1. If \( F(s)=\mathcal{L}\{ f(t)\}\) exists for \(s > a \ge 0\), and \(c\) is a constant, then prove: \[\mathcal{L}\{u(t-c)\} = \frac{e^{-cs}}{s}\] View Video Proof
2. If \( F(s)=\mathcal{L}\{ f(t)\}\) exists for \(s > c \ge 0\), and \(a\) is a constant, then prove: \[\mathcal{L}\{e^{at}f(t)\} = F(s-a)\] View Video Proof
3. If \( F(s)=\mathcal{L}\{ f(t)\}\) exists for \(s > c \ge 0\), and \(a\) is a constant, then prove: \[\mathcal{L}\{ f(t-a) u(t-a)\} = e^{-as}F(s)\] View Video Proof
4. If \( F(s)=\mathcal{L}\{ f(t)\}\) exists for \(s > a \ge 0\), and \(c\) is a constant, then prove: \[\mathcal{L}\{ f(ct) \} = \frac{1}{c} F\left(\frac{s}{c}\right)\] View Video Proof