$(1$pts$)$ Let x$($t$)$ be a signal with Nyquist rate $0.$ Determine the Nyquist rate for each of the following signals: i$.$ x$($t$)+$ x$($t $1)$ ii$.$ d dtx$($t$)$ iii. x$2($t$)$ iv$.$ x$($t$)$cos$($$0$t$)$