what are inverse Laplace transform examplesQ(i) \[L^{-1}\left[\frac{4}{s-3}\right]\](ii)\[f(s) =\frac{5}{(s+1)^4}\](iii) \[f(s)=\frac{s+4}{s^2+8s+37}\](iv) \[\frac{1}{s}-\frac{2}{s^2}\ +\frac{4}{s-3}+\frac{5}{{(s-3)}^4}\]Answer : (i)First Shifting Theorem States thatIf \[L\left[f\left(t\right)\right]=\ F\left(s\right)\] Then \[ L\left[e^{\alpha t}f\left(t\right)\right]=\ F\left(s\ -\ \alpha\right),\ s\ >\ a\ +\ \alpha\]Let \[f\left(t\right)=1,\ \ \alpha=3\]Then by First Shifting Theorem \[L\left[e^{3t}1\right]=\frac{1}{\left(s\ -3\right)}\]\[L^{-1}\left[\frac{1}{s-3}\right]=e^{3t}1=e^{3t}\]Therefore…
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