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: 55



Work Step by Step

$$\lim_{x\to 0}\frac{3\sin{x}+\cos{x}-1}{4x}\\=\lim_{x\to 0}\frac{3\sin{x}}{4x}+\lim_{x\to 0}\frac{\cos{x}-1}{4x}\\=\frac{3}{4}(\lim_{x\to 0}\frac{\sin{x}}{x})+\frac{1}{4}(\lim_{x\to 0}\frac{\cos{x}-1}{x})\\=\frac{3}{4}(1)+\frac{1}{4}(0)\\=\frac{3}{4}.$$
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