1 / 17

3.5 Limits at Infinity

3.5 Limits at Infinity. Determine limits at infinity Determine the horizontal asymptotes, if any, of the graph of function. Standard 4.5a. Do Now: Complete the table. x decreases. x increases. f(x ) approaches 2. f( x ) approaches 2. Limit at negative infinity.

rigg
Download Presentation

3.5 Limits at Infinity

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. 3.5 Limits at Infinity Determine limits at infinity Determine the horizontal asymptotes, if any, of the graph of function. Standard 4.5a

  2. Do Now: Complete the table.

  3. x decreases x increases f(x) approaches 2 f(x) approaches 2

  4. Limit at negative infinity • Limit at positive infinity

  5. We want to investigate what happens when functions go To Infinity and Beyond…

  6. Definition of a Horizontal Asymptote The line y = L is a horizontal asymptote of the graph of f if

  7. Limits at Infinity If r is a positive rational number and c is any real number, then Furthermore, if xr is defined when x < 0, then

  8. Finding Limits at Infinity

  9. Finding Limits at Infinity is an indeterminate form

  10. Divide numerator and denominator by highest degree of x Simplify Take limits of numerator and denominator

  11. Guidelines for Finding Limits at± ∞ of Rational Functions If the degree of the numerator is < the degree of the denominator, then the limit is 0. If the degree of the numerator = the degree of the denominator, then the limit is the ratio of the leading coefficients. If the degree of the numerator is > the degree of the denominator, then the limit does not exist.

  12. For x < 0, you can write

  13. Limits Involving Trig Functions As x approaches ∞, sin x oscillates between -1 and 1. The limit does not exist. By the Squeeze Theorem

  14. Sketch the graph of the equation using extrema, intercepts, and asymptotes.

More Related