2.4 Limits at Infinity
By the end of your studying, you should know:
On-screen applet instructions: The slider generates values of x linearly from x = 0 to x = 20. At this value of x the slider is 3/4 of the way to the right. After that the values of x increase exponentially as the slider is moved the remaining distance to the right end. This allows us to explore "large" values of x.
ExamplesFind the horizontal and vertical asymptotes of
Allyson carries an 80 degree cup of coffee into a room which has been heated to 20 degrees. According to Newton's Law of Cooling, the temperature of the coffee at time t will be
Population growth is often modeled by the equation
AppletsLimits of Functions
VideosSee short videos of worked problems for this section.
ExercisesSee Exercises for 2.4 Limits at Infinity (PDF).
Work online to solve the exercises for this section, or for any other section of the textbook.
Resources on the WebInformation on Newton
Biographical data from St. Andrew's University's Web site
Excerpt from W.W. Rouse Ball's "A Short Account of the History of Mathematics"
Limits as x Approaches Infinity
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Copyright © 2005 Donald L. Kreider, C. Dwight Lahr, Susan J. Diesel