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Limits — Maths STD 11 Science — Question

Maharashtra BoardEnglish MediumSTD 11 ScienceMathsLimits2 Marks
MCQ
$\lim _{x \rightarrow 2} \frac{x^2-4}{x \sqrt{x}-2 \sqrt{2}}=$
  • A
    $\frac{4}{3} \sqrt{3}$
  • B
    $\frac{4}{2} \sqrt{3}$
  • ✓
    $\frac{4}{3} \sqrt{2}$
  • D
    $\frac{4}{2} \sqrt{2}$
✓

Answer

Correct option: C.
$\frac{4}{3} \sqrt{2}$
(C)
$\lim _{x \rightarrow 2} \frac{x^2-4}{x \sqrt{x}-2 \sqrt{2}}=\lim _{x \rightarrow 2} \frac{\left(x^2-4\right)(x \sqrt{x}+2 \sqrt{2})}{(x \sqrt{x}-2 \sqrt{2})(x \sqrt{x}+2 \sqrt{2})}$
$=\lim _{x \rightarrow 2} \frac{\left(x^2-4\right)(x \sqrt{x}+2 \sqrt{2})}{x^3-2^3}$
$=\lim _{x \rightarrow 2} \frac{(x+2)(x \sqrt{x}+2 \sqrt{2})}{x^2+2 x+4}$
$=\frac{(2+2)(2 \sqrt{2}+2 \sqrt{2})}{(2)^2+2(2)+4}=\frac{4}{3} \sqrt{2}$
Alternate method:
Apply L-Hospital's Rule.

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