The power series for f(x)= x²x4 + 21 4! 6! defined as 1- 1 1-X is defined as 1+x+x². +. x2n (2n)! ·+... Σ (-1)^. n=0 Part A: Find the general term of the power series for g(x)= 1. Justify your solution. 8 +...=x", and the power series for cosx is n=0 4 X-6 and evaluate the infinite sum when x= (0.6)3 Round your final 3! Part B: Find an upper bound for the error of the approximation sin(0.6)=0.6-5 answer to five decimal places. Part C: Find a power series for h(x) = In(1-2x) centered at x = 0 and show the work that leads to your conclusion.
The power series for f(x)= x²x4 + 21 4! 6! defined as 1- 1 1-X is defined as 1+x+x². +. x2n (2n)! ·+... Σ (-1)^. n=0 Part A: Find the general term of the power series for g(x)= 1. Justify your solution. 8 +...=x", and the power series for cosx is n=0 4 X-6 and evaluate the infinite sum when x= (0.6)3 Round your final 3! Part B: Find an upper bound for the error of the approximation sin(0.6)=0.6-5 answer to five decimal places. Part C: Find a power series for h(x) = In(1-2x) centered at x = 0 and show the work that leads to your conclusion.
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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Transcribed Image Text:1
The power series for f(x) = -
х2 ха хо
6!
defined as 1- +
2!
4!
1-X
is defined as 1+x+x² +
-+...= Σ (-1)^
n=0
x2n
(2n)!
Part A: Find the general term of the power series for g(x)=
1. Justify your solution.
+... Σx", and the power series for cosx is
=
n=0
4
X-6
and evaluate the infinite sum when x =
Part B: Find an upper bound for the error of the approximation sin(0.6) = 0.6 (0.6)³ Round your final
3!
answer to five decimal places.
Part C: Find a power series for h(x) = ln(1 - 2x) centered at x = 0 and show the work that leads to your
conclusion.
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