$(20$ points$)$ Consider the first$-$order analogue lowpass filter in the s$-$domain:

H$($s$)=(49)/($s$+7)$

$($a$)$ What is the maximum value of the magnitude of H$($j$\backslash$omega $)?$

$($b$)$ Find the analog cut$-$off frequency $\backslash$omega $\_($c$)$ analytically? Show your work step by step.

$($c$)$ Assuming T$\_($s$)=0\mathrm{.}01$ second, use the impulse invariance method to find the approximate

H$($z$).$