x)=4x^{2}-11$. Then, $\displaystyle \lim_{x\rightarrow 2}g(x)=16-11=5$, $\displaystyle \lim_{x\rightarrow 2}f(\mathrm{g}(x))=f(\lim_{x\rightarrow 2}\mathrm{g}(x))=f(5)=2$ The statement is true.
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