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 13.2 Algebra Techniques for Finding Limits - 13.2 Assess Your Understanding - Page 903: 43



Work Step by Step

The general formula for average rate of change from $a$ to $b$ can be written as: $\dfrac{f(b)-f(a)}{b-a}.$ Here, we have: $f(x)=5x-3$ Thus, we find the average rate of change as: $\lim\limits_{x\to 2}\dfrac{f(x)-f(2)}{x-2}=\lim\limits_{x\to 2}\dfrac{(5x-3)-(5(2)-3)}{x-2} \\=\lim\limits_{x\to 2}\dfrac{(5x-3)-7}{x-2} \\=\lim\limits_{x\to 2}\dfrac{5x-10}{x-2} \\=\lim\limits_{x\to 2}\dfrac{5(x-2)}{x-2} \\=\lim\limits_{x\to 2} \ (5) \\=5$
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