Quiz 2, YM-2, KN-2, Tech. Tex-2 Engineering Mathematics-I

Fourier series provide the solution of a complex nature problem in the sum form of ----------------------.

• Sine Series

• Cosine Series

• Both Sine and Cosine Series

• None

is a graph of periodic rectangular wave. What is the nature of this graph.

• Even

• Odd

• Neither even nor odd

• None

Graphs with even nature are the representation of -------------- current.

• Direct Current

• Alternating Current

• Both direct and alternating current

• None

Graphs with odd nature is the representation of ----------------------- current.

• Direct

• Alternating

• Both alternating and direct

• None

What type of nature this function has?

• Even nature

• Odd nature

• Both even and odd

• None

For what values it is true?

• $m\ \ne\ n$

• $m\ =\ n$

• $m\ =n\ or\ m\ \ne\ n$

• none

What is the value of the Fourier coefficient  $b_n$  ?

•  $-\frac{3}{n\pi}\left[1\ -\ \left(-1\right)^n\right]$  

•  $\frac{3}{n\pi}\left[1\ +\ \left(-1\right)^n\right]$  

•  $\frac{3}{n\pi}\left[1-\left(-1\right)^n\right]$  

• None 

What is the Fourier series of given  $f\left(x\right)$  ?

•  $f\left(x\right)\ =\ 3\ -\ 4\sum_{n\ =0}^{\infty}\frac{\left(-1\right)^n}{n}\cos\left(nx\right)$  

•  $f\left(x\right)\ =\ 3\ +\ 4\sum_{n\ =0}^{\infty}\frac{\left(-1\right)^n}{n}\sin\left(nx\right)$  

•  $f\left(x\right)\ =\ 3\ +\ 4\sum_{n\ =\ 0}^{\infty}\frac{\left(-1\right)^n}{n}\left(\cos\left(nx\right)\ +\ \sin\left(nx\right)\right)$  

• None

Let  $f_1\left(x\right)\ =\ x^2,\$  and  $f_2\left(x\right)\ =\ x^4\ +\ x^2$  . The product of these two functions result in -------------------.

• Even

• Odd

• Neither even nor odd

• None

 $\frac{1}{2\pi}\int_{-p}^pf\left(x\right)\ \cos\ \frac{\left(n\pi\right)x}{p}dx$  is the formula of which Fourier coefficient.

•  $a_0$  

•  $a_n$  

•  $b_n$  

• sine series