Determine whether the LTIC systems characterized by the following impulse responses are memoryless, causal, and stable. Justify your answer. For the unstable systems, demonstrate with an example that a bounded input signal produces an unbounded output signal.

$($i$)h1(t)=(t)+e^{-5t}u(t)$;

$($ii$)h2(t)=e^{-2t}u(t)$;

$($iii$)h3(t)=e^{-5t}sin(2t)u(t)$;

$($iv$)h4(t)=e^{-2|t|}+u(t+1)-u(t-1)$;

$($v$)h5(t)=t[u(t+4)-u(t-4)]$;

$($vi$)h6(t)=sin10t$;

$($vii$)h7(t)=cos(5t)u(t)$;

$($viii$)h8(t)={0\mathrm{.}95}^{|t|}$;

$($ix$)h9(t)=\{\begin{array}{cc}1,& -1t<mn>0</mn>\\ -1,& 0t1\\ 0& \text{o}\text{t}\text{h}\text{e}\text{r}\text{w}\text{i}\text{s}\text{e}\text{.}& \end{array}$