Evaluate the limit

by RoRi

August 24, 2015

Evaluate

$\lim_{h \to 0} \frac{(t+h)^2 - t^2}{h}.$

First, we simplify the expression,

$\begin{align*} \frac{(t+h)^2 - t^2}{h} &= \frac{t^2 + 2th + h^2 - t^2}{h} \\ &= \frac{2th + h^2}{h} \\ &= 2t + h. \end{align*}$

Then, we evaluate the limit,

$\lim_{h \to 0} (2t + h) = 2t.$

Stumbling Robot