As x is increased from $$ - \infty \,\,to\,\infty $$, the function $$f(x) = {{{e^x}} \over {1 + {e^x}}}$$

The derivative of the symmetric function drawn in Fig .1 will look like

Match the following and choose the correct combination.

GROUP 1
E- continuous and aperiodic signal
F- continuous and periodic signal
G- discrete and aperiodic signal
H- discrete and periodic signal

Group 2
1- Fourier representation is continuous and aperiodic
2- Fourier representation is discrete and aperiodic
3- Fourier representation is continuous and periodic
4- Fourier representation is discrete and periodic

The value of the integral $$\,I = {1 \over {\sqrt {2\,\,\pi } }}\int\limits_0^\infty {\exp \left( { - {{{x^2}} \over 8}} \right)dx} $$ is