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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{{x\cos x - \sin x}}{{{x^2}\sin x}} = $
  • A
    $\frac{1}{3}$
  • ✓
    $ - \frac{1}{3}$
  • C
    $1$
  • D
    None of these
✓

Answer

Correct option: B.
$ - \frac{1}{3}$
b
(b) $\mathop {\lim }\limits_{x \to 0} \,\,\frac{{x\cos x - \sin x}}{{{x^2}\sin x}}$

$ = \mathop {\lim }\limits_{x \to 0} \,\,\frac{{ - \sin x}}{{2\sin x + x\cos x}}$

(By $L-$ Hospital’s rule)

$ = \mathop {\lim }\limits_{x \to 0} \,\,\frac{{ - \cos x}}{{3\cos x - x\sin x}} = - \frac{1}{3}$, 

(Again by $L-$ Hospital’s rule)

$ = - \frac{1}{3}$

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