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10-61.

Evaluate the following limits.

$\lim\limits _ { x \rightarrow 2 } \frac { 2 x ^ { 3 } - 8 x } { x ^ { 2 } + x - 6 }$
Hint (a):
Try substituting in $x = 2$ . What happens?
Steps (a):
Completely factor both the numerator and denominator. Simplify. Substitute in $x = 2$ .
Answer (a):
$\frac{16}{5}$

$\lim\limits _ { x \rightarrow - \infty } \frac { 2 x ^ { 3 } - 8 x } { x ^ { 2 } + x - 6 }$
Hint (b):
Use the dominant term idea.

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