Let `f(x)` be differentiable on the interval `(0,oo)` such that `f(1)=1` and `lim_(t->x) (t^2f(x)-x^2f(t))/(t-x)=1` for each `x>0`. Then `f(x)=`

Let f(x) be differentiable on the interval (0,oo) such that f(1)=1 and lim_(t rarr x)(t^(2)f(x)-x^(2)f(t))/(t-x)=1 for each x>0 Then f(x)=

Let f(x) be differntiable on the interval (0,oo) such that f(1)=1 and lim_(t tox)(t^(2)f(x)-x^(2)f(t))/(t-x)=1 for each xgt0 . Then f(x) is :

If f(x) is differentiable function in the interval (0,oo) such that f(1) = 1 and lim_(trarrx) (t^(2)f(x)-x^(2)(t))/(t-x)=1 for each x gt 0 , then f((3)/(2)) is equal tv

If f(x) is a differentiable function in the interval (0, oo) such that f(1)=1 and underset(t to x)lim(t^(2)f(x)-x^(2)f(t))/(t-x)=1 , for each x gt 0 then f((3)/(2)) is equal to

Let f:(0, oo)rarr(0, oo) be a differentiable function such that f(1)=e and lim_(trarrx)(t^(2)f^(2)(x)-x^(2)f^(2)(t))/(t-x)=0 . If f(x)=1 , then x is equal to :

Let f(x) be a differentiable function such that f(x)=x^2 +int_0^x e^-t f(x-t) dt then int_0^1 f(x) dx=