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Limits — Maths STD 11 Science — Question

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

Answer

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

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