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Limits — Maths STD 11 Science — Question

Maharashtra BoardEnglish MediumSTD 11 ScienceMathsLimits2 Marks
MCQ
$\lim _{x \rightarrow 0^{+}} \frac{\sin x}{\sqrt{x}}=$
  • ✓
    $0$
  • B
    $\frac{1}{2}$
  • C
    1
  • D
    does not exist
✓

Answer

Correct option: A.
$0$
(A)
$\lim _{x \rightarrow 0^{+}} \frac{\sin x}{\sqrt{x}}=\lim _{x \rightarrow 0^{+}}\left(\frac{\sin x}{x}\right) \sqrt{x}$
$=\lim _{x \rightarrow 0^{+}}\left(\frac{\sin x}{x}\right) \lim _{x \rightarrow 0^{+}} \sqrt{x}$
$=1 \times 0$
$=0$

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