Calculus: Early Transcendentals 8th Edition

Published by Cengage Learning
ISBN 10: 1285741552
ISBN 13: 978-1-28574-155-0

Chapter 2 - Review - Exercises: 4

Answer

$$\lim\limits_{x\to3}\frac{x^2-9}{x^2+2x-3}=0$$

Work Step by Step

$$A=\lim\limits_{x\to3}\frac{x^2-9}{x^2+2x-3}$$ 1) Find the domain of $\frac{x^2-9}{x^2+2x-3}$ $\frac{x^2-9}{x^2+2x-3}$ is defined at any number in $R$ except where $$x^2+2x-3=0$$$$x=1$$ or $$x=-3$$ So $\frac{x^2-9}{x^2+2x-3}$ is defined at any number in $R$ except $x=1$ and $x=-3$. 2) Since $\frac{x^2-9}{x^2+2x-3}$ is a rational function, it is continuous at any number in its domain, including $x=3$. That means $$A=\lim\limits_{x\to3}\frac{x^2-9}{x^2+2x-3}=\frac{3^2-9}{3^2+2\times3-3}$$$$A=0$$
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