f(\vec x)$ exists if and only if the limit exists along
    every possible approach to $\vec c$ and all these limits are
    equal.
  </blockquote>
    <p>There's a fundamental problem with using this theorem to
  check if a limit exists. Once the domain is 2-dimensional or
  higher, there are infinitely many ways to approach a point. There
  is no longer just a left and right side. To prove a limit exists,
  you must check infinitely many cases&mdash;that usually takes a <em>really</em> long time. The real