A) 18
B) 12
C) 36
D) 24
Correct Answer: A
Solution :
\[\underset{x\to 2}{\mathop{\lim }}\,\int_{6}^{f(x)}{\frac{4{{t}^{3}}}{x-2}}dt\] \[=\underset{x\to 2}{\mathop{\lim }}\,\frac{\int_{6}^{f(x)}{4{{t}^{3}}}dt}{(x-2)}\] \[=\underset{x\to 2}{\mathop{\lim }}\,\frac{4{{\{f(x)\}}^{3}}}{1}f'(x)\] \[=4\{f{{(2)}^{3}}\}f'(2)\] \[=4\times {{(6)}^{3}}\times \frac{1}{48}\] \[[\because f(2)=6f'(2)=\frac{1}{48}]\] \[=18\]You need to login to perform this action.
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