Let f(x) = In(x). You may use a calculator for this problem. (a) Find the smallest n such that Taylor's formula implies that the n'h degree Taylor polynomial P,(x) at 1 approximates f(0.65) to within an error of 0.05. Find P„(x) for this value of n. (b) Calculate | In(0.65) – Pn-1(0.65)| (using a calculator) where n is the value you found in part (a). Explain how your answer is consistent with (a).

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
Let f(x) = In(x). You may use a calculator for this problem.
(a) Find the smallest n such that Taylor's formula implies that the n'h degree Taylor
polynomial P,(x) at 1 approximates f(0.65) to within an error of 0.05. Find P(x)
for this value of n.
(b) Calculate | In(0.65) – Pr-1(0.65)| (using a calculator) where n is the value you
found in part (a). Explain how your answer is consistent with (a).
Transcribed Image Text:Let f(x) = In(x). You may use a calculator for this problem. (a) Find the smallest n such that Taylor's formula implies that the n'h degree Taylor polynomial P,(x) at 1 approximates f(0.65) to within an error of 0.05. Find P(x) for this value of n. (b) Calculate | In(0.65) – Pr-1(0.65)| (using a calculator) where n is the value you found in part (a). Explain how your answer is consistent with (a).
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 5 steps with 5 images

Blurred answer
Knowledge Booster
Power Series
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,