A) ln 2
B) ln 3
C) ln 4
D) \[{{e}^{3}}\]
Correct Answer: B
Solution :
[b] Given \[3=\underset{x\to 0}{\mathop{\lim }}\,{{(1+a\,sin\,x)}^{\cos ec\,x}}[{{1}^{\infty }}form]\] Put \[\sin x=4\] \[\therefore \] when \[x\to 0,y\to 0\] \[\therefore \underset{x\to 0}{\mathop{Lim}}\,{{(1+asinx)}^{\cos ecx}}=\underset{y\to 0}{\mathop{Lim}}\,{{(1+ay)}^{1/y}}={{e}^{a}}\] \[\therefore {{e}^{a}}=3\Rightarrow a={{\log }_{e}}3=ln\,3.\]
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