How do you find the limit lim_(x->4)(x^3-64)/(x^2-8x+16) ?

1 Answer
Sep 17, 2014

First factor the denominator...

(x^3-64)/((x-4)(x-4))

Now factor the numerator...

((x-4)(x^2+4x+16))/((x-4)(x-4))

Divide numerator and denominator by x-4...

(x^2+4x+16)/(x-4)

Replace all x's with the limit being approached (4)...

((4)^2+4(4)+16)/((4)-4)

Combine terms...

48/0

The limit approaches infinity since division by 0 is undefined, but division by 0 also approaches infinity.