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    Calculus A Complete Course
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    Exam 10: Sequences, Series, and Power Series
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    Find the Fourier Series of the Function F Having Period\(\pi\)
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Find the Fourier Series of the Function F Having Period π\piπ

Question 109

Question 109

Multiple Choice

Find the Fourier series of the function f having period 2 π\piπ and defined by f(x) = 0 if - π\piπ < x ≤\le≤ 0 and f(x) = 1 if 0 < x π\piπ .


A)  Find the Fourier series of the function f having period 2 \pi   and defined by f(x)  = 0 if - \pi  < x  \le  0 and f(x)  = 1 if 0 < x    \pi . A)    +   sin((2n - 1) x)  B)  1 +   sin((2n - 1) x)  C)    +   sin(2nx)  D)  1 +   sin(2nx)  E)    +   cos((2n - 1) x)  +  Find the Fourier series of the function f having period 2 \pi   and defined by f(x)  = 0 if - \pi  < x  \le  0 and f(x)  = 1 if 0 < x    \pi . A)    +   sin((2n - 1) x)  B)  1 +   sin((2n - 1) x)  C)    +   sin(2nx)  D)  1 +   sin(2nx)  E)    +   cos((2n - 1) x)  sin((2n - 1) x)
B) 1 +  Find the Fourier series of the function f having period 2 \pi   and defined by f(x)  = 0 if - \pi  < x  \le  0 and f(x)  = 1 if 0 < x    \pi . A)    +   sin((2n - 1) x)  B)  1 +   sin((2n - 1) x)  C)    +   sin(2nx)  D)  1 +   sin(2nx)  E)    +   cos((2n - 1) x)  sin((2n - 1) x)
C)  Find the Fourier series of the function f having period 2 \pi   and defined by f(x)  = 0 if - \pi  < x  \le  0 and f(x)  = 1 if 0 < x    \pi . A)    +   sin((2n - 1) x)  B)  1 +   sin((2n - 1) x)  C)    +   sin(2nx)  D)  1 +   sin(2nx)  E)    +   cos((2n - 1) x)  +  Find the Fourier series of the function f having period 2 \pi   and defined by f(x)  = 0 if - \pi  < x  \le  0 and f(x)  = 1 if 0 < x    \pi . A)    +   sin((2n - 1) x)  B)  1 +   sin((2n - 1) x)  C)    +   sin(2nx)  D)  1 +   sin(2nx)  E)    +   cos((2n - 1) x)  sin(2nx)
D) 1 +  Find the Fourier series of the function f having period 2 \pi   and defined by f(x)  = 0 if - \pi  < x  \le  0 and f(x)  = 1 if 0 < x    \pi . A)    +   sin((2n - 1) x)  B)  1 +   sin((2n - 1) x)  C)    +   sin(2nx)  D)  1 +   sin(2nx)  E)    +   cos((2n - 1) x)  sin(2nx)
E)  Find the Fourier series of the function f having period 2 \pi   and defined by f(x)  = 0 if - \pi  < x  \le  0 and f(x)  = 1 if 0 < x    \pi . A)    +   sin((2n - 1) x)  B)  1 +   sin((2n - 1) x)  C)    +   sin(2nx)  D)  1 +   sin(2nx)  E)    +   cos((2n - 1) x)  +  Find the Fourier series of the function f having period 2 \pi   and defined by f(x)  = 0 if - \pi  < x  \le  0 and f(x)  = 1 if 0 < x    \pi . A)    +   sin((2n - 1) x)  B)  1 +   sin((2n - 1) x)  C)    +   sin(2nx)  D)  1 +   sin(2nx)  E)    +   cos((2n - 1) x)  cos((2n - 1) x)

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