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

CBSE BoardEnglish MediumSTD 11 ScienceMathsSTD 11 - 12. limits1 Mark
MCQ
$\mathop {\lim }\limits_{x \to 0} \,\frac{{{{\sin }^2}\,x}}{{\sqrt 2  - \sqrt {1 + \cos \,x} }}$ equals
  • A
    $\sqrt 2 $
  • ✓
    $4\sqrt 2 $
  • C
    $4$
  • D
    $2\sqrt 2 $
✓

Answer

Correct option: B.
$4\sqrt 2 $
b
$\mathop {\lim }\limits_{x \to 0} \frac{{\left( {\frac{{{{\sin }^2}x}}{{{x^2}}}} \right)\left( {\sqrt 2  + \sqrt {1 + \cos x} } \right)}}{{\left( {\frac{{1 - \cos x}}{{{x^2}}}} \right)}}$

$ = \frac{{{{\left( 1 \right)}^2}.\left( {2\sqrt 2 } \right)}}{{\frac{1}{2}}} = 4\sqrt 2 $

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