Section 12.8 Power Series AP Calculus March 25, 2010 CASA.

Slides:

Advertisements

Similar presentations

Appendix E Sigma Notation AP Calculus November 11, 2009 Berkley High School, D1B1

Advertisements

Power Series is an infinite polynomial in x Is a power series centered at x = 0. Is a power series centered at x = a. and.

Section 5.5 – The Real Zeros of a Rational Function

Section 4.4 Limits at Infinity; Horizontal Asymptotes AP Calculus November 2, 2009 Berkley High School, D1B1

9.5 Testing Convergence at Endpoints Quick Review.

11.8 Power Series.

Solve polynomial equations with complex solutions by using the Fundamental Theorem of Algebra. 5-6 THE FUNDAMENTAL THEOREM OF ALGEBRA.

Section 8.5: Power Series Practice HW from Stewart Textbook (not to hand in) p. 598 # 3-17 odd.

Power Series Section 9.1. If the infinite series converges, then.

1 Chapter 9. 2 Does converge or diverge and why?

Power Series A power series is an infinite polynomial.

Copyright © Cengage Learning. All rights reserved.

Section 6.6 The Fundamental Theorem of Algebra

Section 4.10 Antiderivatives

Remainder Theorem Section 5.5 Part 1.

A power series with center c is an infinite series where x is a variable. For example, is a power series with center c = 2.

Rational Zero Theorem Rational Zero Th’m: If the polynomial

Maclaurin and Taylor Series; Power Series

Clicker Question 1 The series A. converges absolutely.

Section 4.5 Summary of Curve Sketching

Section 11.3 – Power Series.

Chapter 5 Series Solutions of Linear Differential Equations.

Clicker Question 1 The series A. converges absolutely.

AP Calculus BC September 22, 2016.

Calculus II (MAT 146) Dr. Day Wednesday May 2, 2018

Math – Power Series.

Section 9.4b Radius of convergence.

Radius and Interval of Convergence

Alternating Series Test

9.4 Radius of Convergence.

Copyright © Cengage Learning. All rights reserved.

Testing Convergence at Endpoints

Unit 5 – Series, Sequences, and Limits Section 5

Section 11.4 – Representing Functions with Power Series

Section 11.3 Power Series.

Section 6.1 Areas Between Curves

182A – Engineering Mathematics

AP Calculus March 22, 2010 Berkley High School, D1B1

Chapter 8 Infinite Series.

Find the sums of these geometric series:

Taylor Series and Maclaurin Series

Copyright © Cengage Learning. All rights reserved.

5.1 Power Series Method Section 5.1 p1.

Clicker Question 1 The series A. converges absolutely.

AP Calculus March 31, 2017 Mrs. Agnew

AP Calculus March 22, 2010 Berkley High School, D1B1

Fundamental Theorem of Algebra

Copyright © Cengage Learning. All rights reserved.

If x is a variable, then an infinite series of the form

Section 10.6 Linear Differential Equations

Representation of Functions by Power Series

Section 10.4 Exponential Growth and Decay

Section 13.6 – Absolute Convergence

Power Series (9.8) March 9th, 2017.

Section 5.5 The Substitution Rule

Section 6: Power Series & the Ratio Test

Approximation and Computing Area

The Real Zeros of a Polynomial Function

The Real Zeros of a Polynomial Function

Calculus, ET First Edition

Find the interval of convergence of the series. {image}

Find the interval of convergence of the series. {image}

Taylor and Maclaurin Series

Section 13.6 – Absolute Convergence

Pre-AP Pre-Calculus Chapter 2, Section 5

Power Series Lesson 9.8.

Polynomial with infinit-degree

TAYLOR SERIES Maclaurin series ( center is 0 )

Power Series Solutions of Linear DEs

Presentation transcript:

Section 12.8 Power Series AP Calculus March 25, 2010 CASA

Calculus, Section 12.8, Todd Fadoir, CASA, 2005 Power Series A power series is a series in the form: We use “c” because they act like coefficients; it looks to be an infinitely long polynomial. Calculus, Section 12.8, Todd Fadoir, CASA, 2005

Power Series Centered at a A power series centered at a is the form: Because of this distinction, we sometimes call a power series centered at zero Calculus, Section 12.8, Todd Fadoir, CASA, 2005

Calculus, Section 12.8, Todd Fadoir, CASA, 2005

Calculus, Section 12.8, Todd Fadoir, CASA, 2005 Insight Power Series are always convergent at their “center” Why? Calculus, Section 12.8, Todd Fadoir, CASA, 2005

Calculus, Section 12.8, Todd Fadoir, CASA, 2005

Calculus, Section 12.8, Todd Fadoir, CASA, 2005

Calculus, Section 12.8, Todd Fadoir, CASA, 2005

Calculus, Section 12.8, Todd Fadoir, CASA, 2005 Theorem Power Series is always convergent in one of three ways Only at the “center” (x=a) For all values x=(-∞,∞) There is some R (called the radius of convergence) that creates an interval of convergence (a-R,a+R). The series may or may not be convergent at the endpoints. Calculus, Section 12.8, Todd Fadoir, CASA, 2005

Calculus, Section 12.8, Todd Fadoir, CASA, 2005

Calculus, Section 12.8, Todd Fadoir, CASA, 2005

Calculus, Section 12.8, Todd Fadoir, CASA, 2005

Calculus, Section 12.8, Todd Fadoir, CASA, 2005

Calculus, Section 12.8, Todd Fadoir, CASA, 2005 Assignment 12.8: 1-27 odd Calculus, Section 12.8, Todd Fadoir, CASA, 2005