A) 1
B) \[{{e}^{1/2}}\]
C) \[{{e}^{2}}\]
D) \[{{e}^{3}}\]
Correct Answer: C
Solution :
Given that \[f:R\to R\] such that \[f(1)=3\]and\[f'(1)=6\] |
Then \[\underset{x\to 0}{\mathop{\lim }}\,{{\left[ \frac{f\left( 1+x \right)}{f\left( 1 \right)} \right]}^{1/x}}\]\[={{e}^{\underset{x\to 0}{\mathop{\lim }}\,\frac{\frac{1}{f(1+x)}f'(1+x)}{1}}}={{e}^{\frac{f'(1)}{f(1)}}}={{e}^{6/3}}={{e}^{2}}\] |
[Using L Hospital rule] |
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