# How do you evaluate the limit e^xcosx as x approaches 0?

Aug 13, 2016

You can plug $x = 0$ in and solve this with hardly any work.

$\textcolor{b l u e}{{\lim}_{x \to 0} {e}^{x} \cos x}$

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

$= 1 \cdot 1 = \textcolor{b l u e}{1}$

Aug 13, 2016

1

#### Explanation:

${\lim}_{x \rightarrow 0} {e}^{x} \cos x = {e}^{0} \cos \left(0\right) = 1 \cdot 1 = 1$