What is the limit of #(x^2-4)/(x-2)# as #x# approaches 2?

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Answer 1 · 2014-10-18T05:12:42

A direct substitution results in the indeterminate form #0/0#. We should then try to simplify the function.

In this example we see that the numerator is a difference of perfect squares.

Remember factoring rules back to Algebra I.

#(a^2-b^2)=(a-b)(a+b)#

In this example

#(x^2-4)=(x^2-2^2)=(x-2)(x+2)#

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

Cancel out the factor #(x-2)#

#lim_(x->2) (x+2)#

Direct substitution

#(2+2) = 4#