CPM Homework Help : PC3 Problem 13-34

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13-34.

Evaluate each of the following limits.

$\lim \limits _ { x \rightarrow 4 } \frac { \sqrt { x } - 2 } { x - 4 }$
Hint (a):
After rationalizing the numerator, did you get:
$\lim_{\text{x}\to4}\frac{\text{x}-4}{(\text{x}-4)(\sqrt{\text{x}}+2)}$

$\lim \limits _ { x \rightarrow 6 } \frac { \sqrt { x + 2 } - \sqrt { 2 } } { x }$
Hint (b):
Is it necessary to rationalize the numerator in this case?
What happens when you just use substitution?

$\lim \limits _ { x \rightarrow 2 } \frac { x ^ { 3 } - 8 } { x - 2 }$
Hint (c):
Recall the cubic factoring formula:
$a^3-b^3=(a-b)(a^2+ab+b^2)$

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