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 - 14.2 Algebra Techniques for Finding Limits - 14.2 Assess Your Understanding - Page 884: 53



Work Step by Step

$$\lim_{x\to 0}\frac{\tan{x}}{x}\\=\lim_{x\to 0}\dfrac{\frac{\sin{x}}{\cos{x}}}{x}\\=\lim_{x\to 0}(\frac{\sin{x}}{\cos{x}}\frac{1}{x})\\=\lim_{x\to 0}(\frac{\sin{x}}{x}\frac{1}{\cos{x}})\\=\lim_{x\to 0}(1\cdot\frac{1}{\cos{x}})\\=\frac{1}{\cos{0}}\\=\frac{1}{1}=1.$$
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