Chapter 2  2012 Pearson Education, Inc. 2.2 Limits Involving Infinity Section 2.2 Limits and Continuity

Slide  2012 Pearson Education, Inc. Quick Review

Slide  2012 Pearson Education, Inc. Quick Review

Slide  2012 Pearson Education, Inc. Quick Review

Slide  2012 Pearson Education, Inc. Quick Review

Slide  2012 Pearson Education, Inc. Quick Review Solutions [  12,12] by [  8,8][  6,6] by [  4,4]

Slide  2012 Pearson Education, Inc. Quick Review Solutions

Slide  2012 Pearson Education, Inc. Quick Review Solutions

Slide  2012 Pearson Education, Inc. Quick Review Solutions

Slide  2012 Pearson Education, Inc. What you’ll learn about  Finite Limits as x→±∞  Sandwich Theorem Revisited  Infinite Limits as x→a  End Behavior Models  Seeing Limits as x→±∞ …and why Limits can be used to describe the behavior of functions for numbers large in absolute value.

Slide  2012 Pearson Education, Inc. 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.

Slide  2012 Pearson Education, Inc. Horizontal Asymptote

Slide  2012 Pearson Education, Inc. [-6,6] by [-5,5] Example Horizontal Asymptote

Slide  2012 Pearson Education, Inc. Example Sandwich Theorem Revisited

Slide  2012 Pearson Education, Inc. Properties of Limits as x→±∞

Slide  2012 Pearson Education, Inc. Properties of Limits as x→±∞

Slide  2012 Pearson Education, Inc. Properties of Limits as x→±∞

Slide  2012 Pearson Education, Inc. Infinite Limits as x→a

Slide  2012 Pearson Education, Inc. Vertical Asymptote

Slide  2012 Pearson Education, Inc. Example Vertical Asymptote [  6,6] by [  6,6]

Slide  2012 Pearson Education, Inc. End Behavior Models

Slide  2012 Pearson Education, Inc. Example End Behavior Models

Slide  2012 Pearson Education, Inc. End Behavior Models

Slide  2012 Pearson Education, Inc. End Behavior Models

Slide  2012 Pearson Education, Inc. Example “Seeing” Limits as x→±∞

Slide  2012 Pearson Education, Inc. Quick Quiz Sections 2.1 and 2.2

Slide  2012 Pearson Education, Inc. Quick Quiz Sections 2.1 and 2.2

Slide  2012 Pearson Education, Inc. Quick Quiz Sections 2.1 and 2.2

Slide  2012 Pearson Education, Inc. Quick Quiz Sections 2.1 and 2.2

Slide  2012 Pearson Education, Inc. Quick Quiz Sections 2.1 and 2.2

Slide  2012 Pearson Education, Inc. Quick Quiz Sections 2.1 and 2.2