Sin(3x) 1 + sin(3x) sin(3x)cos(2x) 10 + cos(10x) + sin_2(x) Let f (x) = Open bra

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Sin(3x) 1 + sin(3x) sin(3x)cos(2x) 10 + cos(10x) + sin_2(x) Let f (x) = Open bracket 0 -2 -1 0 1 2 0 -4 less than x less than -3 -3 less than x less than -2 -2 less than x less than -1 -1 less than x less than 1 be a periodic function with period p = 2L = 8 1 less than x less than 2 2 less than x less than 3 3 less than x less than 4 Sketch f(x) odd, even or neither? Solve for the Fourier series coefficients a_0, a_0, and b_a Write out the Fourier series for f(x) up to the n = 0, 1, 2, 3 terms In a late chapter, it is useful to find the Fourier coefficients of sums of sinusoids by inspire the fundamental period p of the sum, or equivalently finding the fundamental omega_0. For example frequency is such that omega = 3 omega_0. The sine of consine at this frequency is then associated with series summation

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4)

a) f(x) = sin(3x)

f(-x) = sin(3(-x)) = sin(-3x) = -sin(3x)

since f(x) = -f(-x)

Hence the function is an odd function

b) f(x) = 1 + sin(3x)

f(-x) = 1 + sin(-3x) = 1 - sin(3x)

since f(x) is not equal to f(-x) or -f(-x)

Hence the function is neither odd nor even

c) sin(3x)cos(2x)

sin(3x) is an odd function and cos(2x) is an even function

Hence sin(3x)cos(2x) will be an odd function

d) 10 + cos(10x) + sin^2(x)

f(-x) = 10 + cos(10x) + sin^2(x)

Since f(x) = f(-x), hence the function is an even function

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