If `f` is a positive function such that `f(x+T)=f(x)(T>0), AA x in R,` then `lim_(n->oo)n((f(x+T)+2f(x+2T)+.......+nf(x+n T))/(f(x+T)+4f(x+4T)+.......+n^2f(x+n^2T)})=`

If f is a positive function such that f(x+T)=f(x)(T>0),AA x in R, then lim_(n rarr oo)n((f(x+T)+2f(x+2T)+......+nf(x+nT))/(f(x+T)+4f(x+4T)+......+n^(2)f(x+n^(2)T)))=

if f be a differentiable function such that f(x) =x^(2)int_(0)^(x)e^(-t)f(x-t). dt. Then f(x) =

If f(x) is differentiable function and f(x)=x^(2)+int_(0)^(x) e^(-t) (x-t)dt ,then f)-t) equals to

Let f(x) be a continuous and periodic function such that f(x)=f(x+T) for all xepsilonR,Tgt0 .If int_(-2T)^(a+5T)f(x)dx=19(agt0) and int_(0)^(T)f(x)dx=2 , then find the value of int_(0)^(a)f(x)dx .

Let f(x) be a continuous and periodic function such that f(x)=f(x+T) for all xepsilonR,Tgt0 .If int_(-2T)^(a+5T)f(x)dx=19(ag0) and int_(0)^(T)f(x)dx=2 , then find the value of int_(0)^(a)f(x)dx .

Let f(x) be a continuous and periodic function such that f(x)=f(x+T) for all xepsilonR,Tgt0 .If int_(-2T)^(a+5T)f(x)dx=19(ag0) and int_(0)^(T)f(x)dx=2 , then find the value of int_(0)^(a)f(x)dx .

Let f(x) be a continuous and periodic function such that f(x)=f(x+T) for all xepsilonR,Tgt0 .If int_(-2T)^(a+5T)f(x)dx=19(ag0) and int_(0)^(T)f(x)dx=2 , then find the value of int_(0)^(a)f(x)dx .

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

If f is continuous function and F(x)=int_(0)^(x)((2t+3)*int_(t)^(2)f(u)du)dt, then |(F^(n)(2))/(f(2))| is equal to