Question

Question: In problems1-20 find either f(S) or f(t),as indicated$\mathit{L}\left\{t^{10}{e}^{-7t}\right\}$.

Short answer

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

$$\begin{gathered} L\left\{t{\left(e^t+e^{2t}\right)}^2\right\} \\ Lt\left(e^{2t}+2e^{3t}+e^{4t}\right) \end{gathered}$$

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="1664209927817" $L\left\{e^{at}f\left(t\right)\right\}=F\left(s-a\right)$

Step 2: definition of indicated

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

Give the equation:

$\begin{array}{rcl}L\left\{t^{10}{e}^{-7t}\right\}& =& \underset{s\to s-7}{\lim }L\left\{t^{10}{e}^{-7t}\right\}\\ & =& \underset{s\to s-7}{\lim }L\left\{t^{10}\right\}\\ & & \end{array}$

Addition:

$$\begin{gathered} =\begin{array}{rcl}& & \underset{s\to s-7}{\lim }\end{array}\frac{10!}{s^{11}} \\ =\frac{10!}{s{\left(s+7\right)}^{11}} \end{gathered}$$

Hence,$\frac{10!}{s{\left(s+7\right)}^{11}}$