Question

In problems 1-20find either f(S) or f(t), as indicated$\mathit{L}\left\{e^{-2t}cos4t\right\}$

Short answer

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

$$\begin{gathered} L{e}^{-2t}\cos 4t \\ =\underset{s\to s+2}{\lim }\frac{3}{s^2+16} \\ =\frac{s+2}{{\left(s+2\right)}^2+16} \end{gathered}$$

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,

$L\left\{e^{at}f\left(t\right)\right\}=F\left(s-a\right)$

Step 2: definition of indicated

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

$L{e}^{-2t}\cos 4t$

Give the equation:

$$\begin{gathered} =\underset{s\to s(-2)}{\lim }L\left\{\cos 4t\right\} \\ =\underset{s\to s(-2)}{\lim }\frac{3}{s^2+16} \end{gathered}$$

Addition:

$\frac{s+2}{{\left(s+2\right)}^2+16}$

Hence,

$\frac{s+2}{{\left(s+2\right)}^2+16}$