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12. limits — MATHS STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceMATHS12. limits1 Mark
MCQ
$\mathop {\lim }\limits_{x \to 0} \frac{{1 - \cos x}}{{{{\sin }^2}x}} = $
  • ✓
    $\frac{1}{2}$
  • B
    $ - \frac{1}{2}$
  • C
    $2$
  • D
    None of these
✓

Answer

Correct option: A.
$\frac{1}{2}$
a
(a) $\mathop {\lim }\limits_{x \to 0} \,\frac{{2\,{{\sin }^2}\frac{x}{2}.\,({x^2})}}{{4\,{{\sin }^2}x\,.\,\left( {\frac{{{x^2}}}{4}} \right)}} = \frac{1}{2}.$

Aliter : Apply  $ L-$ Hospital’s rule two times.

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