Calculus (3rd Edition)

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

Chapter 2 - Limits - 2.6 Trigonometric Limits - Exercises - Page 76: 2

Answer

$f$ is squeezed by $u$ and $l$ at $x=3$. But $f$ is not squeezed by $u$ and $l$ at $x=2$.

Work Step by Step

We have $ l(x) \leq f(x)\leq u(x)$ and since $ \lim_{x\to 3}l(x)= \lim_{x\to 3}u(x)=1.5$, then by the squeeze theorem, we have $$\lim_{x\to 3}f(x)=1.5$$ and hence $f$ is squeezed by $u$ and $l$ at $x=3$. But $f$ is not squeezed by $u$ and $l$ at $x=2$, since $ \lim_{x\to 2}l(x)\neq \lim_{x\to 2}u(x)$.
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