Question

in problems 1-20 find either f(S)or f(t),as indicated $\mathit{L}\left\{t{e}^{-6t}\right\}$

Short answer

find either f(S)or f(t),as indicated

$\begin{array}{rcl}L\left\{t{e}^{-6t}\right\}& =& \overline{)L{\left\{t\right\}}_{s\to s+6}}\\ & =& \frac{1}{{\left(s+6\right)}^2}\end{array}$

Step-by-step solution

Step1: definition of indicated

The definition of indicate is to refer to, point to, or show something, or to make a brief statement acknowledging something. When you point to Susie, you are indicating

$L\left\{t{e}^{-6t}\right\}$

According to Theorems 7.1.1. and 7.3.1.,

we have

$\begin{array}{rcl}L\left\{t{e}^{-6t}\right\}& =& {\overline{)L\left\{t\right\}}}_{s\to s+6}\\ & =& {\overline{)\frac{1!}{s^2}}}_{s\to s+6}\end{array}$

  solve the expression as,

$$\begin{gathered} =\frac{1!}{{\left(s+6\right)}^2} \\ =\frac{1}{{\left(s+6\right)}^2} \end{gathered}$$

hence$=\frac{1}{{\left(s+6\right)}^2}$