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

1 Answer
Oct 18, 2014

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