### Home > PC3 > Chapter 13 > Lesson 13.1.3 > Problem13-35

13-35.

Without using a calculator, evaluate each of the following limits.

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

$\lim_{x\to -\infty}\frac{x^2}{2x^2}$

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

Since the dominant term is in the denominator, therefore the limit is __.

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

Since the dominant term is in the numerator, the limit is __.
Pay attention to the $−$ in $−∞$.

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

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

1. $\lim \limits _ { x \rightarrow 0 } \frac { 2 x ^ { 3 } - 7 } { 3 x ^ { 3 } + 4 x - 5 }$