  in many cases.
    </p>
<p>
      There are two sources of error from finite differences: One, the truncation
      error arising from using a finite number of samples to cancel out higher order
      terms in the Taylor series. The second is the roundoff error involved in evaluating
      the function. The truncation error goes to zero as <span class="emphasis"><em>h</em></span> &#8594;
      0, but the roundoff error becomes unbounded. By balancing these two sources
      of error, we can choose a value