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W16.2 Decide which of the following functions are periodic. For each periodic functions f provide T such that f(x) = f(x +T); for each non-periodic function f give an argument why ƒ is not periodic (for example, by finding some xo E R such that f(xo) # f(x) for all x different than xo). (a) f(x) = sin(rx) (b) fƒ(x) = sin(x) + sin(7x/5) (c) f(x) = cos(3x) + sin(rx + 5) (d) f(x)= sin(x) + cos(5x + sin(x)

W16.2 Decide which of the following functions are periodic. For each periodic functions f provide T such that f(x) = f(x +T); for each non-periodic function f give an argument why ƒ is not periodic (for example, by finding some xo E R such that f(xo) # f(x) for all x different than xo). (a) f(x) = sin(rx) (b) fƒ(x) = sin(x) + sin(7x/5) (c) f(x) = cos(3x) + sin(rx + 5) (d) f(x)= sin(x) + cos(5x + sin(x)

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter6: Vector Spaces
Section6.5: The Kernel And Range Of A Linear Transformation
Problem 30EQ
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W16.2 Decide which of the following functions are periodic. For each periodic functions f provide T such that f(x) = f(x +T); for each non-periodic function f give an argument why f is not periodic (for example, by finding some xo E R such that f(xo) # f (x) for all æ different than xo). (a) f(x) = sin(rx) (b) f(x) = sin(x)+ sin(7x/5) (c) f(x) = cos(3x) + sin(rx + 5) 2 (d) f(x) = sin(x) + cos(5x + sin(x))
Transcribed Image Text:W16.2 Decide which of the following functions are periodic. For each periodic functions f provide T such that f(x) = f(x +T); for each non-periodic function f give an argument why f is not periodic (for example, by finding some xo E R such that f(xo) # f (x) for all æ different than xo). (a) f(x) = sin(rx) (b) f(x) = sin(x)+ sin(7x/5) (c) f(x) = cos(3x) + sin(rx + 5) 2 (d) f(x) = sin(x) + cos(5x + sin(x))
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