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

$4a $

\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*}