Question

In problems 1-20find either f(S)or f(t),as indicated$\mathit{L}\mathbf{\left\{}{\mathbf{e}}^{\mathbf{t}}\mathbf{sin}\mathbf{3}\mathbf{t}\mathbf{\right\}}$

Short answer

Find either f(S) or f (t), as indicated.

$$\begin{gathered} L\left\{e^t\sin 3t\right\} \\ \underset{s\to s-1}{\lim }\left(L\left\{e^t\sin 3t\right\}\right) \\ =\frac{3}{s{\left(s-1\right)}^2+9} \end{gathered}$$

Step-by-step solution

First translation theorem

If$L\left\{f\left(t\right)\right\}=f\left(S\right)$and a is a any real number.

Then,

role="math" localid="1664212517744" $L\left\{e^{at}f\left(t\right)\right\}=F\left(s-a\right)$

Step 2: definition of indicated

The definition of indicate is point to and show statement acknowledging something. When you point to Susie, you are indicating.

$L\left\{e^t\sin 3t\right\}$

Give the equation:

$$\begin{gathered} =\underset{s+s+1}{\lim }L\left\{e^t\sin 3t\right\} \\ =\underset{s+s+1}{\lim }L\frac{3}{s^2+9} \\ =\frac{3}{s{\left(s-1\right)}^2+9} \end{gathered}$$

Hence,

$=\frac{3}{s{\left(s-1\right)}^2+9}$