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 - Chapter Review - Review Exercises - Page 926: 34



Work Step by Step

The general formula for the average rate of change from $x$ to $y$ can be written as: $\dfrac{f(y)-f(x)}{y-x}$. As $y\rightarrow x$, the rate of change becomes instantaneous (derivative). Here, we have: $f(x)=x^2-3x$ $\lim\limits_{x\to 0}\dfrac{f(x)-f(0)}{x-0}=\lim\limits_{x\to 0}\dfrac{(x^2-3x)-[(0)^2-(3)(0)]}{x} \\=\lim\limits_{x\to 0}\dfrac{x(x-3)}{x} \\=\lim\limits_{x\to 0} (x-3) \\=0-3 \\=-3$
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