Please can you check my answers for the below Laplace questions.
thank you.
Question 1
Find the Laplace transform forms of the following piecewise function:
$$g(t)=\left\{ \begin{align} & (4+t)^2\quad,t>-4 \\ & 0\qquad\quad\quad,t< -4 \\ \end{align} \right.$$
MY Answer:
$$\mathcal{L}(t^2)=\frac{2}{s^3} $$
$$\mathcal{L}{(t^2g(t))}=\frac{2e^{4s}}{s^3}$$
Question 2
Find the inverse Laplace of : $\large\frac{e^{-5s}}{s-2}$
MY Answer:
$$\mathcal{L}^{-1}\left( \frac{e^{-5s}}{s-2}\right) = e^{2(t-5)}$$
Or
$$ u(t-5). e^{2(t-5)}$$