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$\lim\limits_{x\to \large\frac{\pi}{4}}\large\frac{\sqrt 2\cos x-1}{\cot x-1}$=

$(a)\;1\qquad(b)\;\large\frac{1}{2}$$\qquad(c)\;\large\frac{1}{\sqrt 2}$$\qquad(d)\;\large\frac{1}{2\sqrt 2}$

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Given limit $\big(\large\frac{0}{0}\big)$ form
Applying L Hospital rule
$\Rightarrow \lim\limits_{\large x\to \large\frac{\pi}{4}}\large\frac{-\sqrt{2}\sin x}{-cosec^2x}$
$\Rightarrow \large\frac{1}{2}$
Hence (b) is the correct answer.
answered Dec 24, 2013 by sreemathi.v
 

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