 ## 2.3 Limits of Functions

### Summary

The concept of the limit of a function at a point is formally introduced. Rules for computing limits are also given, and some situations are described where the limit does not exist.

By the end of your studying, you should know:

• How to evaluate the limit of f(x) as x approaches a number a.
• How to evaluate left-hand limits and right-hand limits.
• The relationship between the limit of a function at a point, and left-hand and right-hand limits of the function at the point.
• How to evaluate limits of sums, differences, products, and quotients of functions
• How to evaluate limits involving absolute values.

On-screen applet instructions: Use the slider to let h -> 0 and investigate the limiting behavior of f(2 + h) as h -> 0. Compare approaching h = 0 from the right, and from the left. Why does, or doesn't, the limit exist at h = 0?

### Examples Let and What is  Evaluate the limit  Let  Find conditions on coefficients a and e so that ### Applets Limits of Functions

### Videos

See short videos of worked problems for this section.

### Exercises

See Exercises for 2.3 Limits of Functions (PDF).

Work online to solve the exercises for this section, or for any other section of the textbook.

### Resources on the Web

Information on Newton
Biographical data from St. Andrew's University's Web site
Excerpt from W.W. Rouse Ball's "A Short Account of the History of Mathematics"

Calculus Applications
Project Intermath

Limits of Functions
Kouba
Metric

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Copyright © 2005 Donald L. Kreider, C. Dwight Lahr, Susan J. Diesel