Homework Help is Here – Start Your Trial Now!
Math
Advanced Math
4. Show that the Taylor polynomials for f(x) = In(1 + x) can be used to approximate f(s) for s e (-1, 1) by carrying our the following steps. First, show that for t E (-1,1), we have (-t)"+1 1 = 1- t+t? – ... +(-t)" + 1+t 1+t Next, by integrating both sides of this equation, get a new integral estimate for Rn for this function, and finally, show that Rn tends to zero for any s E (-1,1).

4. Show that the Taylor polynomials for f(x) = In(1 + x) can be used to approximate f(s) for s e (-1, 1) by carrying our the following steps. First, show that for t E (-1,1), we have (-t)"+1 1 = 1- t+t? – ... +(-t)" + 1+t 1+t Next, by integrating both sides of this equation, get a new integral estimate for Rn for this function, and finally, show that Rn tends to zero for any s E (-1,1).

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
See similar textbooks
icon
Related questions
Question
4. Show that the Taylor polynomials for f(x) = In(1 + x) can be used to approximate f(s) for s e (-1, 1) by carrying our the following steps. First, show that for t E (-1,1), we have (-t)"+1 1 = 1- t+t? – ... +(-t)" + 1+t 1+t Next, by integrating both sides of this equation, get a new integral estimate for Rn for this function, and finally, show that Rn tends to zero for any s E (-1,1).
Transcribed Image Text:4. Show that the Taylor polynomials for f(x) = In(1 + x) can be used to approximate f(s) for s e (-1, 1) by carrying our the following steps. First, show that for t E (-1,1), we have (-t)"+1 1 = 1- t+t? – ... +(-t)" + 1+t 1+t Next, by integrating both sides of this equation, get a new integral estimate for Rn for this function, and finally, show that Rn tends to zero for any s E (-1,1).
Expert Solution
steps

Step by step

Solved in 2 steps with 2 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
Basic Technical Mathematics
Basic Technical Mathematics
Advanced Math
ISBN:
9780134437705
Author:
Washington
Publisher:
PEARSON
Topology
Topology
Advanced Math
ISBN:
9780134689517
Author:
Munkres, James R.
Publisher:
Pearson,
SEE MORE TEXTBOOKS