m every
  direction exists, and all directional limits are equal. In
  first-semester calculus, this required that you check two
  directions (left and right). This theorem generalizes to higher
  dimensions, but it becomes much more difficult to apply.</p>

  <div class="example">
    Consider the function $\ds f(x,y)=\frac{x^2-y^2}{x^2+y^2}$. Our
    goal is to determine if the function has a limit at the origin
    $(0,0)$. We can approach the origin along many different lines.
    One line through the o