         <p>We'll find that throughout this course, the key difference
  between first-semester calculus and multivariate calculus is that
  we replace the input $x$ and output $y$ of functions with the
  vectors $\vec x$ and $\vec y$.</p>

  <div class="problem">
    <div class="marginpar">
      The point to this problem is to help you learn to recognize
      the dimensions of the domain and codomain of the function. If
      we write $\vec f:\RR^n\to \RR^m$, then $\vec x$ is a vector in
      $\RR^n$ wi