# Differential and Integral Calculus by Feliciano and Uy: Limit of a Function, Exercise 1.2, Problem 3

#### Evaluate $\lim\limits_{x\to \frac{\pi }{4}}\left(tan\:x+sin\:x\right)$

SOLUTION:

$\lim\limits_{x\to \frac{\pi }{4}}\left(tan\:x+sin\:x\right)=\lim\limits_{x\to \frac{\pi }{4}}\left(tan\:x\right)+\lim\limits_{x\to \frac{\pi }{4}}\left(sin\:x\right)$

$=tan\:\frac{\pi }{4}+sin\:\frac{\pi }{4}$

$=1+\frac{\sqrt{2}}{2}$

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