MCQ
$\mathop {\lim }\limits_{x \to 0} \frac{{{a^x} - {b^x}}}{{{e^x} - 1}} =$
- ✓$\log \left( {\frac{a}{b}} \right)$
- B$\log \left( {\frac{b}{a}} \right)$
- C$\log (a\,b)$
- D$\log \,(a + \,b)$
$ = \mathop {\lim }\limits_{x \to 0} \left[ {\frac{{{a^x} - 1}}{x} - \frac{{{b^x} - 1}}{x}} \right]\frac{x}{{{e^x} - 1}}$
$ = ({\log _e}a - {\log _e}b).\frac{1}{{{{\log }_e}e}}$$ = {\log _e}\left( {\frac{a}{b}} \right)$
Trick : Apply $ L-$ Hospital’s rule.
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
( જ્યાં $l$ એ સાન્ત સંખ્યા છે )