 slope as $f(x)=e^x$ does at $x=0$. Set up a system of
      equations and then find the unknowns $a$ and $b$. The next
      two are very similar.</li>

      <li>Find a second degree polynomial $P_2(x)=a+bx+cx^2$ so
      that $P_2(0)=f(0)$, $P'_2(0)=f'(0)$, and $P''_2(0)=f''(0)$.
      In other words, give me a parabola that passes through the
      same point, has the same slope, and has the same concavity as
      $f(x)=e^x$ does at $x=0$.</li>

      <li>Find a third degree polynomial $P_3(x)=a+bx+cx^