Let the `f (x) ` be differentiabe function on the interval `(0,oo) ` such that `f (1) =1 and lim _(t to x) ((t ^(2) f (x) -x ^(2) f (t))/(t ^(2) -x ^(2))) =1/2 AAx gt 0,` 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

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 a diffentiable function in [-1,oo) and f (0) =1 such that Lim _(t to x +1) (t^(2) f(x+1) -(x+1) ^(2) f(t))/(f (t) -f(x+1))=1. Find the value of Lim _(x to 1) (ln (f(x )) -ln 2)/(x-1) .

f (x) = int _(0) ^(x) e ^(t ^(3)) (t ^(2) -1) (t+1) ^(2011) dt (x gt 0) then :

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=

If f(x)=int_(1)^(x)(logt)/(1+t+t^(2)) , AAx ge 1 , then f(2) is equal to

Let f be continuous function on [0,oo) such that lim _(x to oo) (f(x)+ int _(o)^(x) f (t ) (dt)) exists. Find lim _(x to oo) f (x).

Let f:(0,oo)->R be a differentiable function such that f'(x)=2-f(x)/x for all x in (0,oo) and f(1)=1 , then

Let f:RrarrR be such that f(a)=1, f(a)=2 . Then lim_(x to 0)((f^(2)(a+x))/(f(a)))^(1//x) is

Let f (x) =(1)/(x ^(2)) int _(4)^(x) (4t ^(2) -2 f '(t) dt, find 9f'(4)