`T x=2/(3^(x-1))` then find `S_oo` is:

If f:[1,oo) to [1,oo) is defined by f(x) = 2^(x(x-1)) then find f^(-1)(x) .

Let f" [1,2] to (-oo,oo) be given by f(x)=(x^(4)+3x^(2)+1)/(x^(2)+1) then find value of in [f_(max)]" in "[-1,2] where [.] is greatest integer function :

Let f" [1,2] to (-oo,oo) be given by f(x)=(x^(4)+3x^(2)+1)/(x^(2)+1) then find value of in [f_(max)]" in "[-1,2] where [.] is greatest integer function :

If lim_(x->oo) f(x) exists and is finite and nonzero and if lim_(x->oo) {f(x)+(3f(x)−1)/(f^2(x))}=3 ,then find the value of lim_(x->oo) f(x)

If f :[2,oo)rarr(-oo,4], where f(x)=x(4-x) then find f^-1(x)

If S_(n) denotes the sum of first 'n' natural numbers then s_(1)+S_(2)x+S_(3)x^(2)+.........+S_(n) x^(n-1)+......oo=(1-x)^(-n) then n is

Given that lim_(x to oo)(int_(0)^(x)(t^(2))/(sqrt(a+t))dt)/(bx-sinx) = 1 , then find the values of a and b.

If x=int_(0)^(oo)(dt)/((1+t^(2))(1+t^(2017))) , then (3x)/(pi) is equal to

If x=int_(0)^(oo)(dt)/((1+t^(2))(1+t^(2017))) , then (3x)/(pi) is equal to