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The function g(t) in (21) can be expressed in a more

Fundamentals of Differential Equations | 8th Edition | ISBN: 9780321747730 | Authors: R. Kent Nagle, Edward B. Saff, Arthur David Snider ISBN: 9780321747730 43

Solution for problem 42E Chapter 7.6

Fundamentals of Differential Equations | 8th Edition

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Fundamentals of Differential Equations | 8th Edition | ISBN: 9780321747730 | Authors: R. Kent Nagle, Edward B. Saff, Arthur David Snider

Fundamentals of Differential Equations | 8th Edition

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Problem 42E

Problem 42E

The function g(t) in (21) can be expressed in a more convenient form as follows:

(a)Show that for each n = 0, 1, 2, . . . ,

 

for nT < t < (n+1)T.

{Hint: Use the fact that 1 + x + x2+ . . .+ xn = (xn+1-1)/(x-1).]

(b) Let v = t-(n+1)T. Show that When nT < t < (n+1)T, then –T < v < 0 and

(c) Use the facts that the first term in (22) is periodic with period T and the second term is independent of n to sketch the graph of g(t) in (22) for α = 1 and T = 2

Step-by-Step Solution:
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Chapter 7.6, Problem 42E is Solved
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Textbook: Fundamentals of Differential Equations
Edition: 8
Author: R. Kent Nagle, Edward B. Saff, Arthur David Snider
ISBN: 9780321747730

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