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Limits — Maths STD 11 Science — Question

Maharashtra BoardEnglish MediumSTD 11 ScienceMathsLimits2 Marks
MCQ
$\lim _{x \rightarrow 0} \frac{\sqrt{1+2 x}-1}{x}=$
  • A
    $0$
  • B
    -1
  • C
    $\frac{1}{2}$
  • ✓
    1
✓

Answer

Correct option: D.
1
(D)
By rationalising, we get
$\lim _{x \rightarrow 0} \frac{\sqrt{1+2 x}-1}{x}=\lim _{x \rightarrow 0} \frac{1+2 x-1}{x(\sqrt{1+2 x}+1)}$
$=\lim _{x \rightarrow 0} \frac{2}{\sqrt{1+2 x}+1}$
$=1$

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