What is mathcal L^-1\(e^-4s)/(s+1)\?

Exercise · ZW-UNIT-STEP-FUNCTION-007 · ★★☆ Intermediate

What is \(\mathcal L^{-1}\left\{\dfrac{e^{-4s}}{s+1}\right\}\)?

Choose one option.

Show answer

Since \(\mathcal L^{-1}\{1/(s+1)\}=e^{-t}\), the factor \(e^{-4s}\) shifts by 4: evaluate at \(t-4\) and multiply by \(u_4(t)\).

The unit step function \(u_c(t)\), with \(c\ge0\), equals 0 while \(t<c\) and equals 1 from \(t=c\) on; it is a switch that turns on at time \(c\).

\[u_c(t)=\begin{cases}0,&t