Calculus 8th Edition

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

Chapter 2 - Derivatives - 2.4 Derivatives of Trigonometric Functions - 2.4 Exercises - Page 151: 48



Work Step by Step

Given $$\lim _{x\to 0}\frac{\sin x^2}{x}$$ Then \begin{align*} \lim _{x\to 0}\frac{\sin x^2}{x}&=\lim _{x\to 0}\frac{x\sin x^2}{x^2}\\ &=\lim _{x\to 0}(x)\lim _{x \to 0}\frac{ \sin x^2}{x^2}\\ &=\lim _{x\to 0}(x)\left(\lim _{x \to 0}\frac{ \sin x }{x }\right)^2\\ &=(0)(1)\\ &=0 \end{align*}
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