If `f(x)=lim_(n->oo)[2x+4x^3+6x^5++2n x^(2n-1)]` `(0ltxlt1)` then `int f(x)dx` is equal to:

If f(x)=lim_(n->oo) {2x+4x^3+...+2n x^(2n-1)}, 0 < x< 1 and int f(x) dx = F(x) and F(1/sqrt(2)) = 2, then (i) F(0)=1, (ii) F(1/2)=4/3, (iii) F(0)=-1, (iv) F(-1/2)=4/3

If f(x)=lim_(n rarr oo)n^(2)(x^((1)/(n))-x^((1)/(n)+1)),x>0 then int xf(x)dx is

let f(x)=lim_(n rarr oo)(x^(2n)-1)/(x^(2n)+1)

Let f(x)=lim_(n->oo)(2x^(2n)sin(1/x)+x)/(1+x^(2n)) then find (a) lim_(x->oo) xf(x) (b) lim_(x->1) f(x) (c) lim_(x->0) f(x) (d) lim_(x->-oo) f(x)

Let f(x)=lim_( n to oo)(cosx)/(1+(tan^(-1)x)^(n)) . Then the value of int_(o)^(oo)f(x)dx is equal to

Let f(x)=lim_( n to oo)(cosx)/(1+(tan^(-1)x)^(n)) . Then the value of int_(o)^(oo)f(x)dx is equal to

Let f(x)=lim_( n to oo)(cosx)/(1+(tan^(-1)x)^(n)) . Then the value of int_(o)^(oo)f(x)dx is equal to

Let f(x)=lim_(n to oo) sinx/(1+(2 sin x)^(2n)) then f is discontinuous at

int_n^(n+1)f(x) dx=n^2+n then int_(-1)^1 f(x) dx =