FOURIER SERIES- MCQ - QUIZ - 4

Pick out the even function.

• $\sin x$

• $\tan x$

• $x^2$

• $x^3$

The period of  $\sin x$  is 

•  $2π$  

•  $π$  

•  $π/2$  

•  $3π/2$  

The value of  $a_0$ in the Fourier series of  $f(x)=x$  in  $(0,2π)$  is

•  $2π$  

•  $π$  

•  $0$  

•  $-π$  

if $f\left(x\right)$ is an even function, then the value of  $b_n$ in the Fourier series for $f\left(x\right)$  in  $(-π,π)$ is

•  $\left(2/π\right)∫_0^πf(x)\sin nxdx$  

•  $π$  

•  $\left(1/π\right)\int_{-\pi}^{\pi}f(x)\sin nxdx$  

•  $0$  

The value of a $a_0$  in the Cosine series expansion of f(x) = x in (0,5) is

•  $2$  

•  $3$  

•  $5$  

•  $10$  

Pick out one of the conditions of Dirichlet’s condition.

• 
  

  $f\left(x\right)$ is periodic, single-valued and finite
  

• $f\left(x\right)$ has infinite number of infinite discontinuous in any one period

• $f\left(x\right)$ is infinite valued function

• $f\left(x\right)$ has infinite number of maxima and minima

if  $|f(x)|$  is even whenever  $f(x)$  is

• Even only

• Odd only

• Neither even nor odd

• Either even or odd

Which of the following function is neither even nor odd?

• $\sin x$

• $x^2+x$

• $\cos x$

• $x^2$

if $f\left(x\right)$ is an odd function, then the value of  $a_n$  in the Fourier series for  $f\left(x\right)$  in  $(-π,π)$  is

•  $\left(2/π\right)∫_0^πf(x)\sin nxdx$  

•  $π$  

•  $\left(1/π\right)\int_{-\pi}^{\pi}f(x)\sin nxdx$  

•  $0$  

if $f\left(x\right)$ is an even function, then  $a_n$ in the Fourier series for $f\left(x\right)$ in  $(-π,π)$ is given by

•  $\left(2/π\right)∫_0^πf(x)\sin nxdx$  

•  $π$  

•  $\left(2/π\right)∫_0^πf(x)\cos nxdx$  

•  $0$