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Question Number 193803 by cortano12 last updated on 20/Jun/23

$$\underset{x\to 2}{\lim }\frac{\sqrt{11-\mathrm{x}}\cos \left(\frac{\pi }{\mathrm{x}-2}\right)}{\cot (\mathrm{x}-2)}=?$$

Answered by horsebrand11 last updated on 20/Jun/23

$$=\underset{x\to 2}{\lim }\frac{3\sin (\frac{\pi }{2}-\frac{\pi }{\mathrm{x}-2})}{\cot (\mathrm{x}-2)}$$$$=3\underset{x\to 2}{\lim }\sin (\mathrm{x}-2)\sin \pi \left(\frac{\mathrm{x}-4}{\mathrm{x}-2}\right)$$$$=3\times 0=0$$

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