2.3 Limits of Functions

Summary

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. Quiz Take a quiz. 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" Information on Leibniz 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

Interesting Application Nothing yet has been found. Any ideas?

2.2 The Legacy of Galileo, Newton, and Leibniz

Table of Contents

2.4 Limits at Infinity

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