May 9, 2018

The limit is $\frac{2}{\sqrt{2}} = \sqrt{2}$

#### Explanation:

Since we're in the form $\frac{0}{0}$, use l'hospitals rule.

$L = {\lim}_{x \to \frac{\pi}{4}} \frac{\cos x - \left(- \sin x\right)}{1}$

$L = {\lim}_{x \to \frac{\pi}{4}} \cos x + \sin x$

$L = \cos \left(\frac{\pi}{4}\right) + \sin \left(\frac{\pi}{4}\right)$

$L = \frac{2}{\sqrt{2}}$

We can confirm graphically.

Hopefully this helps!