Answer
$$-\frac{1}{4}$$
Work Step by Step
\begin{align*}
\lim _{x \rightarrow 0} \frac{\frac{1}{2+x}-\frac{1}{2}}{x}&=\lim _{x \rightarrow 0} \frac{2-(2+x)}{2 x(2+x)}\\
&=\lim _{x \rightarrow 0} \frac{-1}{4+2 x}\\
&=-\frac{1}{4}
\end{align*}
Thomas' Calculus 13th Edition
by Thomas Jr., George B.
Published by
Pearson
ISBN 10:
0-32187-896-5
ISBN 13:
978-0-32187-896-0
Chapter 2: Limits and Continuity - Practice Exercises - Page 101: 15
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