MCQ
$\mathop {\lim }\limits_{x \to \pi /4} \frac{{\sqrt 2 \cos x - 1}}{{\cot x - 1}} = $
- A$\frac{1}{{\sqrt 2 }}$
- ✓$\frac{1}{2}$
- C$\frac{1}{{2\sqrt 2 }}$
- D$1$
$ = \mathop {\lim }\limits_{x \to \pi /4} \frac{{\sin x\,(1 + \cot x)}}{{(\sqrt 2 + \sec x)}} = \frac{{\frac{1}{{\sqrt 2 }}(2)}}{{\sqrt 2 + \sqrt 2 }} = \frac{1}{2}.$
Aliter : Apply $L-$ Hospital’s rule.
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