Homework Help is Here – Start Your Trial Now!
Math
Advanced Math
Write out Taylor's formula around 0 of degree three, f(x) = P3(x) + E3(x), for f(x) = = COs x.

Write out Taylor's formula around 0 of degree three, f(x) = P3(x) + E3(x), for f(x) = = COs x.

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
100%
We explore how Taylor polynomials can be used to calculate integrals which we otherwise do not know how to handle. Here we consider S V*. cos x dx, r1/4 replace cos x with the polynomial 1 - and give an estimate of the difference between • COs x dx and da = [,"" (»/ . ) 1/4 x2 r1/4 x5/2 So va. (1 *) dr = 1 1 221 2 0.082217269 - 2 2 12 7-27 2688 a) Write out Taylor's formula around 0 of degree three, f(x) = P3(x)+ E3(x), for f(x) = cos x.
Transcribed Image Text:We explore how Taylor polynomials can be used to calculate integrals which we otherwise do not know how to handle. Here we consider S V*. cos x dx, r1/4 replace cos x with the polynomial 1 - and give an estimate of the difference between • COs x dx and da = [,"" (»/ . ) 1/4 x2 r1/4 x5/2 So va. (1 *) dr = 1 1 221 2 0.082217269 - 2 2 12 7-27 2688 a) Write out Taylor's formula around 0 of degree three, f(x) = P3(x)+ E3(x), for f(x) = cos x.
Expert Solution
Step 1

Given that fx=cosx.

To determine the Taylor's formula around 0 of degree three.

That is, fx=P3x+E3x

By definition,

Pnx=f0+f'0x+f"02!x2+⋯⋯+fn0n!xn

Also, 

Enx=xn+1n+1!fn+10

Therefore, here,

P3x=f0+f'0x+f"02!x2+f303!x3

E3x=x44!f4c, where c is in between 0 and x.

steps

Step by step

Solved in 2 steps

Blurred answer
Knowledge Booster
Indefinite Integral
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, advanced-math and related others by exploring similar questions and additional content below.
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