### Home > PC3 > Chapter 13 > Lesson 13.1.3 > Problem13-34

13-34.

Evaluate each of the following limits.

1. $\lim \limits _ { x \rightarrow 4 } \frac { \sqrt { x } - 2 } { x - 4 }$

After rationalizing the numerator, did you get:

$\lim_{\text{x}\to4}\frac{\text{x}-4}{(\text{x}-4)(\sqrt{\text{x}}+2)}$

1. $\lim \limits _ { x \rightarrow 6 } \frac { \sqrt { x + 2 } - \sqrt { 2 } } { x }$

Is it necessary to rationalize the numerator in this case?
What happens when you just use substitution?

1. $\lim \limits _ { x \rightarrow 2 } \frac { x ^ { 3 } - 8 } { x - 2 }$

Recall the cubic factoring formula:

$a^3-b^3=(a-b)(a^2+ab+b^2)$