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My question is a short one: I would like \lim to always be displayed inline using the \displaystyle mode.

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\let\svlim\lim\def\lim{\displaystyle\svlim} –  Steven B. Segletes Feb 18 at 13:50
    
why? This messes up line spacing –  daleif Feb 18 at 13:50
    
I know but for undergraduate student, it is better to see limits in \displaystyle format. –  projetmbc Feb 18 at 13:52
    
@StevenB.Segletes Can you post this as an answer with a few explanations so as to accept it ? –  projetmbc Feb 18 at 13:53
    
@StevenB.Segletes Not unless you want the entire expression to be in displaystyle. –  David Carlisle Feb 18 at 14:05
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1 Answer

up vote 10 down vote accepted

You don't want \displaystyle, but \limits after \lim.

\documentclass{article}
\usepackage{amsmath}

\usepackage{etoolbox}
\apptocmd{\lim}{\limits}{}{}

\begin{document}
Here's a limit: $\lim_{x\to0}\sin x=0$.
\end{document}

enter image description here

On the other hand, students can learn how to properly read symbols; I feel it wrong to attach too much to symbols, which are mainly conventions and not laws cast in stone.

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We sometimes see teachers using $\sum\limits...$ because apparently their students does not recognize a sum unless the limits are above and below. In a similar category they do not use \exp as their students does not know it is the same at e^{...}, so we'll see stuff like e^{\int ....} ... –  daleif Feb 18 at 14:35
    
@egreg Thanks a lot for this solution that uses less vertical space. :-) You're totally right for the conventions but my bachelor student are not corrected by me so I have to follow some recommandations. –  projetmbc Feb 18 at 20:11
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