Calculus: Early Transcendentals (2nd Edition)

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

Chapter 2 - Limits - 2.3 Techniques for Computing Limits - 2.3 Exercises - Page 76: 8

Answer

$\displaystyle \lim_{x\rightarrow 2}g(x)=5$

Work Step by Step

THEOREM 2.5 The Squeeze Theorem: Assume the functions $f,g,$ and $h$ satisfy $f(x)\leq g(x)\leq h(x)$ for all values of $x$ near $a,$ except possibly at $a$ . If $\displaystyle \lim_{x\rightarrow a}f(x)=\lim_{x\rightarrow a}h(x)=L,$ then $\displaystyle \lim_{x\rightarrow a}g(x)=L$ --- By the squeeze theorem, $\displaystyle \lim_{x\rightarrow 2}g(x)=5$
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