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STD 11 - 12. limits — Maths STD 11 Science — Question

CBSE BoardEnglish MediumSTD 11 ScienceMathsSTD 11 - 12. limits1 Mark
MCQ
The value of $\mathop {\lim }\limits_{x \to 2} \frac{{{3^{x/2}} - 3}}{{{3^x} - 9}}$ is
  • A
    $0$
  • B
    $1/3$
  • ✓
    $1/6$
  • D
    $\ln 3$
✓

Answer

Correct option: C.
$1/6$
c
(c) $\mathop {\lim }\limits_{x \to 2} \,\left( {\frac{{{3^{x/2}} - 3}}{{{3^x} - 9}}} \right)$ $ = \mathop {{\rm{lim}}}\limits_{x \to 2} \,\,\left( {\frac{{{3^{x/2}} - 3}}{{{{({3^{x/2}})}^2} - {3^2}}}} \right)$

$ = \mathop {{\rm{lim}}}\limits_{x \to 2} \,\frac{1}{{{3^{x/2}} + 3}} = \frac{1}{6}$.

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