Exercise · ZW-INVERSE-LAPLACE-TRANSFORM-001 · ★☆☆ Basic

What is \(\mathcal L^{-1}\left\{\dfrac1{s-4}\right\}\)?

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  • A. \(e^{4t}\)

Explanation

Since \(\mathcal L\{e^{at}\}=\frac1{s-a}\), with \(a=4\) we get \(e^{4t}\). The sign of \(a\) is opposite to that in \(s-a\).

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Review the concept: Inverse Laplace transform

The inverse transform \(\mathcal L^{-1}\) of a function \(F(s)\) is the function \(f(t)\), defined for \(t\ge0\), whose Laplace transform is \(F(s)\).

\[f(t)=\mathcal L^{-1}\{F(s)\}\iff \mathcal L\{f\}=F\]

More practice problems: inverse laplace transform

ZW-INVERSE-LAPLACE-TRANSFORM-002 →