Question

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

Answer 1

`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`