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A modified equals sign used represent use of L'Hopital's Rule isn't aligning well with other equals signs. How would I fix that? I'd prefer to do so without manually fiddling with spaces, if possible.

My code is as follows:

\documentclass{article}

\usepackage{amssymb}
\usepackage{amsmath}
\usepackage{commath} % Absolute value with /abs{}

\newcommand{\limq}[2]{\displaystyle\lim_{#1 \to #2}}

\begin{document}

\begin{align*}
\limq{n}{\infty} \abs{\frac{a_{n+1}}{a_n}} & = \limq{n}{\infty}\abs{\frac{\frac{(n+1)^2}{2^{n+1}}}{\frac{n^2}{2^n}}} \\
& = \limq{n}{\infty} \abs{\frac{(n^2+2n+1)2^n}{(2n^2)2^n}} \\
& \stackrel{\text{(H)}}{=}  \limq{n}{\infty} \abs{\frac{2n}{4n}} \\
& = 1/2
\end{align*}

\end{document}

The output:

Pesky L'Hopital's Rule

I tried moving the ampersand to the right of each symbol, but that just ended up shifting the (H) slightly to the left of the ordinary equals signs.

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  • 2
    Welcome to TeX.SX! A tip: If you indent lines by 4 spaces, then they're marked as a code sample. You can also highlight the code and click the "code" button ({}) or hit Ctrl+K. Apr 30, 2014 at 6:53
  • 2
    Welcome to TeX.SE. While code snippets are useful in explanations, it is always best to compose a fully compilable MWE that illustrates the problem including the \documentclass and the appropriate packages so that those trying to help don't have to recreate it. Apr 30, 2014 at 6:55

2 Answers 2

19

This is because (H) is wider than =, causing the entire stacked symbol to be wider than the rest of the alignment characters. you can remove the width of (H) by using \mathclap from mathtools:

enter image description here

\documentclass{article}
\usepackage{mathtools}% http://ctan.org/pkg/mathtools
\newcommand{\limq}[2]{\lim_{#1 \rightarrow #2}}
\newcommand{\abs}[1]{\left|#1\right|}
\begin{document}

\begin{align*}
    \limq{n}{\infty} \abs{\frac{a_{n+1}}{a_n}} & = \limq{n}{\infty} \abs{\frac{\frac{(n+1)^2}{2^{n+1}}}{\frac{n^2}{2^n}}} \\
                        & = \limq{n}{\infty} \abs{\frac{(n^2+2n+1)2^n}{(2n^2)2^n}} \\
                        & \stackrel{\mathclap{\text{(H)}}}{=}  \limq{n}{\infty} \abs{\frac{2n}{4n}} \\
                        & = 1/2
\end{align*}
\end{document}
4
  • Thanks for the incredibly quick answer! It worked beautifully.
    – asterac
    Apr 30, 2014 at 7:05
  • 1
    @triested In general it is not considered good taste to add comments like this to equal signs etc. it is better to add it to the text, or add a proper comment via \intertext,
    – daleif
    Apr 30, 2014 at 8:01
  • 1
    @ daleif I'll keep that in mind. My current professor asks for this abbreviated (H) notation, but then, we usually turn in handwritten work, not formal write-ups.
    – asterac
    Apr 30, 2014 at 8:21
  • @triested, we see that a lot. People don't really think about what they are doing and end up giving their students bad habits. It is even worse when students start writing things like (2.3) above an = to explain what happens. It is a better exercise to learn to write this is a much more reader friendly form.
    – daleif
    Apr 30, 2014 at 9:49
11

A simpler solution is to use a personal command such as

\newcommand{\Heq}{\overset{\hidewidth(\mathrm{H})\hidewidth}{=}}

With \hidewidth we insert a very large negative space; in this case it's equivalent to \hspace{-1000pt}, so the superscript will take no space. Using \mathrm is more efficient than \text for a single letter.

This requires just amsmath. However, I'd like to suggest also a couple of other improvements.

  • For \abs it's better to use \DeclarePairedDelimiter, that's more powerful (and correct) than always using \left| and \right|).

  • I don't think that \limq{n}{\infty} is better than \lim_{n\to\infty}, but it's just my opinion.

  • This is also a case where smashed fractions are not nice.

\documentclass{article}
\usepackage{mathtools} % also loads amsmath

% this requires mathtools
\DeclarePairedDelimiter{\abs}{\lvert}{\rvert}
% this requirese amsmath for \overset (better than \stackrel)
\newcommand{\Heq}{\overset{\hidewidth(\mathrm{H})\hidewidth}{=}}

\begin{document}

\begin{align*}
\lim_{n\to\infty} \abs*{\frac{a_{n+1}}{a_n}}
  & =    \lim_{n\to\infty} \abs*{\frac{\dfrac{(n+1)^2}{2^{n+1}}}{\dfrac{n^2}{2^n}}} \\
  & =    \lim_{n\to\infty} \abs*{\frac{(n^2+2n+1)2^n}{(2n^2)2^n}} \\
  & \Heq \lim_{n\to\infty} \abs*{\frac{2n}{4n}} \\
  & = \frac{1}{2}
\end{align*}
\end{document}

enter image description here

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