1 / 11

1.3 Evaluating Limits Analytically

1.3 Evaluating Limits Analytically. Properties of Limits. If f(x) is continuous then direct substitution will find limits Continuous? Lines, polynomials, absolute value → yes Rational, Radical,… → better check Direct substitution also works for trig functions.

Jimmy
Download Presentation

1.3 Evaluating Limits Analytically

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. 1.3Evaluating Limits Analytically

  2. Properties of Limits • If f(x) is continuous then direct substitution will find limits • Continuous? • Lines, polynomials, absolute value → yes • Rational, Radical,… → better check • Direct substitution also works for trig functions

  3. Constant function like y = 3 All are continuous so these are just direct substitution Try Example 1

  4. Other properties: most are obvious… Example 2

  5. Example 3

  6. Example 4-5

  7. General Strategy • Recognize if direct substitution will find the limit at c • If not, try to find an equivalent function where direct substitution will work: • Factor, rationalize, simplify • Use a graph/table to check Problem Set 1.3.1

  8. Is there a difference between the graphs of the following functions?

  9. Finding Limits: Rationalizing • Factor or eliminate radicals to make an equivalent function • Evaluate this equivalent function for the limit at the undefined value Example Find the limit:

  10. Example Find the limit:

  11. 2 Useful Trig Limits Example Find the limit:

More Related