Chapter 2  2012 Pearson Education, Inc. 2.3 Section 2.3 Continuity 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

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  Continuity at a Point  Continuous Functions  Algebraic Combinations  Composites  Intermediate Value Theorem for Continuous Functions …and why Continuous functions are used to describe how a body moves through space and how the speed of a chemical reaction changes with time.

Slide  2012 Pearson Education, Inc. Continuity at a Point

Slide  2012 Pearson Education, Inc. Example Continuity at a Point o

Slide  2012 Pearson Education, Inc. Continuity at a Point

Slide  2012 Pearson Education, Inc. Continuity at a Point

Slide  2012 Pearson Education, Inc. Continuity at a Point The typical discontinuity types are: a)Removable(2.21b and 2.21c) b)Jump (2.21d) c)Infinite(2.21e) d)Oscillating (2.21f)

Slide  2012 Pearson Education, Inc. Continuity at a Point

Slide  2012 Pearson Education, Inc. Example Continuity at a Point [  5,5] by [  5,10]

Slide  2012 Pearson Education, Inc. Continuous Functions

Slide  2012 Pearson Education, Inc. Continuous Functions [  5,5] by [  5,10]

Slide  2012 Pearson Education, Inc. Properties of Continuous Functions

Slide  2012 Pearson Education, Inc. Composite of Continuous Functions

Slide  2012 Pearson Education, Inc. Intermediate Value Theorem for Continuous Functions

Slide  2012 Pearson Education, Inc. The Intermediate Value Theorem for Continuous Functions is the reason why the graph of a function continuous on an interval cannot have any breaks. The graph will be connected, a single, unbroken curve. It will not have jumps or separate branches. Intermediate Value Theorem for Continuous Functions