v class="problem">
  <div class="marginpar"> The polynomial you are
    creating is often called a <a
     href="http://en.wikipedia.org/wiki/Taylor_polynomial">Taylor
    polynomial</a>.</div>

    Now let $f(x)=\sin x$. Find a 7th degree polynomial so
    that the function and the polynomial have the same value and
    same first seven derivatives when evaluated at $x=0$. Evaluate
    the polynomial at $x=0.3$. How close is this value to your
    calculator's estimate of $\sin(0.3)$? You may find it valua