Download presentation

Presentation is loading. Please wait.

Published byBraedon Dendy Modified over 2 years ago

1
11.2 P ROPERTIES OF P OWER S ERIES Math 6B Calculus II

2
P OWER S ERIES Power Series centered at x = 0. Power Series centered at x = a.

3
T HE F UNCTION 1/(1 – X ) The function 1/(1 – x ) can be rewritten into a power series.

4
H OW TO T EST A P OWER S ERIES FOR C ONVERGENCE Use the Ratio test (or Root test) to find the interval where the series converges absolutely. Ordinarily this is an open interval or a – R < x < a + R If the interval of absolute convergence is finite, test for convergence or divergence at each endpoint. Use an appropriate test.

5
H OW TO T EST A P OWER S ERIES FOR C ONVERGENCE If the interval of absolute convergence is a – R < x < a + R, the series diverges for

6
T HE R ADIUS AND I NTERVAL OF C ONVERGENCE Possible behavior of There is a positive number R (also known as the radius of convergence ) such that the series diverges for all but converges for. The series may or may not converge at either endpoint x = a – R and x = a + R.

7
T HE R ADIUS AND I NTERVAL OF C ONVERGENCE The series converges absolutely for every x The series converges at x = a and diverges everywhere else. ( R = 0 )

8
C OMBINING P OWER S ERIES

10
D IFFERENTIATION AND I NTEGRATION OF A P OWER S ERIES

11
The radii of convergence of the power series in Equations (i) and (ii) are both R.

Similar presentations

OK

Power Series. A power series in x (or centered at 0) is a series of the following form:

Power Series. A power series in x (or centered at 0) is a series of the following form:

© 2017 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Ppt on managerial economics introduction Ppt on aerobics oz Ppt on cartesian product proof Sources of energy for kids ppt on batteries Ppt on forest society and colonialism Free ppt on customer service skills Free ppt on brain machine interface Ppt on artificial intelligence and robotics Ppt on l&t finance holding share price Ppt on work and energy for class 9th