For each real `x, -1 lt x lt 1`. Let A(x) be the matrix `(1-x)^(-1) [(1,-x),(-x,1)]` and `z=(x+y)/(1+xy)`. Then

Lt_(x to 1)x^((1)/(1-x))=

For -1 lt x lt 1, if f(x)= cos^(2)(tan^(-1)sqrt((1-x)/(1+x))) then f'(x)=

If |x| lt 1 , then (1)/(2) log((1+x)/(1-x))=

For a real number 'a' with |a| lt 1 , if x = a - a^(3) + a^(5)-…, y = 1+a^(2) + a^(4)+… and z = (1)/(a) + a^(3) + a^(7)+… then show that a^(2)z = xy .

Using monotonicity prove that x lt - ln (1-x) lt x (1-x)^(-1) for 0 lt x lt 1

y = cos^(-1)((1-x^2)/(1+x^2)), 0 lt x lt 1 .

y = sin^(-1)((1-x^2)/(1+x^2)), 0 lt x lt 1 .