MCQ
$\lim_{x \rightarrow 0} \frac{{{a}^{x}}-1}{\sqrt{1+x}-1}=.........$
- ✓$2{{\log }_{e}}a$
- B$\frac{1}{2}{{\log }_{e}}a$
- C$a{{\log }_{e}}2$
- Dએક પણ નહીં.
$\lim_{x \rightarrow 0}\frac{a^x-1}{\sqrt{1+x}-1}$ $(\frac{0}{0})$from L'Hospital rules
$=\lim_{x \rightarrow 0}\frac{a^x\log_{e}{a}}{\frac{1}{2\sqrt{1+x}}}$
$=\frac{a^0\log_{e}{a}}{\frac{1}{2\sqrt{1+0}}}\Rightarrow \frac{\log_{e}{a}}{\frac{1}{2}}\Rightarrow 2\log_{e}{a}$
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