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 - Page 70: 47

Answer

The proof is below.

Work Step by Step

By Theorem 1.2.2., $\lim_{x \to a} [f(x)+g(x)] = \lim_{x \to a} f(x)+\lim_{x \to a} g(x) = R +\lim_{x \to a} g(x)$ where $R$ is a real number. Therefore, for $\lim_{x \to a} [f(x)+g(x)]$ to exist, both $\lim_{x \to a} g(x)$ and $\lim_{x \to a} f(x)$ must exist. Since $\lim_{x \to a} f(x)$ is already given to exist, $\lim_{x \to a} g(x)$ must 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.