### Home > PC > Chapter 10 > Lesson 10.1.3 > Problem10-42

10-42.

Evaluate the following limits.

1. $\lim \limits _ { x \rightarrow \infty } \frac { 3 x ( 2 x - 3 ) ^ { 2 } } { 50 - 3 x ^ { 3 } }$

What are the dominant terms?

The dominant term in the numerator in $12x^{3}$.

1. $\lim \limits _ { x \rightarrow 2 } \frac { 5 x ^ { 2 } - 20 } { x ^ { 2 } + x - 6 }$

Substituting in $x = 2$ gives an undefined value.

Factor and simplify. Then substitute in $x = 2$.