Thomas' Calculus 13th Edition

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


$$2x $$

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*}
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