List of practice Questions

Given a function \(f(t) = e^{-at}\), where \(a\) is a constant. The Laplace transform of the function is \(\mathcal{L}[f(t)] = F(s)\). Which one of the following options is correct?

Let \( f(t) \) be a function of \( t \) defined for all positive values of \( t \). The Laplace transform of \( f(t) \), denoted by \( L\{f(t)\} = \int_0^{\infty} e^{-st}f(t)\,dt \), exists for a parameter \( s \) that may be real or complex, provided the integral exists. The Laplace transform of \( f(t) = \sin 2t\sin 4t \) is

The final value theorem is used to find the

If $\mathcal{L}\{f(t)\} = F(s)$, then $\mathcal{L}\{f(t - T)\}$ is equal to,

The Laplace transform of \( e^{-at} \) is: