A) 1
B) -1
C) 2
D) 3
Correct Answer: D
Solution :
[d] \[\underset{x\to 0}{\mathop{Lt}}\,\frac{{{({{e}^{x}}-1)}^{2}}}{\sin \left( \frac{x}{a} \right)\log \left( 1+\frac{x}{4} \right)}\] \[=\underset{x\to 0}{\mathop{Lt}}\,\frac{\frac{{{({{e}^{x}}-1)}^{2}}}{x}.{{x}^{2}}}{\frac{x}{a}.\frac{\sin \left( \frac{x}{a} \right)}{\left( \frac{x}{a} \right)}.\frac{\log \left( 1+\frac{x}{4} \right)}{\frac{x}{4}}.\frac{x}{4}}\Rightarrow 4a=12\] \[\Rightarrow a=3\]
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