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Evaluate :$\lim\limits_{x\to \Large\frac{\pi}{4}}\large\frac{\sqrt 2-\cos x-\sin x}{(4x-\pi)^2}$

$(a)\;1/16\sqrt 2\qquad(b)\;1/\sqrt 2\qquad(c)\;1/16\qquad(d)\;1$

1 Answer

Applying L Hospital rule to the given limit (%)
$\Rightarrow \lim\limits_{x\to \large\frac{\pi}{4}}\large\frac{\sin x-\cos x}{2.4(4x-\pi)}$
$\Rightarrow \lim\limits_{x\to\large\frac{\pi}{4}}\large\frac{\cos x+\sin x}{8\times 4}$
$\Rightarrow \large\frac{2}{\sqrt 2}.\frac{1}{32}$
$\Rightarrow \large\frac{1}{16\sqrt 2}$
Hence (a) is the correct answer.
answered Dec 23, 2013 by sreemathi.v
 

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