$1\mathrm{.}17.$ Determine whether these continuous$-$time systems are causal or noncausal, have memory or are memoryless. Justify your answers. In the following part $x(t)$ is an arbitrary input and $y(t)$ is the output response to $x(t)$ :

$($a$)y(t)=|x(t)|=\{\begin{array}{ccc}x(t)& \text{w}\text{h}\text{e}\text{n}& x(t)0\\ -x(t)& \text{w}\text{h}\text{e}\text{n}& x(t)<mn>0</mn>\end{array}$

$($b$)y(t)=e^{u(t)}$

$($c$)y(t)=(sint)x(t)$

$($d$)y(t)=\{\begin{array}{ccc}x(t)& \text{w}\text{h}\text{e}\text{n}& |x(t)|10\\ 10& \text{w}\text{h}\text{e}\text{n}& |x(t)|>10\end{array}$

$($e$)y(t)={\displaystyle \underset{0}{\overset{t}{}}}(t-)x()d$

$($f$)y(l)={\displaystyle \underset{0}{\overset{1}{}}}x()d$