Calculus: Early Transcendentals 8th Edition

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

Chapter 2 - Section 2.5 - Continuity - 2.5 Exercises: 17

Answer

Infinite discontinuity at $-2$. See graph.
1508960404

Work Step by Step

$f(-2)$ is undefined. To try and visualize this we use: $\lim\limits_{x \to -2^{-}} f(x) = \lim\limits_{x \to -2^{-}} \frac{1}{x+2}= -\infty$ $\lim\limits_{x \to -2^{+}} f(x) = \lim\limits_{x \to -2^{+}} \frac{1}{x+2}= \infty$ Both of these answers are not the same, so the $\lim\limits_{x \to -2} f(x)$ does not exist.
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.