lim_(x->0) 1/x^2-(x-2)/(x^3-x)= ?

1 Answer
Dec 26, 2017

oo

Explanation:

color(white)(=)lim_(x->0) 1/x^2-(x-2)/(x^3-x)
=lim_(x->0) 1/x^2-(x-2)/(x(x^2-1))
Common denomiator
=lim_(x->0) ((x^2-1)-x(x-2))/(x^2(x^2-1))
=lim_(x->0) (x^2-1-x^2+2x)/(x^2(x^2-1))
=lim_(x->0) (-1+2x)/(x^2(-1+x^2))
=lim_(x->0) 1/x^2(1-2x)/(1-x^2)
=lim_(x->0) 1/x^2 xx lim_(x->0) (1-2x)/(1-x^2) = oo xx 1 = oo