<p>In first semester calculus, we can show that a limit does
  or does not exist by considering what happens from the left, and
  comparing it to what happens on the right. You probably used the
  following theorem extensively.</p>

  <blockquote>
    If $y=f(x)$ is a function defined on some open interval
    containing $c$, then $\ds\lim_{x\to c}f(x)$ exists if and only
    if $\ds\lim_{x\to c^-}f(x) = \ds\lim_{x\to c^+}f(x)$.
  </blockquote>
                <p>A limit exists precisely when the limits fro