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Limits — Maths STD 11 Science — Question

Maharashtra BoardEnglish MediumSTD 11 ScienceMathsLimits2 Marks
MCQ
$\lim _{x \rightarrow-2} \frac{\sqrt{x^2+5}-3}{x+2}$ is equal to
  • ✓
    $-\frac{2}{3}$
  • B
    $0$
  • C
    $\frac{2}{3}$
  • D
    $\frac{2}{9}$
✓

Answer

Correct option: A.
$-\frac{2}{3}$
(A)
Applying L-Hospital's Rule, we get
$\lim _{x \rightarrow-2} \frac{\sqrt{x^2+5}-3}{x+2}=\lim _{x \rightarrow-2} \frac{\frac{1}{2 \sqrt{x^2+5}}(2 x)}{1}=\frac{-2}{3}$

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