Multicols balancing with equations

Question

I'm giving students a problem involving eight limit/function requirements and would like them to be equally spaced onto two lines. Here's the code:

\documentclass[11pt, bothsides]{exam}
\usepackage{multicol}
\usepackage{amsmath}
\extrawidth{1in}
\begin{document}
\begin{questions}
\question[10] Draw an example of a function $f(x)$ that satisfies the following conditions:
\newline
\begin{multicols}{4}
    $$\lim_{x\to-2}f(x)=1$$
    $$f(-2)=\text{DNE}$$
    $$\lim_{x\to2^-}f(x)=-4$$
    $$f(2)=3$$
    $$\lim_{x\to2}f(x)=\text{DNE}$$
    $$f(4)=-2$$
    $$\lim_{x\to4}f(x) \hspace{.1in} \text{exists}$$
    $$\lim_{x\to4}f(x)\neq f(4)$$
\end{multicols}
\end{questions}
\end{document}

But here's the output:

Any ideas why this might be the case? I think it may be due to the extrawidth command, but removing it just screws things up a bit more:

Any ideas? It's not a deal-breaker, but would like to help understand things. Perhaps an array would be better?

Answer 1

Since you're also loading the amsmath package, you might as well make use of its alignat* environment to line up the 8 equations. In the example below, I've set a distance of 4em (equivalent to 4 "quads") between the columns; feel free to modify the spacing as you see fit.

\documentclass[11pt, bothsides]{exam}
\usepackage{amsmath}
\extrawidth{1in}
\begin{document}
\begin{questions}
\question[10] Draw an example of a function $f(x)$ that satisfies the following conditions:

\begin{alignat*}{4}
&\lim_{x\to-2}f(x)=1&\hspace{4em}&
 f(-2)=\text{DNE}&\hspace{4em}&
 \lim_{x\to2^-}f(x)=-4&\hspace{4em}&
 f(2)=3\\
&\lim_{x\to2}f(x)=\text{DNE}&&
 f(4)=-2&&
 \lim_{x\to4}f(x) \text{ exists}&&
 \lim_{x\to4}f(x)\neq f(4)
\end{alignat*}
\end{questions}
\end{document}

---

I think of the multicols environment as something meant primarily for text. Using (abusing?!) this environment to typeset a bunch of displayed equations probably raises all kinds of issues that the package's author never considered. If, for some reason, you simply must use it in your code, I would suggest you use a gather* environment instead of 8 individual displayed equations. Oh, and observe the use of \noindent after \begin{multicols}{4}.

\documentclass[11pt, bothsides]{exam}
\usepackage{amsmath,multicol}
\allowdisplaybreaks
\extrawidth{1in}
\begin{document}
\begin{questions}
\question[10] Draw an example of a function $f(x)$ that satisfies the following conditions:

\begin{multicols}{4}
\noindent
\begin{gather*}
\lim_{x\to-2}f(x)=1\\
f(-2)=\text{DNE}\\
\lim_{x\to2^-}f(x)=-4\\
f(2)=3\\
\lim_{x\to2}f(x)=\text{DNE}\\
f(4)=-2\\
\lim_{x\to4}f(x) \text{ exists}\\
\lim_{x\to4}f(x)\neq f(4)
\end{gather*}
\end{multicols}
\end{questions}
\end{document}