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Question

Let F:RR be a differentiable function such that F(x)=f(x)416t3x3dt,f(3)=4 & f(3)=116 then the value of limx3F(x) is

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Solution

F(x)=f(x)416t3x3dt
limx3F(x)=limx3f(x)416t3x3dt=limx316(f(x))3f(x)1 (00,L-Hospital)=16×431×116=64

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