Consider the periodic function $f(t)$ defined as follows: $$f(t) = 2-e^{-3t} \mbox { for } 0\leq t < 2, \mbox{ and } f(t+2) = f(t).$$
Sketch a graph of $f(t)$ over several periods and compute its Laplace transform.

$\displaystyle F(s) = {\mathcal L}\left\lbrace f(t) \right\rbrace =$ $\displaystyle \cdot \int_A^B$ $\ \ $ where $A =$ and $B =$

$\displaystyle \phantom{F(s) = {\mathcal L}\left\lbrace f(t) \right\rbrace} =$ help (formulas)