1. Find the power series representing the function 1/ (z - 5) in the region |z- 4| < 1. (10 pts)
1. Find the power series representing the function 1/ (z - 5) in the region |z- 4| < 1. (10 pts)
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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![1. Find the power series representing the function 1/ (z - 5) in the region |z - 4| < 1.
(10 pts)
2. Find the MacLaurin series of f(x) = sinh(3x). Express your answer in the form
E an(x – c)". The proper limits should also be indicated. (15 pts)
3. What is the sum of the first two terms of the standard Taylor series expansion of the
function cos(x) centered at x = TT. (10 pts)
4. Find the Fourier series of f(t) = t³ where t e [-4,4] and f(t + 8) = f (t). (25 pts)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fba8b2d65-46ec-47d6-9e4c-92a41fcc4e4f%2F44a8b4a3-9f3e-4395-a1a4-867b0dc2b961%2Ft3tpdn6_processed.jpeg&w=3840&q=75)
Transcribed Image Text:1. Find the power series representing the function 1/ (z - 5) in the region |z - 4| < 1.
(10 pts)
2. Find the MacLaurin series of f(x) = sinh(3x). Express your answer in the form
E an(x – c)". The proper limits should also be indicated. (15 pts)
3. What is the sum of the first two terms of the standard Taylor series expansion of the
function cos(x) centered at x = TT. (10 pts)
4. Find the Fourier series of f(t) = t³ where t e [-4,4] and f(t + 8) = f (t). (25 pts)
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