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12. limits — MATHS STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceMATHS12. limits1 Mark
MCQ
$\mathop {\lim }\limits_{x \to 0} \frac{{{a^{\sin x}} - 1}}{{{b^{\sin x}} - 1}} = $
  • A
    $\frac{a}{b}$
  • B
    $\frac{b}{a}$
  • ✓
    $\frac{{\log a}}{{\log b}}$
  • D
    $\frac{{\log b}}{{\log a}}$
✓

Answer

Correct option: C.
$\frac{{\log a}}{{\log b}}$
c
(c) $\mathop {{\rm{lim}}}\limits_{x \to 0} \frac{{{a^{\sin x}} - 1}}{{{b^{\sin x}} - 1}} = \mathop {{\rm{lim}}}\limits_{x \to 0} \frac{{{a^{\sin x}} - 1}}{{\sin x}} \times \frac{{\sin x}}{{{b^{\sin x}} - 1}}$ 

$ = {\log _e}a \times \frac{1}{{{{\log }_e}b}} = \frac{{\log a}}{{\log b}}$.

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