Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (3rd Edition)

Published by Pearson
ISBN 10: 0-32193-104-1
ISBN 13: 978-0-32193-104-7

Chapter 13 - A Preview of Calculus: The Limit, Derivative, and Integral of a Function - Section 13.4 The Tangent Problem; The Derivative - 13.4 Assess Your Understanding - Page 917: 32



Work Step by Step

Consider the tangent line that contains the point $(x, c)$. The slope the tangent line to the graph of $f(x)$ at $(x, c)$ can be written as $f'(x) =\lim\limits_{x \to c} \dfrac{f(x)-f(c)}{x-c}$ Consider $c=0$ and $f(x)=\cos x$. Thus, we have: $f'(0) =\lim\limits_{x \to 0} \dfrac{f(x)-f(0)}{x-0} \\=\lim\limits_{x \to 0} \dfrac{\cos x -\cos 0}{x}\\=\lim\limits_{x \to 0} \dfrac{\cos x-1 }{x}\\=0$
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.