The coeff. of `x^4` in `(3 - 2x)^(-3//4)`; for `|x| lt 1` is

The coeff. Of x^2 in (1+x^2)/((1-x)^3) is

Find the coeff of x^(100) in (3-5x)/((1-x)^(2))

The equation x^(4) -2x^(3) - 3x^(2) + 4x-1=0 has four distinct real roots x_1,x_2,x_3,x_4 such that x_1 lt x_2 lt x_3 lt x_4 and product of two roots is unity , then : x_1x_2+x_1x_3 + x_2x_4+x_3x_4 is equal to :

The equation x^(4) -2x^(3) - 3x^(2) + 4x-1=0 has four distinct real roots x_1,x_2,x_3,x_4 such that x_1 lt x_2 lt x_3 lt x_4 and product of two roots is unity , then : x_2^(3)+x_4^3 is equal to :

Let w(x) = 4x^(3) - 3x^(2) on - (1)/(4) lt x lt (3)/(4) . Discuss the extrema of w .

If 1+ 2x + 3x^(2) + 4x^(3) + …oo= (9)/(4) (|x| lt 1) then x=

3(1-x) lt 2(x+4)

3(1-x) lt 2(x+4)