Limits and Continuity Section 2.3 Continuity.

Slides:

Advertisements

Similar presentations

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

Advertisements

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.

Section 1.4.  “open interval”- an interval where the function values at the endpoints are undefined (a, b)  “closed interval”- an interval where the.

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.

Continuity Section 2.3a.

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

1.5 Infinite Limits. Copyright © Houghton Mifflin Company. All rights reserved Figure 1.25.

1 Continuity at a Point and on an Open Interval. 2 In mathematics, the term continuous has much the same meaning as it has in everyday usage. Informally,

Section 1.4: Continuity and One-Sided Limits

2.3 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.

Continuity Section 2.3.

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.

MAT 125 – Applied Calculus 2.5 – One-Sided Limits & Continuity.

Section 2.5 Continuity. CONTINUITY AT A NUMBER a Definition: A function f is continuous at a number a if.

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.

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

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.

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.

1-4: Continuity and One-Sided Limits

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.

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

2.7: Continuity and the Intermediate Value Theorem Objectives: Define and explore properties of continuity Introduce Intermediate Value Theorem ©2002.

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

LIMITS OF FUNCTIONS. CONTINUITY Definition (p. 110) If one or more of the above conditions fails to hold at C the function is said to be discontinuous.

Limits and Continuity Unit 1 Day 4.

DEFINITION Continuity at a Point f (x) is defined on an open interval containingopen interval x = c. If, then f is continuous at x = c. If the limit does.

CALCULUS CHAPTER 1 Section 1.4: Continuity and One-Sided Limits Calculus Chapter 1 Section 4 1.

Definition: Continuous A continuous process is one that takes place gradually, without interruption or abrupt change.

Copyright © 2016, 2012, and 2010 Pearson Education, Inc. 1 What you ’ ll learn about Definition of continuity at a point Types of discontinuities Sums,

Section 1.8 Continuity. CONTINUITY AT A NUMBER a.

1 Limits and Continuity. 2 Intro to Continuity As we have seen some graphs have holes in them, some have breaks and some have other irregularities. We.

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

Calculus 1-4 Continuity and One-Sided Limits. Vocabulary Continuous: A function that is uninterrupted in the given interval None of these is continuous.

Chapter 2.3 Continuity. Objectives Continuity at a Point Continuous Functions Algebraic Combinations Composites Intermediate Value Theorem for Continuous.

1.4 Continuity Calculus.

Ch. 2 – Limits and Continuity

Continuity and One-Sided Limits (1.4)

Rates of Change and Limits

Rates of Change and Limits

Ch. 2 – Limits and Continuity

Section 3.4 – Combinations of Functions

2.3 Continuity Grand Canyon, Arizona

Continuity Sec. 2.3.

Continuity Grand Canyon, Arizona.

INFINITE LIMITS Section 1.5.

AP Calculus Honors Ms. Olifer

Continuous & Types of Discontinuity

1.6 Continuity Objectives:

Cornell Notes Section 1.3 Day 2 Section 1.4 Day 1

Definite Integrals and Antiderivatives

Chapter 2 Limits and Continuity Section 2.3 Continuity.

Sec 2.5: Continuity Continuous Function

Continuity A function is Continuous if it can be drawn without lifting the pencil, or writing utensil, from the paper. A continuous function has no breaks,

Definite Integrals & Antiderivatives

Chapter 2 Limits and Continuity Section 2.3 Continuity.

INFINITE LIMITS Section 1.5.

Rates of Change and Limits

Combinations of Functions

Sec 2.5: Continuity Continuous Function

Chapter 2 Limits and Continuity Section 2.3 Continuity.

Limits and Their Properties

Presentation transcript:

Limits and Continuity Section 2.3 Continuity

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

Solution

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 Example

1 2 3 4

Intermediate Value Theorem for Continuous Functions

Intermediate Value Theorem for Continuous Functions

Example

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.

1 2 3