Solved

Consider the Following Periodic Function with Period :
F an=1(2n1)π,n=1,2,3, a_{n}=\frac{1}{(2 n-1) \pi}, n=1,2,3, \ldots

Question 4

Multiple Choice

Consider the following periodic function with period  Consider the following periodic function with period   : F (t)  =   F   = f (t)  The Fourier representation has the form   Which of these are the coefficients   ? A)    a_{n}=\frac{1}{(2 n-1)  \pi}, n=1,2,3, \ldots   B)    a_{n}=-\frac{2}{\pi} \cdot \frac{1}{2 n-1}, n=1,2,3, \ldots   C)    a_{2 n}=0, a_{2 n-1}=-\frac{2}{\left(4 n^{2}-1\right)  \pi}, n=1,2,3, \ldots   D)    a_{2 n}=-\frac{2}{\left(4 n^{2}-1\right)  \pi}, a_{2 n-1}=0, n=1,2,3, \ldots   E)    a_{n}=0, n=1,2,3, \ldots :
F (t) =  Consider the following periodic function with period   : F (t)  =   F   = f (t)  The Fourier representation has the form   Which of these are the coefficients   ? A)    a_{n}=\frac{1}{(2 n-1)  \pi}, n=1,2,3, \ldots   B)    a_{n}=-\frac{2}{\pi} \cdot \frac{1}{2 n-1}, n=1,2,3, \ldots   C)    a_{2 n}=0, a_{2 n-1}=-\frac{2}{\left(4 n^{2}-1\right)  \pi}, n=1,2,3, \ldots   D)    a_{2 n}=-\frac{2}{\left(4 n^{2}-1\right)  \pi}, a_{2 n-1}=0, n=1,2,3, \ldots   E)    a_{n}=0, n=1,2,3, \ldots
F  Consider the following periodic function with period   : F (t)  =   F   = f (t)  The Fourier representation has the form   Which of these are the coefficients   ? A)    a_{n}=\frac{1}{(2 n-1)  \pi}, n=1,2,3, \ldots   B)    a_{n}=-\frac{2}{\pi} \cdot \frac{1}{2 n-1}, n=1,2,3, \ldots   C)    a_{2 n}=0, a_{2 n-1}=-\frac{2}{\left(4 n^{2}-1\right)  \pi}, n=1,2,3, \ldots   D)    a_{2 n}=-\frac{2}{\left(4 n^{2}-1\right)  \pi}, a_{2 n-1}=0, n=1,2,3, \ldots   E)    a_{n}=0, n=1,2,3, \ldots = f (t)
The Fourier representation has the form  Consider the following periodic function with period   : F (t)  =   F   = f (t)  The Fourier representation has the form   Which of these are the coefficients   ? A)    a_{n}=\frac{1}{(2 n-1)  \pi}, n=1,2,3, \ldots   B)    a_{n}=-\frac{2}{\pi} \cdot \frac{1}{2 n-1}, n=1,2,3, \ldots   C)    a_{2 n}=0, a_{2 n-1}=-\frac{2}{\left(4 n^{2}-1\right)  \pi}, n=1,2,3, \ldots   D)    a_{2 n}=-\frac{2}{\left(4 n^{2}-1\right)  \pi}, a_{2 n-1}=0, n=1,2,3, \ldots   E)    a_{n}=0, n=1,2,3, \ldots
Which of these are the coefficients  Consider the following periodic function with period   : F (t)  =   F   = f (t)  The Fourier representation has the form   Which of these are the coefficients   ? A)    a_{n}=\frac{1}{(2 n-1)  \pi}, n=1,2,3, \ldots   B)    a_{n}=-\frac{2}{\pi} \cdot \frac{1}{2 n-1}, n=1,2,3, \ldots   C)    a_{2 n}=0, a_{2 n-1}=-\frac{2}{\left(4 n^{2}-1\right)  \pi}, n=1,2,3, \ldots   D)    a_{2 n}=-\frac{2}{\left(4 n^{2}-1\right)  \pi}, a_{2 n-1}=0, n=1,2,3, \ldots   E)    a_{n}=0, n=1,2,3, \ldots ?


A) an=1(2n1) π,n=1,2,3, a_{n}=\frac{1}{(2 n-1) \pi}, n=1,2,3, \ldots
B) an=2π12n1,n=1,2,3, a_{n}=-\frac{2}{\pi} \cdot \frac{1}{2 n-1}, n=1,2,3, \ldots
C) a2n=0,a2n1=2(4n21) π,n=1,2,3, a_{2 n}=0, a_{2 n-1}=-\frac{2}{\left(4 n^{2}-1\right) \pi}, n=1,2,3, \ldots
D) a2n=2(4n21) π,a2n1=0,n=1,2,3, a_{2 n}=-\frac{2}{\left(4 n^{2}-1\right) \pi}, a_{2 n-1}=0, n=1,2,3, \ldots
E) an=0,n=1,2,3, a_{n}=0, n=1,2,3, \ldots

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