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x^2 + 1/x^2 +2 -2x -2/x...

`x^2 + 1/x^2 +2 -2x -2/x`

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Without expanding, find the value of: (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

Solve: |[x^2-1, x^2+2x+1, 2x^2+3x+1], [2x^2+x-1, 2x^2+5x-3, 2x^2+4x-3], [6x^2-x-2, 6x^2-7x+2, 12x^2-5x-2]|=0.

Solve: |[x^2-1, x^2+2x+1, 2x^2+3x+1], [2x^2+x-1, 2x^2+5x-3, 2x^2+4x-3], [6x^2-x-2, 6x^2-7x+2, 12x^2-5x-2]|=0.

Solve: |x^2-1x^2+2x+1 2x^2+3x+1 2x^2+x-1 2x^2+5x-3 2x^2+4x-3 6x^2-x-2 6x^2-7x+2 12 x^2-5x-2|=0.

If : cot theta = (2x(x+1))/(2x+1), "then" : cos theta = A) (2x + 1 )/(2x^(2) + 2x + 1 ) B) (2x )/(2x^(2) + 2x + 1 ) C) (2x(x+1) )/(2x^(2) + 2x + 1 ) D) (x+1)/(2x+1)

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

int((1-x^(-2))/(x^(1/2)-x^(-1/2))-(2)/(x^(3/2))+(x^(-2)-x)/(x^(1/2)-x^(-1/2)))dx

int((1-x^(- 2))/(x^(1//2)-x^(-1//2))-2/(x^(3//2))+(x^(- 2)-x)/(x^(1//2)-x^(-1//2)))dx

Evaluate the following limit: (lim)_(x->2)(1/(x-2)-2/(x^2-2x))