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$\lim\limits_{x\to \large\frac{\pi}{4}}\big(\large\frac{1-\tan x}{1\sqrt 2\sin x}\big)$=

$(a)\;0\qquad(b)\;1\qquad(c)\;-2\qquad(d)\;2$

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$\lim\limits_{x\to \large\frac{\pi}{4}}\big(\large\frac{1-\tan x}{1\sqrt 2\sin x}\big)\qquad\big(\large\frac{0}{0}\big)$
$\Rightarrow \lim\limits_{x\to 0}\large\frac{-\sec^2x}{\sqrt 2\cos x}$
$\Rightarrow \large\frac{-(\sqrt 2)^2}{-\sqrt 2\big(\Large\frac{1}{\sqrt 2}\big)}$
$\Rightarrow 2$
Hence (d) is the correct answer.
answered Dec 30, 2013 by sreemathi.v
 

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