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Question

Let f:RR be a continuously differentiable function such that f(2)=6 and f(2)=148.
If f(x)64t3 dt=(x2)g(x), then limx2 g(x) is equal to

A
12
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B
18
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C
24
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D
36
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Solution

The correct option is B 18
f(x)64t3 dt=(x2)g(x)
g(x)=f(x)64t3 dtx2; x2
limx2 g(x)=limx2f(x)64t3 dtx2
Apply L'Hospital Rule,
limx2 g(x)=limx24(f(x))3f(x)1
limx2 g(x)=4(f(2))3f(2)=463148=18

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