" (iw) "(x+1)(2x+1)^(1/3)

Let f: RvecRf(x)=x^3-3x^2+3x-2, then f^(-1)(x) is given by 1+(x+1)^(1/3) (2) 1+(x-1)^(1/3) x+1 3-1 (4) x-1 3-1

Value of ((x-1)^(3)+(2x-1)^(3)-(3x2)^(3))/((x-1)(2x-1)(3x-2)) is equal to (A)-3(B)0(C)1(D)3

If D(x)=det[[(x-1),(x-1)^(2),x^(3)(x-1),x^(2),(x+1)^(3)x,(x+1)^(2),(x+1)^(3) then the coefficient of x in D(x), is ]]

Coefficient of x^(n) in ((1+x)(1+2x)(1+3x))/((1-x)(1-2x)(1-3x)) is

Without expanding, find the value of: (i) (x + 1)^4 - 4(x + 1)^3 (x - 1) + 6(x + 1)^2 (x - 1)^2 - 4(x + 1) (x - 1)^3 + (x -1)^4 (ii) (2x - 1)^4 + 4(2x - 1)^3 (3 - 2x) + 6(2x - 1)^2 (3 - 2x)^2 + 4(2x - 1) (3 - 2x)^3 + (3 - 2x)^4

Let a,b,c be such that (1)/((1-x)(1-2x)(1-3x))=(a)/(1-x)+(b)/(1-2x)+(c)/(1-3x) then (a)/(1)+(b)/(3)+(c)/(5)

Let a, b, c such that (1)/((1-x)(1-2x)(1-3x))=(a)/(1-x)+(b)/(1-2x)+(c)/(1-3x), a/1+b/3+c/5=

(x)/(x+1)+(1)/(2)((x)/(x+1))^(2)+(1)/(3)((x)/(x+1))^(3)+....=