1 / 6

INFINITE LIMITS (1.5)

September 11th, 2017. INFINITE LIMITS (1.5). I. INFINITE LIMITS.

cbrinkley
Download Presentation

INFINITE LIMITS (1.5)

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. September 11th, 2017 INFINITE LIMITS (1.5)

  2. I. INFINITE LIMITS Def: An infinite limit is a limit in which f(x) increases or decreases without bound as x approaches c. Although we may assign the values of infinity or negative infinity for these limits, the limits still fail to exist because they lack a real number value.

  3. II. VERTICAL ASYMPTOTES Def: If f(x) approaches infinity (or negative infinity) as x approaches c from the right or left, then the line x=c is a vertical asymptote of the graph of f.

  4. Thm. 1.14: Vertical Asymptotes: Let f and g be continuous on an open interval containing c. If and there exists an open interval containing c such that for all in the interval, then the graph of the function given by has a vertical asymptote at x=c.

  5. Thm. 1.15: Properties of Infinite Limits: Let c and L be real numbers and f and g be functions such that • and • 1. Sum or difference: • 2. Product: • 3. Quotient: • Similar properties hold for one-sided limits and for functions for which the limit as x approaches c is negative infinity.

  6. Ex. 1: Find each limit.

More Related