### Home > PC3 > Chapter 13 > Lesson 13.1.2 > Problem13-21

13-21.

Evaluate each the following limits.

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

The dominant term is in the denominator.
Therefore as $x→−∞$, the fraction gets closer to __.

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

The dominant term is $\left|x\right|$ in the numerator (square root of $x^{2}$ is $\left|x\right|$) and $2x$ in the denominator.