Limits and Continuity
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Limits and Continuity Chapter 2:
description
Limits and Continuity. Chapter 2:. Aim #2.2 How do we solve limits as x approaches +/- infinity?. We use infinity when the values in its domain or range outgrow all finite bounds . Graph y = 1/x What happens as x approaches to + infinity? What happens as x approaches to - infinity?. - PowerPoint PPT Presentation
Transcript of Limits and Continuity
Limits and Continuity
Chapter 2:
Aim #2.2 How do we solve limits as x approaches +/- infinity?
• We use infinity when the values in its domain or range outgrow all finite bounds.
• Graph y = 1/x • What happens as x approaches to + infinity?• What happens as x approaches to - infinity?
Definition: Horizontal Asymptote
Example 1: Looking for Horizontal Asymptotes
Graph the following f(x)
Theorem 5
Example 5: Using the Theorem 5
Infinite Limits as x ---a
• Graph the function f(x)= 1/x. What happens as x approaches 0 from the right?
• From the left? What does y approach?
Definition: Vertical Asymptotes
Example 4: Finding the Vertical Asymptote
What does f(x) approach as x approaches 0 from the right? From the left?
Example 5: Finding Vertical Asymptotes
• What are the vertical asymptotes of • f(x)= tan x?
End Behavior Models
• For numerically large values of x, we can sometimes model the behavior of a
complicated function by a simpler one that acts virtually the same way.
Example 6:
Definition End Behavior Models
Example 7:
Seeing Limits as x approaches +/- infinity
• We can investigate the graph of y =f(x) as x approaches +/- infinity by investigating the graph of y =f(1/x) as x approaches infinity.
Example 9: Using Substitution
Summary: Answer in complete sentences.• Explain why there is no value L for which lim
as x approaches infinity for sin x = L
