b. Use the result in item 2(a) to find the 4th degree Taylor polynomial of ƒ about 1.5. c. Use the result in item 2(b) to approximate f(1.55). Express your answer in decimal form.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
icon
Related questions
Question

Can you please guide me with items b and c? Thank you!

4х — 6
2. Let f(x) =
1- (2х — 3)3*
a. Find the Taylor series representation for f about x = 1.5 that is valid for all x E (1,2).
+o0
1
Hint: Use the equation
1- t
E ", where t e (-1,1), to find the Taylor series representation for
n=0
1
about x = 1.5. Then, use this series to find the desired series representation for f.
1- (2x – 3)3
b. Use the result in item 2(a) to find the 4th degree Taylor polynomial of f about 1.5.
c. Use the result in item 2(b) to approximate f(1.55). Express your answer in decimal form.
Transcribed Image Text:4х — 6 2. Let f(x) = 1- (2х — 3)3* a. Find the Taylor series representation for f about x = 1.5 that is valid for all x E (1,2). +o0 1 Hint: Use the equation 1- t E ", where t e (-1,1), to find the Taylor series representation for n=0 1 about x = 1.5. Then, use this series to find the desired series representation for f. 1- (2x – 3)3 b. Use the result in item 2(a) to find the 4th degree Taylor polynomial of f about 1.5. c. Use the result in item 2(b) to approximate f(1.55). Express your answer in decimal form.
Expert Solution
steps

Step by step

Solved in 2 steps with 1 images

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,