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

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#.

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