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Let f:RtoR be a differentiable function ...

Let `f:RtoR` be a differentiable function such that `f(x)=x^(2)+int_(0)^(x)e^(-t)f(x-t)dt`.
`y=f(x)` is

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The correct Answer is:
2
`g(x)=int_(x)^((pi)/2)(f'(t)cosect-f(t)cosectcott)dt`
`=int_(x)^((pi)/2)d/(dt)(f(t)cosect)dt`
`f((pi)/2)cosec((pi)/2)-(f(x))/(sinx)=3-(f(x))/(sinx)`
`:.lim_(xto0) g(x)=3-log_(xto 0)(f(x))/(sinx)`
`=lim_(xto 0)g(x)`
`=3-log(f'(x))(cosx)` (using L'Hopital Rule)
`=3-1 ( :' f'(0)=1)`
`=2`
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