Chapter 6.3, Problem 40P

(a)

To determine

To sketch: The graph of the function $p\left(t\right)=\{\begin{array}{l}t,\text{ 0}\le t<1\\ 2-t,\text{ 1}\le t<2\end{array}$ and $p\left(t+2\right)=p\left(t\right)$.

(b)

To determine

To find: The Laplace transform of the function $p\left(t\right)=\{\begin{array}{l}t,\text{ 0}\le t<1\\ 2-t,\text{ 1}\le t<2\end{array}$.

(c)

To determine

To find: The Laplace transform of the function $p\left(t\right)={\displaystyle {\int }_0^{t}f\left(t\right)dt}$ where $f\left(t\right)=\{\begin{array}{l}1,\text{ 0}\le t<1\\ -1,\text{ 1}\le t<2\end{array}$ and $f\left(t+2\right)=f\left(t\right)$.