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Limits — Maths STD 11 Science — Question

Maharashtra BoardEnglish MediumSTD 11 ScienceMathsLimits2 Marks
MCQ
$\lim _{x \rightarrow 0}\left(\frac{x}{\sqrt{1+x}-\sqrt{1-x}}\right)$ is equal to
  • A
    $0$
  • ✓
    1
  • C
    2
  • D
    -1
✓

Answer

Correct option: B.
1
(B)
$\lim _{x \rightarrow 0}\left(\frac{x}{\sqrt{1+x}-\sqrt{1-x}}\right)$
$=\lim _{x \rightarrow 0} \frac{x(\sqrt{1+x}+\sqrt{1-x})}{(1+x)-(1-x)}$
$=\lim _{x \rightarrow 0} \frac{x}{2 x}(\sqrt{1+x}+\sqrt{1-x})$
$=1$

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