1 / 12

Limits Involving Infinity

Photo by Vickie Kelly, 2006. Greg Kelly, Richland, Washington. Limits Involving Infinity. North Dakota Sunset. As the denominator gets larger, the value of the fraction gets smaller. There is a horizontal asymptote if:. or. This number becomes insignificant as .

Antony
Télécharger la présentation

Limits Involving 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. Photo by Vickie Kelly, 2006 Greg Kelly, Richland, Washington Limits Involving Infinity North Dakota Sunset

  2. As the denominator gets larger, the value of the fraction gets smaller. There is a horizontal asymptote if: or

  3. This number becomes insignificant as . There is a horizontal asymptote at 1. Example 1:

  4. Find: When we graph this function, the limit appears to be zero. so for : by the squeeze theorem: Example 2:

  5. Example 3: Find:

  6. Infinite Limits: As the denominator approaches zero, the value of the fraction gets very large. vertical asymptote at x=0. If the denominator is positive then the fraction is positive. If the denominator is negative then the fraction is negative.

  7. Example 4: The denominator is positive in both cases, so the limit is the same.

  8. A function g is: a right end behavior model for f if and only if a left end behavior model for f if and only if End Behavior Models: End behavior models model the behavior of a function as x approaches infinity or negative infinity.

  9. As , approaches zero. becomes a right-end behavior model. As , increases faster than x decreases, therefore is dominant. becomes a left-end behavior model. Example 7: (The x term dominates.) Test of model Our model is correct. Test of model Our model is correct.

  10. becomes a right-end behavior model. On your calculator, graph: Use: becomes a left-end behavior model. Example 7:

  11. Example 7: Right-end behavior models give us: dominant terms in numerator and denominator

  12. Often you can just “think through” limits.

More Related