MyLab Math with Pearson eText -- 24 Month Access -- for Calculus with Integrated Review
MyLab Math with Pearson eText -- 24 Month Access -- for Calculus with Integrated Review
3rd Edition
ISBN: 9780135243435
Author: Bill Briggs
Publisher: Pearson Education (US)
bartleby

Videos

Textbook Question
Book Icon
Chapter 11.2, Problem 52E

Differentiating and integrating power series Find the power series representation for g centered at 0 by differentiating or integrating the power series for f (perhaps more than once). Give the interval of convergence for the resulting series.

42. g ( x ) = 1 ( 1 − x ) 3 using f ( x ) = 1 1 − x

Expert Solution & Answer
Check Mark

Want to see the full answer?

Check out a sample textbook solution
Blurred answer
Previous
Chapter 11.2, Problem 51E
Next
Chapter 11.2, Problem 53E
Students have asked these similar questions
Let V be the volume of the solid obtained by rotating about the y-axis the region bounded y = √16x and y V = Draw a diagram to explain your method. 15 10 5 y 15 10 5 y = Find V by slicing. 16 X О -15 -10 -5 5 10 15 О -15 -10 -5 5 10 15 15 10 y 15 10 5 y x -15 -10 -5 5 10 -15 -10 -5 5 10 15 10 X 15
a) let SSK : A->R be function and let c be acluster Point of A if lim S, (x) exists for each i=1, 2, .-,k then K i) lim Si (x)= lim fi (x) X->C 1=1 11), im π fi (x) = lim fi (x) YC il i=1 1) let f(x) = ) x² Sin (1/x), xe Q/{o} f(x) = { x² cos(\/x), x&Q Show that lim f(x)= 0 X = 0 c) Give an example of aset ASR, a cluster Point C of Aand two fun. & 9: AR st lim f(x)9(x) exsis bat limfex) does not exist X-C
2. [-/4 Points] DETAILS MY NOTES SESSCALCET2 7.3.002. Let S be the solid obtained by rotating the region shown in the figure about the y-axis. (Assume a = 6 and b = 2.) ASK YOUR TEACHER 0 y = a sin(bx²) Sketch a typical approximating shell. y 6 4 2 x π/b y 2 1 x 0.5 1.0 1.5 0.2 0.4 0.6 0.8 1.0 -2 -1 -4

Chapter 11 Solutions

MyLab Math with Pearson eText -- 24 Month Access -- for Calculus with Integrated Review

Ch. 11.1 - Verify that p3 satisfies p3(k)(a)=f(k)(a), for k =...Ch. 11.1 - Prob. 2QCCh. 11.1 - Prob. 3QCCh. 11.1 - Write out the next two Taylor polynomials p4 and...Ch. 11.1 - Prob. 5QCCh. 11.1 - Prob. 6QCCh. 11.1 - Suppose you use a second-order Taylor polynomial...Ch. 11.1 - Does the accuracy of an approximation given by a...Ch. 11.1 - The first three Taylor polynomials for f(x)=1+x...Ch. 11.1 - Prob. 4E
Ch. 11.1 - Suppose f(0) = 1, f(0) = 0, f"(0) = 2, and f(3)(0)...Ch. 11.1 - Prob. 6ECh. 11.1 - Prob. 7ECh. 11.1 - Suppose you want to estimate 26 using a...Ch. 11.1 - Linear and quadratic approximation a. Find the...Ch. 11.1 - Linear and quadratic approximation a. Find the...Ch. 11.1 - Linear and quadratic approximation a. Find the...Ch. 11.1 - Linear and quadratic approximation a. Find the...Ch. 11.1 - Linear and quadratic approximation a. Find the...Ch. 11.1 - Linear and quadratic approximation a. Find the...Ch. 11.1 - Linear and quadratic approximation a. Find the...Ch. 11.1 - Linear and quadratic approximation a. Find the...Ch. 11.1 - Find the Taylor polynomials p1, , p4 centered at a...Ch. 11.1 - Find the Taylor polynomials p1, , p5 centered at a...Ch. 11.1 - Find the Taylor polynomials p3, , p4 centered at a...Ch. 11.1 - Find the Taylor polynomials p4 and p5 centered at...Ch. 11.1 - Find the Taylor polynomials p1, p2, and p3...Ch. 11.1 - Find the Taylor polynomials p3 and p4 centered at...Ch. 11.1 - Find the Taylor polynomial p3 centered at a = e...Ch. 11.1 - Find the Taylor polynomial p2 centered at a = 8...Ch. 11.1 - Graphing Taylor polynomials a. Find the nth-order...Ch. 11.1 - Prob. 26ECh. 11.1 - Graphing Taylor polynomials a. Find the nth-order...Ch. 11.1 - Graphing Taylor polynomials a. Find the nth-order...Ch. 11.1 - Approximations with Taylor polynomials a. Use the...Ch. 11.1 - Approximations with Taylor polynomials a. Use the...Ch. 11.1 - Approximations with Taylor polynomials a. Use the...Ch. 11.1 - Approximations with Taylor polynomials a. Use the...Ch. 11.1 - Approximations with Taylor polynomials a....Ch. 11.1 - Prob. 34ECh. 11.1 - Approximations with Taylor polynomials a....Ch. 11.1 - Prob. 36ECh. 11.1 - Approximations with Taylor polynomials a....Ch. 11.1 - Prob. 38ECh. 11.1 - Prob. 39ECh. 11.1 - Prob. 40ECh. 11.1 - Prob. 41ECh. 11.1 - Prob. 42ECh. 11.1 - Prob. 43ECh. 11.1 - Prob. 44ECh. 11.1 - Prob. 45ECh. 11.1 - Prob. 46ECh. 11.1 - Prob. 47ECh. 11.1 - Estimating errors Use the remainder to find a...Ch. 11.1 - Estimating errors Use the remainder to find a...Ch. 11.1 - Prob. 50ECh. 11.1 - Prob. 51ECh. 11.1 - Prob. 52ECh. 11.1 - Prob. 53ECh. 11.1 - Prob. 54ECh. 11.1 - Prob. 55ECh. 11.1 - Prob. 56ECh. 11.1 - Prob. 57ECh. 11.1 - Prob. 58ECh. 11.1 - Prob. 59ECh. 11.1 - Prob. 60ECh. 11.1 - Prob. 61ECh. 11.1 - Prob. 62ECh. 11.1 - Prob. 63ECh. 11.1 - Prob. 64ECh. 11.1 - Prob. 65ECh. 11.1 - Prob. 66ECh. 11.1 - Prob. 67ECh. 11.1 - Prob. 68ECh. 11.1 - Prob. 69ECh. 11.1 - Prob. 70ECh. 11.1 - Prob. 71ECh. 11.1 - Prob. 72ECh. 11.1 - Prob. 73ECh. 11.1 - Prob. 74ECh. 11.1 - Prob. 75ECh. 11.1 - Prob. 76ECh. 11.1 - Prob. 77ECh. 11.1 - Prob. 78ECh. 11.1 - Prob. 79ECh. 11.1 - Best center point Suppose you wish to approximate...Ch. 11.1 - Prob. 81ECh. 11.1 - Prob. 82ECh. 11.1 - Prob. 83ECh. 11.1 - Prob. 84ECh. 11.1 - Prob. 85ECh. 11.1 - Prob. 86ECh. 11.1 - Prob. 87ECh. 11.1 - A different kind of approximation When...Ch. 11.2 - By substituting x = 0 in the power series for g,...Ch. 11.2 - What are the radius and interval of convergence of...Ch. 11.2 - Use the result of Example 4 to write a series...Ch. 11.2 - Verify that the power series in Example 5b does...Ch. 11.2 - Write the first four terms of a power series with...Ch. 11.2 - Prob. 2ECh. 11.2 - Prob. 3ECh. 11.2 - Is k=0x2ka power series? If so, find the center a...Ch. 11.2 - Prob. 5ECh. 11.2 - Prob. 6ECh. 11.2 - Prob. 7ECh. 11.2 - Prob. 8ECh. 11.2 - Radius and interval of convergence Determine the...Ch. 11.2 - Radius and interval of convergence Determine the...Ch. 11.2 - Radius and interval of convergence Determine the...Ch. 11.2 - Prob. 12ECh. 11.2 - Radius and interval of convergence Determine the...Ch. 11.2 - Radius and interval of convergence Determine the...Ch. 11.2 - Radius and interval of convergence Determine the...Ch. 11.2 - Radius and interval of convergence Determine the...Ch. 11.2 - Radius and interval of convergence Determine the...Ch. 11.2 - Radius and interval of convergence Determine the...Ch. 11.2 - Radius and interval of convergence Determine the...Ch. 11.2 - Radius and interval of convergence Determine the...Ch. 11.2 - Radius and interval of convergence Determine the...Ch. 11.2 - Radius and interval of convergence Determine the...Ch. 11.2 - Radius and interval of convergence Determine the...Ch. 11.2 - Radius and interval of convergence Determine the...Ch. 11.2 - Radius and interval of convergence Determine the...Ch. 11.2 - Radius and interval of convergence Determine the...Ch. 11.2 - Radius and interval of convergence Determine the...Ch. 11.2 - Radius and interval of convergence Determine the...Ch. 11.2 - Radius and interval of convergence Determine the...Ch. 11.2 - Prob. 30ECh. 11.2 - Radius and interval of convergence Determine the...Ch. 11.2 - Prob. 32ECh. 11.2 - Prob. 33ECh. 11.2 - Prob. 34ECh. 11.2 - Prob. 35ECh. 11.2 - Prob. 36ECh. 11.2 - Radius of convergence Find the radius of...Ch. 11.2 - Prob. 38ECh. 11.2 - Radius of convergence Find the radius of...Ch. 11.2 - Radius of convergence Find the radius of...Ch. 11.2 - Combining power series Use the geometric series...Ch. 11.2 - Combining power series Use the geometric series...Ch. 11.2 - Combining power series Use the geometric series...Ch. 11.2 - Combining power series Use the geometric series...Ch. 11.2 - Combining power series Use the geometric series...Ch. 11.2 - Combining power series Use the geometric series...Ch. 11.2 - Combining power series Use the power series...Ch. 11.2 - Prob. 48ECh. 11.2 - Prob. 49ECh. 11.2 - Prob. 50ECh. 11.2 - Differentiating and integrating power series Find...Ch. 11.2 - Differentiating and integrating power series Find...Ch. 11.2 - Differentiating and integrating power series Find...Ch. 11.2 - Differentiating and integrating power series Find...Ch. 11.2 - Differentiating and integrating power series Find...Ch. 11.2 - Differentiating and integrating power series Find...Ch. 11.2 - Functions to power series Find power series...Ch. 11.2 - Functions to power series Find power series...Ch. 11.2 - Functions to power series Find power series...Ch. 11.2 - Prob. 60ECh. 11.2 - Prob. 61ECh. 11.2 - Prob. 62ECh. 11.2 - Prob. 63ECh. 11.2 - Prob. 64ECh. 11.2 - Prob. 65ECh. 11.2 - Prob. 66ECh. 11.2 - Prob. 67ECh. 11.2 - Series to functions Find the function represented...Ch. 11.2 - Prob. 69ECh. 11.2 - Prob. 70ECh. 11.2 - Prob. 71ECh. 11.2 - Prob. 72ECh. 11.2 - Exponential function In Section 11.3, we show that...Ch. 11.2 - Prob. 74ECh. 11.2 - Prob. 75ECh. 11.2 - Prob. 76ECh. 11.2 - Prob. 77ECh. 11.2 - Prob. 78ECh. 11.3 - Verify that if the Taylor series for f centered at...Ch. 11.3 - Prob. 2QCCh. 11.3 - Verify that the series k=0(1)k+1(x5)k4k+1 from...Ch. 11.3 - Find the first three terms of the Maclaurin series...Ch. 11.3 - Evaluate the binomial coefficients (32) and (123).Ch. 11.3 - Prob. 6QCCh. 11.3 - Prob. 1ECh. 11.3 - Prob. 2ECh. 11.3 - Prob. 3ECh. 11.3 - Prob. 4ECh. 11.3 - Suppose you know the Maclaurin series for f and...Ch. 11.3 - For what values of p does the Taylor series for...Ch. 11.3 - In terms of the remainder, what does it mean for a...Ch. 11.3 - Find the Maclaurin series for sin(x) using the...Ch. 11.3 - Taylor series and interval of convergence a. Use...Ch. 11.3 - Taylor series and interval of convergence a. Use...Ch. 11.3 - Taylor series and interval of convergence a. Use...Ch. 11.3 - Prob. 12ECh. 11.3 - Taylor series and interval of convergence a. Use...Ch. 11.3 - Taylor series and interval of convergence a. Use...Ch. 11.3 - Taylor series and interval of convergence a. Use...Ch. 11.3 - Taylor series and interval of convergence a. Use...Ch. 11.3 - Taylor series and interval of convergence a. Use...Ch. 11.3 - Taylor series and interval of convergence a. Use...Ch. 11.3 - Taylor series and interval of convergence a. Use...Ch. 11.3 - Prob. 20ECh. 11.3 - Prob. 21ECh. 11.3 - Prob. 22ECh. 11.3 - Taylor series and interval of convergence a. Use...Ch. 11.3 - Taylor series and interval of convergence a. Use...Ch. 11.3 - Taylor series and interval of convergence a. Use...Ch. 11.3 - Taylor series and interval of convergence a. Use...Ch. 11.3 - Prob. 27ECh. 11.3 - Prob. 28ECh. 11.3 - Prob. 29ECh. 11.3 - Taylor series centered at a 0 a. Find the first...Ch. 11.3 - Taylor series centered at a 0 a. Find the first...Ch. 11.3 - Taylor series centered at a 0 a. Find the first...Ch. 11.3 - Prob. 33ECh. 11.3 - Taylor series a. Use the definition of a Taylor...Ch. 11.3 - Prob. 35ECh. 11.3 - Prob. 36ECh. 11.3 - Manipulating Taylor series Use the Taylor series...Ch. 11.3 - Prob. 38ECh. 11.3 - Prob. 39ECh. 11.3 - Prob. 40ECh. 11.3 - Manipulating Taylor series Use the Taylor series...Ch. 11.3 - Prob. 42ECh. 11.3 - Prob. 43ECh. 11.3 - Prob. 44ECh. 11.3 - Binomial series a. Find the first four nonzero...Ch. 11.3 - Prob. 46ECh. 11.3 - Prob. 47ECh. 11.3 - Prob. 48ECh. 11.3 - Binomial series a. Find the first four nonzero...Ch. 11.3 - Binomial series a. Find the first four nonzero...Ch. 11.3 - Working with binomial series Use properties of...Ch. 11.3 - Prob. 52ECh. 11.3 - Prob. 53ECh. 11.3 - Prob. 54ECh. 11.3 - Prob. 55ECh. 11.3 - Prob. 56ECh. 11.3 - Working with binomial series Use properties of...Ch. 11.3 - Working with binomial series Use properties of...Ch. 11.3 - Prob. 59ECh. 11.3 - Prob. 60ECh. 11.3 - Prob. 61ECh. 11.3 - Prob. 62ECh. 11.3 - Prob. 63ECh. 11.3 - Prob. 64ECh. 11.3 - Prob. 65ECh. 11.3 - Prob. 66ECh. 11.3 - Prob. 67ECh. 11.3 - Prob. 68ECh. 11.3 - Prob. 69ECh. 11.3 - Prob. 70ECh. 11.3 - Any method a. Use any analytical method to find...Ch. 11.3 - Prob. 72ECh. 11.3 - Prob. 73ECh. 11.3 - Prob. 74ECh. 11.3 - Prob. 75ECh. 11.3 - Prob. 76ECh. 11.3 - Prob. 78ECh. 11.3 - Prob. 80ECh. 11.3 - Prob. 81ECh. 11.3 - Prob. 82ECh. 11.3 - Prob. 83ECh. 11.3 - Prob. 84ECh. 11.3 - Prob. 85ECh. 11.3 - Composition of series Use composition of series to...Ch. 11.3 - Prob. 87ECh. 11.3 - Prob. 88ECh. 11.3 - Prob. 89ECh. 11.3 - Prob. 90ECh. 11.3 - Prob. 91ECh. 11.4 - Use the Taylor series sin x = x - x3/6+ to verify...Ch. 11.4 - Prob. 2QCCh. 11.4 - Prob. 3QCCh. 11.4 - Prob. 1ECh. 11.4 - Prob. 2ECh. 11.4 - Prob. 3ECh. 11.4 - Prob. 4ECh. 11.4 - Prob. 5ECh. 11.4 - Prob. 6ECh. 11.4 - Prob. 7ECh. 11.4 - Prob. 8ECh. 11.4 - Prob. 9ECh. 11.4 - Prob. 10ECh. 11.4 - Limits Evaluate the following limits using Taylor...Ch. 11.4 - Prob. 12ECh. 11.4 - Prob. 13ECh. 11.4 - Prob. 14ECh. 11.4 - Prob. 15ECh. 11.4 - Prob. 16ECh. 11.4 - Limits Evaluate the following limits using Taylor...Ch. 11.4 - Prob. 18ECh. 11.4 - Limits Evaluate the following limits using Taylor...Ch. 11.4 - Prob. 20ECh. 11.4 - Prob. 21ECh. 11.4 - Prob. 22ECh. 11.4 - Prob. 23ECh. 11.4 - Prob. 24ECh. 11.4 - Power series for derivatives a. Differentiate the...Ch. 11.4 - Power series for derivatives a. Differentiate the...Ch. 11.4 - Prob. 27ECh. 11.4 - Prob. 28ECh. 11.4 - Power series for derivatives a. Differentiate the...Ch. 11.4 - Prob. 30ECh. 11.4 - Power series for derivatives a. Differentiate the...Ch. 11.4 - Prob. 32ECh. 11.4 - Differential equations a. Find a power series for...Ch. 11.4 - Prob. 34ECh. 11.4 - Prob. 35ECh. 11.4 - Differential equations a. Find a power series for...Ch. 11.4 - Approximating definite integrals Use a Taylor...Ch. 11.4 - Approximating definite integrals Use a Taylor...Ch. 11.4 - Approximating definite integrals Use a Taylor...Ch. 11.4 - Prob. 40ECh. 11.4 - Approximating definite integrals Use a Taylor...Ch. 11.4 - Prob. 42ECh. 11.4 - Prob. 43ECh. 11.4 - Approximating definite integrals Use a Taylor...Ch. 11.4 - Approximating real numbers Use an appropriate...Ch. 11.4 - Approximating real numbers Use an appropriate...Ch. 11.4 - Prob. 47ECh. 11.4 - Approximating real numbers Use an appropriate...Ch. 11.4 - Approximating real numbers Use an appropriate...Ch. 11.4 - Prob. 50ECh. 11.4 - Prob. 51ECh. 11.4 - Prob. 52ECh. 11.4 - Evaluating an infinite series Write the Taylor...Ch. 11.4 - Prob. 54ECh. 11.4 - Representing functions by power series Identify...Ch. 11.4 - Prob. 56ECh. 11.4 - Prob. 57ECh. 11.4 - Prob. 58ECh. 11.4 - Prob. 59ECh. 11.4 - Prob. 60ECh. 11.4 - Prob. 61ECh. 11.4 - Prob. 62ECh. 11.4 - Prob. 63ECh. 11.4 - Prob. 64ECh. 11.4 - Prob. 65ECh. 11.4 - Limits with a parameter Use Taylor series to...Ch. 11.4 - Prob. 67ECh. 11.4 - Prob. 68ECh. 11.4 - A limit by Taylor series Use Taylor series to...Ch. 11.4 - Prob. 70ECh. 11.4 - Prob. 71ECh. 11.4 - Prob. 72ECh. 11.4 - Prob. 73ECh. 11.4 - Prob. 74ECh. 11.4 - Prob. 75ECh. 11.4 - Prob. 76ECh. 11.4 - Prob. 77ECh. 11.4 - Sine integral function The function...Ch. 11.4 - Fresnel integrals The theory of optics gives rise...Ch. 11.4 - Prob. 80ECh. 11.4 - Prob. 81ECh. 11.4 - Prob. 83ECh. 11.4 - Prob. 84ECh. 11 - Explain why or why not Determine whether the...Ch. 11 - Taylor polynomials Find the nth-order Taylor...Ch. 11 - Taylor polynomials Find the nth-order Taylor...Ch. 11 - Taylor polynomials Find the nth-order Taylor...Ch. 11 - Taylor polynomials Find the nth-order Taylor...Ch. 11 - Taylor polynomials Find the nth-order Taylor...Ch. 11 - Taylor polynomials Find the nth-order Taylor...Ch. 11 - Taylor polynomials Find the nth-order Taylor...Ch. 11 - Prob. 9RECh. 11 - Approximations a. Find the Taylor polynomials of...Ch. 11 - Prob. 11RECh. 11 - Prob. 12RECh. 11 - Approximations a. Find the Taylor polynomials of...Ch. 11 - Prob. 14RECh. 11 - Prob. 15RECh. 11 - Prob. 16RECh. 11 - Prob. 17RECh. 11 - Prob. 18RECh. 11 - Prob. 19RECh. 11 - Prob. 20RECh. 11 - Radius and interval of convergence Use the Ratio...Ch. 11 - Prob. 22RECh. 11 - Radius and interval of convergence Use the Ratio...Ch. 11 - Radius and interval of convergence Use the Ratio...Ch. 11 - Radius and interval of convergence Use the Ratio...Ch. 11 - Radius and interval of convergence Use the Ratio...Ch. 11 - Radius of convergence Find the radius of...Ch. 11 - Radius of convergence Find the radius of...Ch. 11 - Prob. 29RECh. 11 - Prob. 30RECh. 11 - Prob. 31RECh. 11 - Prob. 32RECh. 11 - Prob. 33RECh. 11 - Power series from the geometric series Use the...Ch. 11 - Prob. 35RECh. 11 - Taylor series Write out the first three nonzero...Ch. 11 - Prob. 37RECh. 11 - Taylor series Write out the first three nonzero...Ch. 11 - Taylor series Write out the first three nonzero...Ch. 11 - Prob. 40RECh. 11 - Taylor series Write out the first three nonzero...Ch. 11 - Prob. 42RECh. 11 - Prob. 43RECh. 11 - Prob. 44RECh. 11 - Prob. 45RECh. 11 - Prob. 46RECh. 11 - Convergence Write the remainder term Rn(x) for the...Ch. 11 - Convergence Write the remainder term Rn(x) for the...Ch. 11 - Limits by power series Use Taylor series to...Ch. 11 - Prob. 50RECh. 11 - Limits by power series Use Taylor series to...Ch. 11 - Prob. 52RECh. 11 - Prob. 53RECh. 11 - Prob. 54RECh. 11 - Prob. 55RECh. 11 - Prob. 56RECh. 11 - Definite integrals by power series Use a Taylor...Ch. 11 - Prob. 58RECh. 11 - Approximating real numbers Use an appropriate...Ch. 11 - Prob. 60RECh. 11 - Approximating real numbers Use an appropriate...Ch. 11 - Prob. 62RECh. 11 - Prob. 63RECh. 11 - Prob. 64RECh. 11 - Prob. 65RECh. 11 - Prob. 66RE
Knowledge Booster
Background pattern image
Calculus
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.
Similar questions
SEE MORE QUESTIONS
Recommended textbooks for you
Text book image
Calculus: Early Transcendentals
Calculus
ISBN:9781285741550
Author:James Stewart
Publisher:Cengage Learning
Text book image
Thomas' Calculus (14th Edition)
Calculus
ISBN:9780134438986
Author:Joel R. Hass, Christopher E. Heil, Maurice D. Weir
Publisher:PEARSON
Text book image
Calculus: Early Transcendentals (3rd Edition)
Calculus
ISBN:9780134763644
Author:William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz
Publisher:PEARSON
Text book image
Calculus: Early Transcendentals
Calculus
ISBN:9781319050740
Author:Jon Rogawski, Colin Adams, Robert Franzosa
Publisher:W. H. Freeman
Text book image
Precalculus
Calculus
ISBN:9780135189405
Author:Michael Sullivan
Publisher:PEARSON
Text book image
Calculus: Early Transcendental Functions
Calculus
ISBN:9781337552516
Author:Ron Larson, Bruce H. Edwards
Publisher:Cengage Learning
SEE MORE TEXTBOOKS
Power Series; Author: Professor Dave Explains;https://www.youtube.com/watch?v=OxVBT83x8oc;License: Standard YouTube License, CC-BY
Power Series & Intervals of Convergence; Author: Dr. Trefor Bazett;https://www.youtube.com/watch?v=XHoRBh4hQNU;License: Standard YouTube License, CC-BY