A) \[\log 2\]
B) \[\log 4\]
C) \[\log \sqrt{2}\]
D) None of these
Correct Answer: B
Solution :
\[\underset{x\to 0}{\mathop{\lim }}\,\frac{{{2}^{x}}-1}{{{(1+x)}^{1/2}}-1}=\underset{x\to 0}{\mathop{\lim }}\,\frac{{{2}^{x}}\log 2}{\frac{1}{2}{{(1+x)}^{-1/2}}}\] \[=2\log 2\left[ \because \underset{x\to a}{\mathop{\lim }}\,\frac{f(x)}{g(x)}=\underset{x\to a}{\mathop{\lim }}\,\frac{f'(x)}{g'(x)} \right]\] \[=\log 4\]You need to login to perform this action.
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