Find the limit of the following equation

Question

As x approaches 2

(x³-8)/(x-2)

Answer 1

x³ - 8 = (x - 2)(x² + 2x + 4)

So when we divide by (x - 2), the "x - 2" 's will cancel leaving limit as x approaches 2 of x² + 2x + 4

Now, we can plug in x = 2

2² + 2(2) + 4 = 3 + 4 + 4 = 12

Answer 2

Hello Velesia,

There are a few different ways to do this, including graphing the function, factoring out the (x-2), and using the technique from calculus known as l'Hospital's rule.

Since you listed "calculus" in the description, I've uploaded a short video which will walk you through the steps of using l'Hospital's rule. It looks like William W. already explained how to factor and then plug in two, and that works just as well for this problem, but your teacher will probably ask you to use l'Hospital's rule on things that can't be factored as well.

Best,

Mark R.