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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} \left( {\frac{{{a^x} - {b^x}}}{x}} \right) = $
  • A
    $\log \left( {\frac{b}{a}} \right)$
  • ✓
    $\log \left( {\frac{a}{b}} \right)$
  • C
    $\frac{a}{b}$
  • D
    $\log {a^b}$
✓

Answer

Correct option: B.
$\log \left( {\frac{a}{b}} \right)$
b
(b)$\mathop {\lim }\limits_{x \to 0} \,\frac{{{a^x} - {b^x}}}{x} = \mathop {\lim }\limits_{x \to 0} \,\left( {\frac{{{a^x} - 1}}{x}} \right) - \mathop {\lim }\limits_{x \to 0} \,\left( {\frac{{{b^x} - 1}}{x}} \right)$

$ = \log \,\,a - \log \,\,b = \log \,(a/b)$.

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