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Question Number 116029 by bemath last updated on 30/Sep/20

$$\underset{x\to \frac{\pi }{2}}{\lim }\frac{\cos x}{{(1-\sin x)}^{\frac{2}{3}}}=?$$

Answered by bobhans last updated on 30/Sep/20

$$setx=\frac{\pi }{2}+z$$$$\underset{z\to 0}{\lim }\frac{-\sin z}{{(1-\cos z)}^{\frac{2}{3}}}=\underset{z\to 0}{\lim }\frac{-z}{{\left(\frac{z^2}{2}\right)}^{\frac{2}{3}}}{doesn}^{\prime }texist$$

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