# How do you evaluate the limit lim (e^t-1)/sint as t->0?

Dec 18, 2016

Currently we're in indeterminate form, $\frac{0}{0}$, so we can use l'Hopitals rule to solve the problem.

${\lim}_{x \to c} \frac{f \left(x\right)}{g \left(x\right)} = {\lim}_{x \to c} \frac{f ' \left(x\right)}{g ' \left(x\right)}$

${\lim}_{t \to 0} \frac{{e}^{t} - 1}{\sin} t = {\lim}_{t \to 0} \frac{{e}^{t}}{\cos} t$

$= {e}^{0} / \cos \left(0\right)$

$= \frac{1}{1}$

$= 1$

Hopefully this helps!