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12. limits — MATHS STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceMATHS12. limits1 Mark
MCQ
$\mathop {\lim }\limits_{x \to \pi /2} \frac{{{a^{\cot x}} - {a^{\cos x}}}}{{\cot x - \cos x}} = $
  • ✓
    $\log a$
  • B
    $\log 2$
  • C
    $a$
  • D
    $log\ x$
✓

Answer

Correct option: A.
$\log a$
a
(a) $\mathop {{\rm{lim}}}\limits_{x \to \pi /2} \,\left( {\frac{{{a^{\cot x}} - {a^{\cos x}}}}{{\cot x - \cos x}}} \right)$

$ = \mathop {{\rm{lim}}}\limits_{x \to \pi /2} {a^{\cos x}}\left( {\frac{{{a^{\cot x - \cos x}} - 1}}{{\cot x - \cos x}}} \right)$

$ = {a^{\cos (\pi /2)}}\mathop {{\rm{lim}}}\limits_{x \to \pi /2} \left( {\frac{{{a^{\cot x - \cos x}} - 1}}{{\cot x - \cos x}}} \right)$$ = 1.\log a = \log a$.

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