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Question Number 116039 by bobhans last updated on 30/Sep/20

$$\underset{x\to \frac{\pi }{2}}{\lim }\frac{\sqrt[3]{\cos {}^4\left(x\right)}}{{(1-\sin \left(x\right))}^{\frac{2}{3}}}?$$

Answered by Dwaipayan Shikari last updated on 30/Sep/20

$$\underset{x\to \frac{\pi }{2}}{\lim }\frac{{\left(\mathrm{cosx}\right)}^{\frac{4}{3}}}{{(1-\mathrm{sinx})}^{\frac{2}{3}}}=\frac{{\left({\cos }^2\mathrm{x}\right)}^{\frac{2}{3}}}{{(1-\mathrm{sinx})}^{\frac{2}{3}}}={(1+\mathrm{sinx})}^{\frac{2}{3}}=2^{\frac{2}{3}}$$

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