Calculus 8th Edition

Published by Cengage
ISBN 10: 1285740629
ISBN 13: 978-1-28574-062-1

Chapter 1 - Functions and Limits - 1.6 Calculating Limits Using the Limit Laws - 1.6 Exercises: 23

Answer

$-\frac{1}{9}$

Work Step by Step

$\lim\limits_{x \to 3}\frac{\frac{1}{x}-\frac{1}{3}}{x-3}=\lim\limits_{x \to 3}\frac{\frac{3}{3x}-\frac{x}{3x}}{x-3}=\lim\limits_{x \to 3}\frac{3-x}{3x(x-3)}=\lim\limits_{x \to 3}\frac{-(x-3)}{3x(x-3)}=\lim\limits_{x \to 3}\frac{-1}{3x}=\frac{-1}{3(3)}=-\frac{1}{9}$
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