Example Problem 1. Limits Involving Infinity | Rice University

University
Rice University
Course
Preparing for the AP Calculus AB Exam
Pages

1

Academic year

2022
Author

Incapbosh
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82

p {margin: 0; padding: 0;} .ft00{font-size:20px;font-family:Arial;color:#000000;} .ft01{font-size:16px;font-family:ArialMT;color:#000000;} .ft02{font-size:16px;line-height:21px;font-family:ArialMT;color:#000000;} Limits Involving Infinity. Example Problem 1 When doing limits to infinity, the only thing of significance is the degree of the numerator andthe degree of the denominator. In this problem, we're looking at a numerator degree of 3, and the denominator degree is 6.When analyzing this function, we are looking at its behavior as a whole. This functionbehaves like 10x cubed over 3x to the sixth. Which, when reduced, and the coefficientsare effectively negligible, this will behave like 1 over x cubed.When you consider that the graph of 1 over x cubed has a vertical asymptote at 0, it can beseen to be in quadrants III and I.Thus, if we consider the limit of x as x approaches infinity, as x increases without bound, they-value becomes smaller and smaller.By looking at the equivalent term here, 1 over infinity cubed, you can see that an infinitelylarge number divided by an infinitely large number results in a very small number. So we'llsay that the limit is 0. We can also say that y = 0 is a horizontal asymptote of the graph.