(17) a) Find the third order Taylor polynomial T,(x) for f(x)= In x centered at a=1; identify the interval and radius of convergence. b) Use your answer in a) to find an approximation to In(1.05) . c) Using the nth remainder term for Taylor's Theorem, R,(x)|<- M ;(x-1)*1 , and the (n+1)!

(17) a) Find the third order Taylor polynomial T,(x) for f(x)= In x centered at a=1; identify the interval and radius of convergence. b) Use your answer in a) to find an approximation to In(1.05) . c) Using the nth remainder term for Taylor's Theorem, R,(x)|<- M ;(x-1)*1 , and the (n+1)!

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

(17) a) Find the third order Taylor polynomial T;(x) for f(x)= In x centered at a=1;
identify the interval and radius of convergence.
b) Use your answer in a) to find an approximation to In(1.05).
c) Using the nth remainder term for Taylor's Theorem, R,(x)|<
M
(x-1)*1 , and the
(n+1)!
graph of the fourth derivative of Inx given below determine the accuracy of your answer in
part b).
1
1.02
1.04
--2-
-4.
-6-

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