Do the Laplace transforms for the following functions exist? Explain your answers. (You do not need to find the transforms , just show if they exist or not)

a)

b)

Reeves
2020-12-16
Answered

Existence of Laplace Transform

Do the Laplace transforms for the following functions exist? Explain your answers. (You do not need to find the transforms , just show if they exist or not)

a)$f(t)={t}^{2}\mathrm{sin}(\omega t)$

b)$f(t)={e}^{{t}^{2}}\mathrm{sin}(\omega t)$

Do the Laplace transforms for the following functions exist? Explain your answers. (You do not need to find the transforms , just show if they exist or not)

a)

b)

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$${\int}_{0}^{\mathrm{\infty}}{e}^{-st}d({\alpha}_{2}(t))?$$

I wanted to calculate ${\alpha}^{\prime}(x)$ and then write as the differential the integration of $({\alpha}^{\prime}\ast f)$

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