A) \[2{{\log }_{e}}3\]
B) \[{{(2{{\log }_{e}}3)}^{2}}\]
C) \[{{\log }_{e}}6\]
D) none of these
Correct Answer: B
Solution :
[b] Given f(x) is continuous at x=0. Therefore, \[\underset{x\to 0}{\mathop{\lim }}\,f(x)=f(0)\] Or \[\underset{x\to 0}{\mathop{\lim }}\,\frac{{{({{3}^{x}}-1)}^{2}}}{\sin x\,\ln (1+x)}=f(0)\] Or \[f(0)=\underset{x\to 0}{\mathop{\lim }}\,\frac{{{\left( \frac{{{3}^{x}}-1}{x} \right)}^{2}}}{\left( \frac{\sin x}{x} \right)\left( \frac{\ln (1+x)}{x} \right)}={{(ln3)}^{2}}\]
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