CPM Homework Help : PC Problem 10-42

Evaluate the following limits.

$\lim \limits _ { x \rightarrow \infty } \frac { 3 x ( 2 x - 3 ) ^ { 2 } } { 50 - 3 x ^ { 3 } }$
Hint (a):
What are the dominant terms?
Step (a):
The dominant term in the numerator in $12x^{3}$ .

$\lim \limits _ { x \rightarrow 2 } \frac { 5 x ^ { 2 } - 20 } { x ^ { 2 } + x - 6 }$
Hint (b):
Substituting in $x = 2$ gives an undefined value.
Step (b):
Factor and simplify. Then substitute in $x = 2$ .