Presentation is loading. Please wait.

Presentation is loading. Please wait.

Chapter 2 Limits and Continuity Section 2.3 Continuity.

Published byLester Davis Modified over 5 years ago

Similar presentations

Presentation on theme: "Chapter 2 Limits and Continuity Section 2.3 Continuity."— Presentation transcript:

1 Chapter 2 Limits and Continuity Section 2.3 Continuity

2 Quick Review

3 Quick Review

4 Quick Review

5 Quick Review

6 Quick Review Solutions

7 Quick Review Solutions

8 Quick Review Solutions

9 Quick Review Solutions

10 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.

11 Continuity at a Point

12 Example Continuity at a Point

13 Continuity at a Point

14 Continuity at a Point

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

16 Continuity at a Point

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

18 Continuous Functions

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

20 Properties of Continuous Functions

21 Composite of Continuous Functions

22 Intermediate Value Theorem for Continuous Functions

23 Intermediate Value Theorem for Continuous Functions

24 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.

Download ppt "Chapter 2 Limits and Continuity Section 2.3 Continuity."

Similar presentations

AP Calculus Review First Semester Differentiation to the Edges of Integration Sections 1.2-3.7, 3.9, (7.7)

AP Calculus Review First Semester Differentiation to the Edges of Integration Sections , 3.9, (7.7)
2.3 Continuity When you plot function values generated in a laboratory or collected in a field, you can connect the plotted points with an unbroken curve.

2.3 Continuity When you plot function values generated in a laboratory or collected in a field, you can connect the plotted points with an unbroken curve.
1.5 Continuity. Most of the techniques of calculus require that functions be continuous. A function is continuous if you can draw it in one motion without.

1.5 Continuity. Most of the techniques of calculus require that functions be continuous. A function is continuous if you can draw it in one motion without.
Sec 2.5: CONTINUITY. Study continuity at x = 4 Sec 2.5: CONTINUITY Study continuity at x = 2.

Sec 2.5: CONTINUITY. Study continuity at x = 4 Sec 2.5: CONTINUITY Study continuity at x = 2.
Continuity Section 2.3a.

Continuity Section 2.3a.
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 2- 1.

Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 2- 1.
1.5 Infinite Limits. Copyright © Houghton Mifflin Company. All rights reserved. 21-2 Figure 1.25.

1.5 Infinite Limits. Copyright © Houghton Mifflin Company. All rights reserved Figure 1.25.
Chapter Two Limits and Their Properties. Copyright © Houghton Mifflin Company. All rights reserved. 2 | 2 The Tangent Line Problem.

Chapter Two Limits and Their Properties. Copyright © Houghton Mifflin Company. All rights reserved. 2 | 2 The Tangent Line Problem.
Continuity Section 2.3.

Continuity Section 2.3.
Continuity Grand Canyon, Arizona Greg Kelly, Hanford High School, Richland, WashingtonPhoto by Vickie Kelly, 2002.

Continuity Grand Canyon, Arizona Greg Kelly, Hanford High School, Richland, WashingtonPhoto by Vickie Kelly, 2002.
2.3 Continuity. What you’ll learn about Continuity at a Point Continuous Functions Algebraic Combinations Composites Intermediate Value Theorem for Continuous.

2.3 Continuity. What you’ll learn about Continuity at a Point Continuous Functions Algebraic Combinations Composites Intermediate Value Theorem for Continuous.
SAT Prep. Continuity and One-Sided Limits Determine continuity at a point and an open interval Determine one-sided limits and continuity on a closed interval.

SAT Prep. Continuity and One-Sided Limits Determine continuity at a point and an open interval Determine one-sided limits and continuity on a closed interval.
Continuity Chapter 2: Limits and Continuity.

Continuity Chapter 2: Limits and Continuity.
A function, f, is continuous at a number, a, if 1) f(a) is defined 2) exists 3)

A function, f, is continuous at a number, a, if 1) f(a) is defined 2) exists 3)
2.3 Continuity.

2.3 Continuity.
Informal Description f(x) is continuous at x=c if and only if there are no holes, jumps, skips or gaps in the graph of f(x) at c.

Informal Description f(x) is continuous at x=c if and only if there are no holes, jumps, skips or gaps in the graph of f(x) at c.
Review Limits When you see the words… This is what you think of doing…  f is continuous at x = a  Test each of the following 1.

Review Limits When you see the words… This is what you think of doing…  f is continuous at x = a  Test each of the following 1.
Chapter 2 Review Calculus. Quick Review 1.) f(2) = 0 2.) f(2) = 11/12 3.) f(2) = 0 4.) f(2) = 1/3.

Chapter 2 Review Calculus. Quick Review 1.) f(2) = 0 2.) f(2) = 11/12 3.) f(2) = 0 4.) f(2) = 1/3.
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall 2.3 Continuity.

Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall 2.3 Continuity.
1.4 Continuity  f is continuous at a if 1. is defined. 2. exists. 3.

1.4 Continuity  f is continuous at a if 1. is defined. 2. exists. 3.

Similar presentations

Ads by Google