Find the cofficient of `x^(50)` In `(1+x)^(101) x(1-x+x^(2))^(100)`.

Find the coefficient of x^(2) in ((a)/(a+x))^(1//2)+ ((a)/(a-x))^(1//2)

If |x| lt 1 , then find the coefficient of x^(n) in the expansion of (1+2x+3x^(2)+4x^(3)+….)^(1//2)

Find the derivative of tan^(-1)"" ( 2 x )/( 1 - x^(2)) w.r.t. sin ^(-1) "" ( 2 x)/( 1 + x^(2))

Find the range of f(x) = cot^(-1)(2x - x^2)

If sin^(-1)x+sin^(-1) y + sin ^(-1) z = (3pi)/2 , the value of x^(100)+y^(100)+z^(100) -9/(x^(101)+y^(101)+z^(101)) is : (i)0 (ii)1 (iii)2 (iv)3

Find the derivative of f(x)=(2x+3)/(x-1)

Find the range of the function f(x)=(1+x^2)/(x^2)