How do you determine the limit of #(x^2 -2x) / (x^2 - 4x + 4)# as x approaches 2-?

1 Answer
Bdub
Apr 13, 2016

#lim_(x->2^-) (x^2-2x)/(x^2-4x+4) = -oo#

Explanation:

#lim_(x->2^-) (x(x-2))/((x-2)(x-2))#
#lim_(x->2^-) x/(x-2)#

If we put in values close to 2 from the left of 2 like 1.9, 1.99..etc we see that our answer gets bigger in the negative direction going to negative infinity.

#lim_(x->2^-) x/(x-2) =-oo#

If you graph it as well you will see that as x comes to 2 from the left y drops without bound going to negative infinity.

You can also use L'Hopital's Rule but it will be the same answer.

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