Question

In Problems 3-24 fill in the blanks or answer true or false.

If fis not piecewise continuous on $\left[0,\infty \right)\mathbf{}\mathit{t}\mathit{h}\mathit{e}\mathit{n}\mathbf{}\mathcal{L}\left\{f\left(t\right)\right\}$will not exist.

Short answer

The given statement is False.

Step-by-step solution

Find whether the statement is true or false

The given statement f is not piecewise continuous on $\left[0,\infty \right)then\mathcal{L}\left\{f\left(t\right)\right\}$then will not exist.

The given statement is False.

For example, the function $f\left(t\right)=t^{-1/3}$is not piecewise continuous but its Laplace Transform exists as follows:

$\mathcal{L}\left\{t^{-1/3}\right\}=\frac{\Gamma \left(\frac{2}{3}\right)}{s^{2/3}}$

Thus, the given statement is false.