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}

 

 

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