Calculus (3rd Edition)

Published by W. H. Freeman
ISBN 10: 1464125260
ISBN 13: 978-1-46412-526-3

Chapter 2 - Limits - Chapter Review Exercises - Page 94: 18


$4a $

Work Step by Step

\begin{align*} \lim _{h \rightarrow 0}\frac{2(a+h)^2-2a^2}{h}&= \lim _{h \rightarrow 0}\frac{2(a^2+h^2+2ah)-2a^2}{h}\\ &= \lim _{h \rightarrow 0}\frac{2h^2+4ah}{h}\\ &=\lim _{h \rightarrow 0} 2h +4a \\ &=4a. \end{align*}
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