Question

Question: in problems 1-20find either f(S)or f(t),as indicated$\mathit{L}\left\{t{e}^{10t}\right\}$.

Short answer

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

$\begin{array}{rcl}L\left\{t{e}^{10t}\right\}& =& \underset{X\to \infty -10}{\lim }L\left\{t\right\}\\ & =& \frac{1}{{\left(S-10\right)}^2}\end{array}$

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.

$\begin{array}{rcl}L\left\{t{e}^{10t}\right\}& =& \underset{S\to -10}{\lim }L\left\{t\right\}\\ & =& \underset{S\to -10}{\lim }\frac{1}{s^2}\\ & =& \frac{1}{{\left(S-10\right)}^2}\\ & & \\ & & \end{array}$

 first translation theorem

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

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

Hence,

$=\frac{1}{{\left(S-10\right)}^2}$