If |x|<1 and |y|<1, find the sum to infinity of the series : `(x+y)+(x^2+x y+y^2)+(x^3+x^2y+x y^2+y^3)+` .......

If f(x) = tan^-1x,g(x) = tan^-1((1+x)/(1-x)) fo |x| < 1, show that f' (x) = g' (x) and g(x) - f(x) = pi/4

If {x} and [x] represent fractional and integral part of x respectively then solve the equation x-1=(x-[x])(x-{x})

If f(x) = |(sin x, cos x , tan x),(x^3, x^2 ,x),(2x, 1,x)| then Lim_(x to 0) (f(x))/(x^2) equals

Statement I f(x) = |x| sin x is differentiable at x = 0. Statement II If g(x) is not differentiable at x = a and h(x) is differentiable at x = a, then g(x).h(x) cannot be differentiable at x = a

If f(x) = x/(x-1) , then show that fof (x) = x.

If f(x) =x/(x-1) then show that (fof)(x) = x.

If f(x) = log x and g(x) = e^x then fog(x) is :

If f(x) = |x| + |x-1|-|x-2| , then f(x)

If f(x)=x.e^(x(1-x), then f(x) is