$2\mathrm{.}22$ Determine whether or not each of the following LTI systems is $($i$)$ causal and$/$or $($ii$)$ BIBO stable. If the system is not BIBO stable, provide an example of a bounded input that yields an unbounded output. $($a$)$ y$($t$)=$ dx dt $($b$)$ y$($t$)=$ R t $$ x$($$)$ d $($c$)$ y$($t$)=$ R t $$ x$($$)$ cos$($t $$$)$ d $*($d$)$ y$($t$)=$ x$($t $+1)($e$)$ y$($t$)=$ R t$+1$ t$1$ x$($$)$ d $($f$)$ y$($t$)=$ R t x$($$)$ e $2($t$$$)$ d