Differential and Integral Calculus| Feliciano and Uy| Limit of a Function| Exercise 1.2| Problem 4


Evaluate \displaystyle \lim\limits _{x\to \frac{\pi }{3}}\left(\frac{sin\:2x}{sin\:x}\right).


Solution:

Plug in the value \displaystyle x=\frac{\pi }{3}

\displaystyle \lim\limits_{x\to \frac{\pi }{3}}\left(\frac{sin\:2x}{sin\:x}\right)=\frac{sin\left(2\cdot \frac{\pi }{3}\right)}{sin\:\left(\frac{\pi }{3}\right)}

\displaystyle =\frac{\frac{\sqrt{3}}{2}}{\frac{\sqrt{3}}{2}}

\displaystyle =1


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