Answer
$$2x $$
Work Step by Step
\begin{align*}
\lim _{h \rightarrow 0} \frac{(x+h)^{2}-x^{2}}{h}&=\lim _{h \rightarrow 0} \frac{\left(x^{2}+2 h x+h^{2}\right)-x^{2}}{h}\\
&=\lim _{h \rightarrow 0}(2 x+h)\\
&=2 x
\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: 13
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