Limits Involving Infinity

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Presentation transcript:

Limits Involving Infinity Chapter 2 Limits and Continuity Section 2.2 Limits Involving Infinity

Quick Review

Quick Review

Quick Review

Quick Review

Quick Review Solutions [12,12] by [8,8] [6,6] by [4,4]

Quick Review Solutions

Quick Review Solutions

Quick Review Solutions

What you’ll learn about The Squeeze Theorem for limits at infinity Asymptotic and unbounded behavior of functions End behavior of functions …and why Limits can be used to describe the behavior of functions for numbers large in absolute value.

Finite limits as x→±∞ The symbol for infinity (∞) does not represent a real number. We use ∞ to describe the behavior of a function when the values in its domain or range outgrow all finite bounds. For example, when we say “the limit of f as x approaches infinity” we mean the limit of f as x moves increasingly far to the right on the number line. When we say “the limit of f as x approaches negative infinity (–∞)” we mean the limit of f as x moves increasingly far to the left on the number line.

Horizontal Asymptote

Example Horizontal Asymptote [-6,6] by [-5,5]

Example Sandwich Theorem Revisited

Properties of Limits as x→±∞

Properties of Limits as x→±∞

Properties of Limits as x→±∞

Infinite Limits as x→a

Vertical Asymptote

Example Vertical Asymptote

End Behavior Models

End Behavior Models

Example End Behavior Models

End Behavior Models

Example “Seeing” Limits as x→±∞

Quick Quiz Sections 2.1 and 2.2

Quick Quiz Sections 2.1 and 2.2

Quick Quiz Sections 2.1 and 2.2

Quick Quiz Sections 2.1 and 2.2

Quick Quiz Sections 2.1 and 2.2

Quick Quiz Sections 2.1 and 2.2

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