Home > APCALC > Chapter 10 > Lesson 10.2.1 > Problem10-111

10-111.

Evaluate each of the following limits. Homework Help ✎

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

Which term is the dominant term? (Or you can use l'Hôpital's Rule.)

1. $\lim\limits _ { x \rightarrow 0 } \frac { \operatorname { sin } ^ { - 1 } ( x ) } { x ^ { 2 } }$

Use l'Hôpital's Rule.

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

$n$ is a number. The variable is $x$.

$= \lim\limits_{x\to 3}nx^{n-1}$

1. $\lim\limits _ { x \rightarrow 1 ^ { - } } \frac { \operatorname { ln } ( 1 - x ) } { \operatorname { cot } ( \pi x ) }$

Use l'Hôpital's Rule twice.

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

$=\lim\limits_{x\to\infty}\frac{2x}{2^x\ln(2)}$