Differential and Integral Calculus| Feliciano and Uy|Limit of a Function| Exercise 1.2| Problem 3


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


Solution:

\displaystyle \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)

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

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

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


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