Calculus, 10th Edition (Anton)

Published by Wiley
ISBN 10: 0-47064-772-8
ISBN 13: 978-0-47064-772-1

Chapter 1 - Limits and Continuity - 1.2 Computing Limits - Exercises Set 1.2: 17

Answer

$\lim\limits_{x \to 3}\frac{x}{x-3}$ does not exist.

Work Step by Step

$\lim\limits_{x \to 3^{+}}\frac{x}{x-3}$ = $+\infty$. See exercise 15. $\lim\limits_{x \to 3^{-}}\frac{x}{x-3}$ = $-\infty$. See exercise 16. As $\lim\limits_{x \to 3^{+}}\frac{x}{x-3}$ $\ne$ $\lim\limits_{x \to 3^{-}}\frac{x}{x-3}$, we conclude that $\lim\limits_{x \to 3}\frac{x}{x-3}$ does not exist.
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