University Calculus: Early Transcendentals (3rd Edition)

Published by Pearson
ISBN 10: 0321999584
ISBN 13: 978-0-32199-958-0

Chapter 4 - Section 4.5 - Indeterminate Forms and L'Hôpital's Rule - Exercises - Page 248: 13



Work Step by Step

Consider: $\lim\limits_{t \to 0}f(t)=\lim\limits_{t \to 0}\dfrac{\sin t^2}{t}$ Now, $f(0)=\dfrac{\sin 0}{0}=\dfrac{0}{0}$ The limit shows an indeterminate form. Thus, apply L-Hospital's rule: $\lim\limits_{a \to b}f(x)=\lim\limits_{a \to b}\dfrac{g'(x)}{h'(x)}$ Thus: $\lim\limits_{t \to 0}\dfrac{(2t) \cos t^2}{1}= \lim\limits_{t \to 0}\dfrac{ \cos 0}{1}=0$
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