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Limits — Maths STD 11 Science — Question

Maharashtra BoardEnglish MediumSTD 11 ScienceMathsLimits2 Marks
MCQ
$\lim _{x \rightarrow 0} \frac{\log (\cos x)}{x^2}$ is equal to
  • A
    $0$
  • B
    1
  • C
    $\frac{1}{2}$
  • ✓
    $-\frac{1}{2}$
✓

Answer

Correct option: D.
$-\frac{1}{2}$
(D)
Applying L-Hospital's rule, we get
$\lim _{x \rightarrow 0} \frac{\log (\cos x)}{x^2}=\lim _{x \rightarrow 0} \frac{-\tan x}{2 x}$
$=\lim _{x \rightarrow 0} \frac{-\sec ^2 x}{2}=\frac{-1}{2}$

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