How do you find the limit of (x^3 - x)/(x-1)^2 as x approaches 1?

1 Answer
May 22, 2017

lim_(x->1-)[(x^3-x)/(x-1)^2]=-oo
lim_(x->1+)[(x^3-x)/(x-1)^2]=+oo

Explanation:

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

However when lim_(x->1-)[(x^3-x)/(x-1)^2]=-oo and lim_(x->1+)[(x^3-x)/(x-1)^2]=+oo. This is because you can approach 1 at either side and this is important because it will determine the sign of x-1.