Exercises
=========

#. Prove that the Laplace transform of $Ae^{st}$ equals $A/(s+a)$.

#. What is the transfer function
   $H(s)=\frac{U_{\mbox{out}}(s)}{U_{\mbox{in}}(s)}$ for the
   electronic scheme shown below.

   .. tikz::

      \draw
      (0,1) node[anchor=east]{$u_{\mbox{in}}(t)$}
      (0,2)  to[C, l=$10\mu F$, o-] (2,2)
      (2,2) to[generic, l=$8\Omega$] (2,0)
      (2,2) to[short, -o] (4,2)
      (0,0) to[short, o-o]  (4,0)
      (4,1) node[anchor=west]{$u_{\mbox{out}}(t)$};


#. Plot the frequency response of the filter sketched above.