### Home > PC > Chapter 8 > Lesson 8.1.3 > Problem8-40

8-40.

Without using your calculator, find the following limits.

1. $\lim\limits _ { x \rightarrow - \infty } \frac { x ^ { 2 } + 3 } { 2 x ^ { 2 } - 5 x }$

Since the dominant term is in both the numerator and the denominator, the limit is

$\frac {1}{2}; \text{ (the ratio of their coefficients).}$

2. $\lim\limits _ { x \rightarrow - \infty } \frac { 5 x ^ { 3 } + 7 x } { x ^ { 4 } - 4 x }$

Since the dominant term is in the denominator, the limit is $0$.

3. $\lim\limits _ { x \rightarrow - \infty } \frac { - 6 x ^ { 3 } + 8 x ^ { 2 } } { 15 x ^ { 2 } - 2 }$

Since the dominant term is in the numerator, the limit is $+∞$.
The negative input will be multiplied by itself $4$ times.