Download presentation

Presentation is loading. Please wait.

Published byKathleen Elwood Modified over 3 years ago

1
Chapter 3: Applications of Differentiation L3.5 Limits at Infinity

2
Limits at Infinity End behavior of a function over an infinite interval left end behavior right end behavior If a function grows without bound or oscillates as x→ − ∞ or x→∞, then dne If the line y = L is a horizontal asymptote of the graph of f, then or The above implies that a function can have up to two horizontal asymptotes (HAs) –Rational functions have at most one HA –Functions that are not rational can have up to two HAs

3
Limits at Infinity: Rational Functions Rational Functions have up to one horizontal asymptote: –HA is y = 0 if deg(numerator) < deg(denominator) –HA is y = ‘ratio of leading coefficients’ if deg(num) = deg(denom) –Otherwise, no horizontal asymptote Examples: 1. a. b. 2. 3. 4.

4
Limits at Infinity: Non Rational Functions Functions that are not rational (include ) may approach different horizontal asymptotes at the left and right ends. Example: For x > 0,. So For x < 0,. So Recall that

Similar presentations

OK

1.5: Limits Involving Infinity Learning Goals: © 2009 Mark Pickering Calculate limits as Identify vertical and horizontal asymptotes.

1.5: Limits Involving Infinity Learning Goals: © 2009 Mark Pickering Calculate limits as Identify vertical and horizontal asymptotes.

© 2018 SlidePlayer.com Inc.

All rights reserved.

To make this website work, we log user data and share it with processors. To use this website, you must agree to our Privacy Policy, including cookie policy.

Ads by Google

Ppt on inhabiting other planets found Ppt on l&t finance holding share price Ppt on motivation for management students Ppt on endangered species of plants and animals Ppt on c language operators Ppt on history of cricket for class 9 Ppt on effects of global warming on weather Ppt on asymptotic notation of algorithms meaning Ppt on stock market Ppt on linear equations in two variables worksheet