Let \[f:R\to R\]be a differentiable function having \[f(2)=6,f'(2)=\left( \frac{1}{48} \right).\] Then \[\underset{x\to 2}{\mathop{\lim }}\,\int\limits_{6}^{f(x)}{\frac{4{{t}^{3}}}{x-2}}\]dt equals [AIEEE 2005]

Let \[f:R\to R\]be a differentiable function having \[f(2)=6,f'(2)=\le

1.	Let \[f:R\to R\]be a differentiable function having \[f(2)=6,f'(2)=\left( \frac{1}{48} \right).\] Then \[\underset{x\to 2}{\mathop{\lim }}\,\int\limits_{6}^{f(x)}{\frac{4{{t}^{3}}}{x-2}}\]dt equals [AIEEE 2005]
A.	12
B.	18
C.	24
D.	36
Answer» C. 24

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Let \[f:R\to R\]be a differentiable function having \[f(2)=6,f'(2)=\left( \frac{1}{48} \right).\] Then \[\underset{x\to 2}{\mathop{\lim }}\,\int\limits_{6}^{f(x)}{\frac{4{{t}^{3}}}{x-2}}\]dt equals [AIEEE 2005]

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