Homework Help is Here – Start Your Trial Now!
Math
Advanced Math
3. (a) Find the 5th order Taylor polynomial about a = 7 for sin x. (b) Use this Taylor polynomial to approximate sin in terms of powers of 2. 11T (c) The remainder term for a polynomial of order n expanded about x = a is R„(x) = f(n+1)(c). (x – a)n+1 (n + 1)! where c lies between a and x. Write down the remainder term for the polynomial that you have found in part (a). (d) Use the remainder term that you have found in part (c) to show that theTaylor polynomial approximation to sin that you found in part (b) is within 10-6 of the actual value of sin . Use your calculator to verify that the difference between sin and your approximation is, indeed, less than 10-6. 12 : 11T

3. (a) Find the 5th order Taylor polynomial about a = 7 for sin x. (b) Use this Taylor polynomial to approximate sin in terms of powers of 2. 11T (c) The remainder term for a polynomial of order n expanded about x = a is R„(x) = f(n+1)(c). (x – a)n+1 (n + 1)! where c lies between a and x. Write down the remainder term for the polynomial that you have found in part (a). (d) Use the remainder term that you have found in part (c) to show that theTaylor polynomial approximation to sin that you found in part (b) is within 10-6 of the actual value of sin . Use your calculator to verify that the difference between sin and your approximation is, indeed, less than 10-6. 12 : 11T

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

Can you please help me on this exercise for the Taylor's series topic, question 3 part b,c and d, please?

3. (a) Find the 5th order Taylor polynomial about a = 1 for sin x. (b) Use this Taylor polynomial to approximate sin in terms of powers of . 11T 12 (c) The remainder term for a polynomial of order n expanded about x = a is R„(x) = f(n+1)(c)- (x – a)n+1 (n+ 1)! where c lies between a and x. Write down the remainder term for the polynomial that you have found in part (a). (d) Use the remainder term that you have found in part (c) to show that theTaylor polynomial approximation to sin that you found in part (b) is within 10-6 of the actual value of sin . Use your calculator to verify that the difference between your approximation is, indeed, less than 10-6. 11т 12 11T and sin 12
Transcribed Image Text:3. (a) Find the 5th order Taylor polynomial about a = 1 for sin x. (b) Use this Taylor polynomial to approximate sin in terms of powers of . 11T 12 (c) The remainder term for a polynomial of order n expanded about x = a is R„(x) = f(n+1)(c)- (x – a)n+1 (n+ 1)! where c lies between a and x. Write down the remainder term for the polynomial that you have found in part (a). (d) Use the remainder term that you have found in part (c) to show that theTaylor polynomial approximation to sin that you found in part (b) is within 10-6 of the actual value of sin . Use your calculator to verify that the difference between your approximation is, indeed, less than 10-6. 11т 12 11T and sin 12
Expert Solution
steps

Step by step

Solved in 4 steps

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Similar questions
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