How do you find the limit of # (x^3 - x) / (x -1)# as x approaches 1?
1 Answer
Aug 28, 2016
The limit can be evaluated by cancelling out
#color(blue)(lim_(x->1) (x^3 - x)/(x - 1))#
#= lim_(x->1) (x(x^2 - 1))/(x - 1)#
Since
#=> lim_(x->1) (x(x + 1)cancel((x - 1)))/cancel((x - 1))#
#= lim_(x->1) x(x + 1)#
Now you can just plug
#=> (1)(1 + 1) = color(blue)(2)#
And you can see from Wolfram Alpha that it is indeed correct.