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Limits — Maths STD 11 Science — Question

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

Answer

Correct option: C.
$0$
(C)
On rationalising, we get
$\lim _{x \rightarrow \infty}\left(\sqrt{x^2+1}-x\right)=\lim _{x \rightarrow \infty} \frac{x^2+1-x^2}{\sqrt{x^2+1}+x}$
$=\lim _{x \rightarrow \infty} \frac{1}{\sqrt{x^2+1}+x}=0$

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