How do you find the limit of (x^3 - x)/(x-1)^2 as x approaches 1? Calculus Limits Determining Limits Algebraically 1 Answer Altrigeos 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. Answer link Related questions How do you find the limit lim_(x->5)(x^2-6x+5)/(x^2-25) ? How do you find the limit lim_(x->3^+)|3-x|/(x^2-2x-3) ? How do you find the limit lim_(x->4)(x^3-64)/(x^2-8x+16) ? How do you find the limit lim_(x->2)(x^2+x-6)/(x-2) ? How do you find the limit lim_(x->-4)(x^2+5x+4)/(x^2+3x-4) ? How do you find the limit lim_(t->-3)(t^2-9)/(2t^2+7t+3) ? How do you find the limit lim_(h->0)((4+h)^2-16)/h ? How do you find the limit lim_(h->0)((2+h)^3-8)/h ? How do you find the limit lim_(x->9)(9-x)/(3-sqrt(x)) ? How do you find the limit lim_(h->0)(sqrt(1+h)-1)/h ? See all questions in Determining Limits Algebraically Impact of this question 1531 views around the world You can reuse this answer Creative Commons License