Precalculus (10th Edition)

Published by Pearson
ISBN 10: 0-32197-907-9
ISBN 13: 978-0-32197-907-0

Chapter 14 - A Preview of Calculus: The Limit, Derivative, and Integral of a Function - 14.4 The Tangent Problem; The Derivative - 14.4 Assess Your Understanding - Page 898: 31



Work Step by Step

$$f'(0)\\=\lim_{x\to 0}\frac{f(x)-f(0)}{x-0}\\=\lim_{x\to 0}\frac{\sin{x}-\sin{0}}{x}\\=\lim_{x\to 0}\frac{\sin{x}-0}{x}\\=\lim_{x\to 0}\frac{\sin{x}}{x}=1.$$
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