[" 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)" is "]

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 :

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)=

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 :

If lim_(t rarr x)(x^2f^2(t)-t^2f^2(x))/(t-x)=0 and f(1)=e then solution of f(x)=1 is