Answer
Shown below.
Work Step by Step
Let $a = 0, f(x) = \frac{1}{x}, g(x) = -\frac{1}{x}$. Neither of the two individual limits exist, but since $f(x) + g(x) = 0$, we have $\lim_{x \to a}[f(x) + g(x)]$ exists and is 0.
Calculus: Early Transcendentals 8th Edition
by Stewart, James
Published by
Cengage Learning
ISBN 10:
1285741552
ISBN 13:
978-1-28574-155-0
Chapter 2 - Section 2.3 - Calculating Limits Using the Limit Laws - 2.3 Exercises - Page 104: 62
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