Presentation is loading. Please wait.

Presentation is loading. Please wait.

Section 11.4 – Representing Functions with Power Series 10.5.

Published byBrianna Joseph Modified over 9 years ago

Similar presentations

Presentation on theme: "Section 11.4 – Representing Functions with Power Series 10.5."— Presentation transcript:

1 Section 11.4 – Representing Functions with Power Series 10.5

2 4.Find the power series representation for centered about x = 0 and specify its radius of convergence. Infinite geometric with first term 1/3 and r = -2x/3 Converges when |r| < 1

3 8. Find the power series representation for centered about x = 0 and specify its radius of convergence. Radius of Convergence is 1

4 26.Use an appropriate identity to find the Maclaurin series for f(x) = sin x cos x

5 30. Given the function f defined by a.Find the first three nonzero terms in the Maclaurin series for the function f.

6 30. Given the function f defined by b. Find the first three terms in the Maclaurin series for the function g defined by

7 30. Given the function f defined by c. Find the first four terms in the Maclaurin series for the function h defined by

8 Converges for all x

9

Download ppt "Section 11.4 – Representing Functions with Power Series 10.5."

Similar presentations

Section 11.4 – Representing Functions with Power Series.

Section 11.4 – Representing Functions with Power Series.
9.2 day 2 Finding Common Maclaurin Series Liberty Bell, Philadelphia, PA.

9.2 day 2 Finding Common Maclaurin Series Liberty Bell, Philadelphia, PA.
What is the sum of the following infinite series 1+x+x2+x3+…xn… where 0

What is the sum of the following infinite series 1+x+x2+x3+…xn… where 0
Example: Obtain the Maclaurin’s expansion for

Example: Obtain the Maclaurin’s expansion for
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.

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.
(a) an ordered list of objects.

(a) an ordered list of objects.
Sequences and Series & Taylor series

Sequences and Series & Taylor series
9.10 Taylor and Maclaurin Series Colin Maclaurin 1698-1746.

9.10 Taylor and Maclaurin Series Colin Maclaurin
Taylor Series (11/12/08) Given a nice smooth function f (x): What is the best constant function to approximate it near 0? Best linear function to approximate.

Taylor Series (11/12/08) Given a nice smooth function f (x): What is the best constant function to approximate it near 0? Best linear function to approximate.
Copyright © Cengage Learning. All rights reserved.

Copyright © Cengage Learning. All rights reserved.
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 9- 1.

Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 9- 1.
Taylor Series. Theorem Definition The series is called the Taylor series of f about c (centered at c)

Taylor Series. Theorem Definition The series is called the Taylor series of f about c (centered at c)
Taylor Series (4/7/06) We have seen that if f(x) is a function for which we can compute all of its derivatives (i.e., first derivative f '(x), second derivative.

Taylor Series (4/7/06) We have seen that if f(x) is a function for which we can compute all of its derivatives (i.e., first derivative f '(x), second derivative.
Maclaurin and Taylor Series; Power Series Objective: To take our knowledge of Maclaurin and Taylor polynomials and extend it to series.

Maclaurin and Taylor Series; Power Series Objective: To take our knowledge of Maclaurin and Taylor polynomials and extend it to series.
Find the local linear approximation of f(x) = e x at x = 0. Find the local quadratic approximation of f(x) = e x at x = 0.

Find the local linear approximation of f(x) = e x at x = 0. Find the local quadratic approximation of f(x) = e x at x = 0.
Polynomial Approximations BC Calculus. Intro: REM: Logarithms were useful because highly involved problems like Could be worked using only add, subtract,

Polynomial Approximations BC Calculus. Intro: REM: Logarithms were useful because highly involved problems like Could be worked using only add, subtract,
Consider the following: Now, use the reciprocal function and tangent line to get an approximation. Lecture 31 – Approximating Functions 1 12 3.

Consider the following: Now, use the reciprocal function and tangent line to get an approximation. Lecture 31 – Approximating Functions
Sequences Definition - A function whose domain is the set of all positive integers. Finite Sequence - finite number of values or elements Infinite Sequence.

Sequences Definition - A function whose domain is the set of all positive integers. Finite Sequence - finite number of values or elements Infinite Sequence.
Do Now: Find both the local linear and the local quadratic approximations of f(x) = e x at x = 0 Aim: How do we make polynomial approximations for a given.

Do Now: Find both the local linear and the local quadratic approximations of f(x) = e x at x = 0 Aim: How do we make polynomial approximations for a given.
Warm up Construct the Taylor polynomial of degree 5 about x = 0 for the function f(x)=ex. Graph f and your approximation function for a graphical comparison.

Warm up Construct the Taylor polynomial of degree 5 about x = 0 for the function f(x)=ex. Graph f and your approximation function for a graphical comparison.

Similar presentations

Ads by Google