Download presentation

Presentation is loading. Please wait.

Published byRiley Toop Modified over 2 years ago

1
**3.5 Limits at Infinity Determine limits at infinity**

Determine the horizontal asymptotes, if any, of the graph of function. Standard 4.5a

2
**Do Now: Complete the table.**

x -∞ -100 -10 -1 1 10 100 ∞ f(x)

3
**x decreases x increases f(x) approaches 2 f(x) approaches 2 x -∞ -100**

1 10 100 ∞ f(x) 2 1.99 1.96 .667 f(x) approaches 2 f(x) approaches 2

4
**Limit at negative infinity**

Limit at positive infinity

5
**To Infinity and Beyond…**

We want to investigate what happens when functions go To Infinity and Beyond…

7
**Definition of a Horizontal Asymptote**

The line y = L is a horizontal asymptote of the graph of f if

8
Limits at Infinity If r is a positive rational number and c is any real number, then Furthermore, if xr is defined when x < 0, then

9
**Finding Limits at Infinity**

10
**Finding Limits at Infinity**

is an indeterminate form

11
**Divide numerator and denominator by highest degree of x**

Simplify Take limits of numerator and denominator

14
**Guidelines for Finding Limits at ± ∞ of Rational Functions**

If the degree of the numerator is < the degree of the denominator, then the limit is 0. If the degree of the numerator = the degree of the denominator, then the limit is the ratio of the leading coefficients. If the degree of the numerator is > the degree of the denominator, then the limit does not exist.

15
For x < 0, you can write

16
**Limits Involving Trig Functions**

As x approaches ∞, sin x oscillates between -1 and 1. The limit does not exist. By the Squeeze Theorem

17
**Sketch the graph of the equation using extrema, intercepts, and asymptotes.**

Similar presentations

© 2017 SlidePlayer.com Inc.

All rights reserved.

Ads by Google