Exercise · ZW-LAPLACE-TRANSFORM-003 · ★☆☆ Basic
Compute \(\mathcal L\{e^{3t}\}(s)\) for \(s>3\).
Choose one option.
Show answer
- C. \(\tfrac1{s-3}\)
Explanation
\(\int_0^\infty e^{-(s-3)t}dt=\tfrac1{s-3}\). The sign is \(s-3\), not \(s+3\).
Review the concept: Laplace transform
The Laplace transform \(\mathcal L\) assigns to a function \(f(t)\), defined for \(t\ge0\), the function \(F(s)\) obtained by integrating \(f\) times \(e^{-st}\) over \([0,\infty)\).
\[\mathcal L\{f\}(s)=F(s)=\int_0^\infty e^{-st}f(t)\,dt\]
More practice problems: laplace transform
- ZW-LAPLACE-TRANSFORM-001 Compute mathcal L\1\(s) for s>0.
- ZW-LAPLACE-TRANSFORM-002 Compute mathcal L\t\(s).
- ZW-LAPLACE-TRANSFORM-004 Compute mathcal L\sin 3t\(s).
- ZW-LAPLACE-TRANSFORM-005 Compute mathcal L\cos 2t\(s).
- ZW-LAPLACE-TRANSFORM-006 Compute mathcal L\t^2\(s).
- ZW-LAPLACE-TRANSFORM-007 Use linearity to compute mathcal L\3+2t\(s).
- ZW-LAPLACE-TRANSFORM-008 Compute mathcal L\te^t\(s).
- ZW-LAPLACE-TRANSFORM-009 For which values of s does the integral defining mathcal L\e^2t\(s) converge?