$\frac{1}{2}\left[F_s\left(A+S\right)-F_s\left(A-S\right)\right]$  

 $\frac{1}{2}\left[F_s\left(A+S\right)+F_s\left(A-S\right)\right]$  

 $\frac{1}{2}\left[F_c\left(A+s\right)+F_c\left(A-s\right)\right]$  

 $\frac{1}{2}\left[F_c\left(A+s\right)-F_c\left(A-s\right)\right]$  

 $F\left[af+bg\right]\ =aF\left[s\right]\ \ +bG\left[s\right]$  

 $F\left[f\cdot g\right]\ =F\left[s\right]\ \ \cdot G\left[s\right]$  

 $F\left[af\right]\ =\frac{1}{\left|a\right|}F\left[\frac{s}{a}\right]\ \$  

 $F\left[f'\left(x\right)\right]\ =-isF\left[s\right]\ \$  

 $F_s\left[e^{-5x}\right]=\sqrt{\frac{2}{\pi}}\ \frac{5}{5^2+s^2}$  

 $F_s\left[e^{-5x}\right]=\sqrt{\frac{2}{\pi}}\ \frac{s}{5^2+s^2}$  

 $F_s\left[e^{-5x}\right]=\sqrt{\frac{2}{\pi}}\ \frac{s}{a^2+s^2}$  

none of the above

 $\frac{d}{ds}\ F_c\left[s\right]$  

 $-\frac{d}{ds}\ F_c\left[s\right]$  

 $\frac{d}{ds}\ F_s\left[s\right]$  

 $\frac{d}{ds}\ F_s\left[s\right]$  

true

false

some times

none

$\int_{-\infty}^{\infty}\left|f\left(x\right)\right|^2dx=\int_{-\infty}^{\infty}\left|f\left(s\right)\right|^2ds$

$\int_0^{\infty}\left|f\left(x\right)\right|^2dx=\int_0^{\infty}\left|f\left(s\right)\right|^2ds$

$\int_{-\infty}^{\infty}\left|f\left(x\right)\right|^{ }dx=\int_{-\infty}^{\infty}\left|f\left(s\right)\right|^{ }ds$

$\int_{-\infty}^{\infty}f\left(x\right)^2dx=\int_{-\infty}^{\infty}f\left(s\right)^2ds$

 $\ \frac{\pi}{2}$  

 $\ \frac{\pi}{4}$  

 $\ \pi$  

0

 $\frac{1}{\sqrt{2\pi}}\int_{-\infty}^{\infty}\ F\left[s\right]\ dx\ =\ f\left(x\right)$  

 $\frac{1}{\sqrt{2\pi}}\int_{-\infty}^{\infty}F\left[s\right]e^{isx}\ ds\ =f\left(x\right)$  

 $\frac{1}{\sqrt{2\pi}}\int_{-\infty}^{\infty}F\left[s\right]\ e^{-isx}ds\ =f\left(x\right)$  

 $\frac{1}{\sqrt{2\pi}}\int_{-\infty}^{\infty}F\left[s\right]\ \ \cos sx\ ds\ =\ f\left(x\right)$  

 $\frac{1}{\sqrt{2\pi}}\int_{-\infty}^{\infty}f\left(x\right)\ \cos sx\ dx\ =\ F_c\left[s\right]$  

 $\frac{1}{\sqrt{2\pi}}\int_0^{\infty}f\left(x\right)\ \cos sx\ dx\ =\ F_c\left[s\right]$  

 $\sqrt{\frac{2}{\pi}}\int_0^{\infty}f\left(x\right)\ \cos sx\ dx\ =\ F_c\left[s\right]$  

 $\frac{1}{\sqrt{2\pi}}\int_{-\infty}^{\infty}f\left(x\right)\ \ \cos sx\ dx\ =\ F_s\left[s\right]$