`x(x^2+2x)=`

Let f (x) =x + sqrt(x^(2) +2x) and g (x) = sqrt(x^(2) +2x)-x, then:

Prove that sqrt(x^2+2x+1)-sqrt(x^2-2x+1)={-2, x 1

Prove that sqrt(x^2+2x+1)-sqrt(x^2-2x+1)={-2, x 1

Prove that sqrt(x^2+2x+1)-sqrt(x^2-2x+1) ={ -2, x 1 }

Evaluate the following limit: (lim)_(x->2)(x/(x-2)-4/(x^2-2x))

The expression x^4+4 can be factorized as (a) (x^2+2x+2)(x^2-2x+2) (b) (x^2+2x+2)(x^2+2x-2) (c) (x^2-2x-2)(x^2-2x+2) (d) (x^2+2)(x^2-2)

Evaluate: int(2+x+x^2)/(x^2(2+x))+(2x-1)/((x+1)^2)\ dx

lim_(x->oo) ((x^2-2x+1)/(x^2-4x+2))^x is equal to

int(x^3)/(x+1)\ dx is equal to (a) x+(x^2)/2+(x^3)/3-log|1-x|+C (b) x+(x^2)/2-(x^3)/3-log|1-x|+C (c) x-(x^2)/2-(x^3)/3-log|1+x|+C (d) x-(x^2)/2+(x^3)/3-log|1+x|+C

Simplify the product: (x^2+2x+2)(x^2-2x+2)