Use algebra to evaluate the limit. limx →∞ x e^-x

Name: Problem 32, Chapter 1: Calculus Single Variable
Uploaded: 2021-04-23T15:31:23-08:00
Duration: 1 min 1 s
Channel: Suzanne W.
Description: Use algebra to evaluate the limit. limx →∞ x e^-x

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Limits of Functions

This concept involves analyzing the behavior of a function as its variable approaches a particular value, such as infinity. It is fundamental in calculus for understanding the long-term trends of functions.

Exponential Functions

Exponential functions are characterized by constant relative growth or decay rates. When the exponent is negative, as in e^(-x), the function rapidly decreases towards zero as the variable increases.

Growth Rate Comparison

This concept focuses on comparing the rates at which different types of functions either grow or decay. In many cases, exponential decay outpaces polynomial growth, leading to a product that approaches zero as the variable becomes large.

Algebraic Manipulation

Algebraic manipulation involves rewriting and simplifying expressions to make the evaluation of limits more straightforward. This may include factoring, canceling terms, or rearranging factors to reveal the dominant behavior as the variable approaches infinity.

Transcript

Please give Ace some feedback