Power Series, Interval of Convergence

Slides:



Advertisements
Similar presentations
A series converges to λ if the limit of the sequence of the n-thpartial sum of the series is equal to λ.
Advertisements

Series: Guide to Investigating Convergence. Understanding the Convergence of a Series.
Series: Guide to Investigating Convergence. Understanding the Convergence of a Series.
Warm Up 6.0 Students find the derivatives of parametrically defined functions and use implicit differentiation in a wide variety of problems in physics,
Thursday, November 08, 2018Thursday, November 08, 2018
Chapter 8.7 LaGrange Error Bound
Chapter 8.7 Taylor Polynomials and Approximations
Find the Limit Chapter 7.7 L’Hopital’s Rule Tuesday, November 27, 2018
Warm Up Chapter 3.4 Concavity and the Second Derivative Test
Chapter 5.4 Integrating with e Friday, November 30, 2018
Radius and Interval of Convergence
Power Series, Interval of Convergence
Chapter Graphs Functions
Warm Up Chapter Sine and Cosine Graphs
Wednesday, December 05, 2018Wednesday, December 05, 2018
Warm Up Chapter 4.4 The Fundamental Theorem of Calculus
Chapter 8.2 Geometric Series Wednesday, December 05, 2018
Chapter 12.1 Finding Numeric Limits
Chapter 8.5 Alternating Series Saturday, December 08, 2018
Warm Up Chapter 5.4 e derivatives Saturday, December 08, 2018
Warm Up Chapter 8.10 Taylor and Maclaurin Series
Warm Up Chapter 2.2 Basic Differentiation Rules and Rates of Change
Chapter Graphs Functions
Chapter 8.6 Ratio Test Sunday, December 30, 2018
5.) Given: Carlos is tall. Paul is short.
Warm Up Logarithmic Functions and Their Graphs
Warm Up 1 Chapter 1.2 Thursday, January 03, 2019
Warm Up Chapter 5.4 e derivatives Monday, January 14, 2019
Warm Up Chapter 1.3 Wednesday, January 16, 2019
Warm Up Chapter Sine and Cosine Graphs
Warm Up Five Chapter 2.5 More Implicit Differentiation 2/17/2019
Warm Up Chapter 1.3 Monday, February 18, 2019
Evaluate Expressions and use exponents
Warm Up Chapter Sine and Cosine Graphs Friday, February 22, 2019
Chapter 12.1 Finding Numeric Limits
Warm Up Find the distance between the two points
Warm Up Chapter Sine and Cosine Graphs Monday, February 25, 2019
Wednesday, February 27, 2019Wednesday, February 27, 2019
Warm Up Chapter 8.1 Sequences 2/27/2019
Approximate the integral
Chapter 8.8 Improper Integrals
Chapter 12.2 Removable Discontinuities and Algebraic Methods
Warm Up Chapter Radians and Degrees Thursday, February 28, 2019
5.) Given: Carlos is tall. Paul is short.
P-Series and Integral Test
If x is a variable, then an infinite series of the form
Wednesday, April 10, 2019.
Chapter 7.3 Partial Fractions
Warm Up Logarithmic Functions and Their Graphs
Warm Up Chapter 05.3 Trig Equations Thursday, April 25, 2019
Warm Up Asymptotes Thursday, April 25, 2019 TBA
Warm Up Chapter 3.4 Concavity and the Second Derivative Test
P-Series and Integral Test
Warm Up Chapter 5.4 e derivatives Friday, May 10, 2019
Warm Up Chapter 8.1 Sequences 5/7/2019
Warm Up Chapter Log Properties Friday, May 17, 2019
12.8 Power Series. Radius and interval of convergence
Power Series, Geometric
Warm Up Chapter 4.3 Riemann Sums and Definite Integrals
Chapter 12.2 Removable Discontinuities and Algebraic Methods
Power Series, Geometric
Chapter Functions Tuesday, May 28, 2019
Find the interval of convergence of the series. {image}
Find the interval of convergence of the series. {image}
Warm Up Chapter 2.5 Implicit Differentiation
Warm Up Chapter Radians and Degrees Friday, July 05, 2019
Warm Up Chapter 3.4 Concavity and the Second Derivative Test
Chapter Combinations of Functions
Warm Up Asymptotes Tuesday, June 25, 2019 TBA
Telescoping and Partial Sums
Presentation transcript:

Power Series, Interval of Convergence Chapter 9.8 Power Series, Interval of Convergence 23.0 Students demonstrate an understanding of the definitions of convergence and divergence of sequences and series of real numbers. By using such tests as the comparison test, ratio test, and alternate series test, they can determine whether a series converges. 4/20/2019 ESLR -Tracy High Graduates will be Independent Learners Who Set realistic and challenging goals

Power Series, Interval of Convergence Chapter 9.8 Power Series, Interval of Convergence 23.0 Students demonstrate an understanding of the definitions of convergence and divergence of sequences and series of real numbers. By using such tests as the comparison test, ratio test, and alternate series test, they can determine whether a series converges. 4/20/2019 ESLR -Tracy High Graduates will be Independent Learners Who Set realistic and challenging goals

For what value(s) of x does the power series converge? Chapter 9.8 Power Series, Interval of Convergence 23.0 Students demonstrate an understanding of the definitions of convergence and divergence of sequences and series of real numbers. By using such tests as the comparison test, ratio test, and alternate series test, they can determine whether a series converges. For what value(s) of x does the power series converge? 4/20/2019 ESLR -Tracy High Graduates will be Independent Learners Who Set realistic and challenging goals

Informal investigation: Chapter 9.8 Power Series, Interval of Convergence 23.0 Students demonstrate an understanding of the definitions of convergence and divergence of sequences and series of real numbers. By using such tests as the comparison test, ratio test, and alternate series test, they can determine whether a series converges. Informal investigation: For what value(s) of x does the power series converge? 4/20/2019 ESLR -Tracy High Graduates will be Independent Learners Who Set realistic and challenging goals

Informal investigation: Chapter 9.8 Power Series, Interval of Convergence 23.0 Students demonstrate an understanding of the definitions of convergence and divergence of sequences and series of real numbers. By using such tests as the comparison test, ratio test, and alternate series test, they can determine whether a series converges. Informal investigation: For what value(s) of x does the series converge? 4/20/2019 ESLR -Tracy High Graduates will be Independent Learners Who Set realistic and challenging goals

Ratio Test Chapter 9.8 Power Series, Interval of Convergence 4/20/2019 23.0 Students demonstrate an understanding of the definitions of convergence and divergence of sequences and series of real numbers. By using such tests as the comparison test, ratio test, and alternate series test, they can determine whether a series converges. Ratio Test 4/20/2019 ESLR -Tracy High Graduates will be Independent Learners Who Set realistic and challenging goals

For what value(s) of x does the power series converge? Chapter 9.8 Power Series, Interval of Convergence 23.0 Students demonstrate an understanding of the definitions of convergence and divergence of sequences and series of real numbers. By using such tests as the comparison test, ratio test, and alternate series test, they can determine whether a series converges. For what value(s) of x does the power series converge? Radius of convergence Centered at x=0 4/20/2019 ESLR -Tracy High Graduates will be Independent Learners Who Set realistic and challenging goals

Power Series, Interval of Convergence Chapter 9.8 Power Series, Interval of Convergence 23.0 Students demonstrate an understanding of the definitions of convergence and divergence of sequences and series of real numbers. By using such tests as the comparison test, ratio test, and alternate series test, they can determine whether a series converges. 4/20/2019 ESLR -Tracy High Graduates will be Independent Learners Who Set realistic and challenging goals

Remember that the ratio test is inconclusive when the ratio = 1. Chapter 9.8 Power Series, Interval of Convergence 23.0 Students demonstrate an understanding of the definitions of convergence and divergence of sequences and series of real numbers. By using such tests as the comparison test, ratio test, and alternate series test, they can determine whether a series converges. MUST PLUG IN ENDPOINTS AND CHECK TO SEE IF x=1 or x=3 cause convergence or divergence. Remember that the ratio test is inconclusive when the ratio = 1. 4/20/2019 ESLR -Tracy High Graduates will be Independent Learners Who Set realistic and challenging goals

Power Series, Interval of Convergence Chapter 9.8 Power Series, Interval of Convergence 23.0 Students demonstrate an understanding of the definitions of convergence and divergence of sequences and series of real numbers. By using such tests as the comparison test, ratio test, and alternate series test, they can determine whether a series converges. 4/20/2019 ESLR -Tracy High Graduates will be Independent Learners Who Set realistic and challenging goals

Power Series, Interval of Convergence Chapter 9.8 Power Series, Interval of Convergence 23.0 Students demonstrate an understanding of the definitions of convergence and divergence of sequences and series of real numbers. By using such tests as the comparison test, ratio test, and alternate series test, they can determine whether a series converges. 4/20/2019 ESLR -Tracy High Graduates will be Independent Learners Who Set realistic and challenging goals

Power Series, Interval of Convergence Chapter 9.8 Power Series, Interval of Convergence 23.0 Students demonstrate an understanding of the definitions of convergence and divergence of sequences and series of real numbers. By using such tests as the comparison test, ratio test, and alternate series test, they can determine whether a series converges. 4/20/2019 ESLR -Tracy High Graduates will be Independent Learners Who Set realistic and challenging goals

Power Series, Interval of Convergence Chapter 9.8 Power Series, Interval of Convergence 23.0 Students demonstrate an understanding of the definitions of convergence and divergence of sequences and series of real numbers. By using such tests as the comparison test, ratio test, and alternate series test, they can determine whether a series converges. 4/20/2019 ESLR -Tracy High Graduates will be Independent Learners Who Set realistic and challenging goals

Power Series, Interval of Convergence Chapter 9.8 Power Series, Interval of Convergence 23.0 Students demonstrate an understanding of the definitions of convergence and divergence of sequences and series of real numbers. By using such tests as the comparison test, ratio test, and alternate series test, they can determine whether a series converges. 4/20/2019 ESLR -Tracy High Graduates will be Independent Learners Who Set realistic and challenging goals

Practice: Chapter 9.8 Power Series, Interval of Convergence 4/20/2019 23.0 Students demonstrate an understanding of the definitions of convergence and divergence of sequences and series of real numbers. By using such tests as the comparison test, ratio test, and alternate series test, they can determine whether a series converges. Practice: 4/20/2019 ESLR -Tracy High Graduates will be Independent Learners Who Set realistic and challenging goals