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STD 11 - 12. limits — Maths STD 11 Science — Question

CBSE BoardEnglish MediumSTD 11 ScienceMathsSTD 11 - 12. limits1 Mark
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
    $1$
✓

Answer

Correct option: B.
$\frac{1}{2}$
b
(b) $\mathop {\lim }\limits_{x \to \pi /4} \,\frac{{(\sqrt 2 - \sec x)\,\cos x\,(1 + \cot x)}}{{\cot x\,[2 - {{\sec }^2}x]}}$

$ = \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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