Chapter 2 Limits and Continuity Section 2.3 Continuity.

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Presentation transcript:

Chapter 2 Limits and Continuity Section 2.3 Continuity

Quick Review

Quick Review

Quick Review

Quick Review

Quick Review Solutions

Quick Review Solutions

Quick Review Solutions

Quick Review Solutions

What you’ll learn about Definition of continuity at a point Types of discontinuities Sums, differences, products, quotients, and compositions of continuous functions Common continuous functions Continuity and the Intermediate Value Theorem …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.

Continuity at a Point

Example Continuity at a Point

Continuity at a Point

Continuity at a Point

Continuity at a Point The typical discontinuity types are: Removable (2.21b and 2.21c) Jump (2.21d) Infinite (2.21e) Oscillating (2.21f)

Continuity at a Point

Example Continuity at a Point [5,5] by [5,10]

Continuous Functions

Continuous Functions [5,5] by [5,10]

Properties of Continuous Functions

Composite of Continuous Functions

Intermediate Value Theorem for Continuous Functions

Intermediate Value Theorem for Continuous Functions

Intermediate Value Theorem for Continuous Functions 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.