# Subscript, Superscript, and Bracket

I want to write like this:

But when I write

\documentclass{article} \usepackage{mathtools} \begin{document} $$\lim\limits_{\Delta\rightarrow0}\Delta{}_{t=0}^{t=T}\left\vert\dfrac{df(t)}{dt}\right\vert^2 dt$$ \end{document}

The output was like this

Anyone can tell me what is my mistake?

• As always on this site please post a full minimal example, not just a sniplet like this. Please post something others can copy and test as is without adding anything – daleif Aug 4 '20 at 15:18
• Use this \lim\limits_{\Delta\to 0}\; \Delta_{t=0}^{t=T}\;\left| \dfrac{d\,f(t)}{dt} \right|^2\; dt – Tanvir Aug 4 '20 at 15:18
• @daleif thank you, I've edited it. – Wind Aug 4 '20 at 16:05

The _{t=0}^{t=T} in your line makes these things the superscript and subscript of the \lim\limits_{\Delta\rightarrow0}{}. I would do it using \prescript from mathtools package.

\usepackage{mathtools}


and then in the math environment:

\lim\limits_{\Delta\rightarrow0}{} \Delta\prescript{t=T}{t=0}{\left\vert\dfrac{df(t)}{dt}\right\vert^2 dt}


This provides the result as follows:

• The upper prescript is higher than necessary. Unfortunately, I don't know how to modify it using this method. – barbara beeton Aug 4 '20 at 18:14
• @barbarabeeton I have used \lower command. See my update 1. – Sebastiano Aug 4 '20 at 22:24

Here's an attempt to faithfully reproduce the first screenshot you posted.

\documentclass{article}
\usepackage{array}
\usepackage{newtxtext,newtxmath} % optional
\begin{document}
$\lim_{\Delta\phantom{\to}0} \Delta \begin{array}{>{\scriptstyle}l@{}} t=T \\ t=0 \end{array} \Bigl| \frac{df\!(t)}{dt} \Bigr|^2 dt$
\end{document}

• I feel the original image posted is missing tends to in the limits. It's a strange equation as it means nothing. – Tanvir Aug 4 '20 at 15:29
• @Tanvir - The OP stated that he/she wanted to reproduce the first image. The code in my answer achieves that. – Mico Aug 4 '20 at 15:31
• @Tanvir yes, you're right. there is something missing and a strange equation, because the source file that I used has incomplete equation. – Wind Aug 4 '20 at 16:10
• @Mico thank you for your answer. – Wind Aug 4 '20 at 16:10

Using...tensor package.....with the enviroment mathtools...an alternative a bit more complicated :-)

\documentclass[12pt]{article}
\usepackage{mathtools}
\usepackage{tensor}

\begin{document}
$\lim_{\Delta\phantom{\to}0} \Delta \tensor*[^T_t]{\bigg\lvert \frac{df(t)}{dt}\bigg\rvert}{^2} dt$
\end{document}


## Update 1

Using \lower-0.01em with \hbox and \scriptstyle it is possible a nice alignment between T and 2.

\documentclass[a4paper,12pt]{article}
\usepackage{mathtools}
\usepackage{tensor}

\begin{document}
$\lim_{\Delta\to 0} \Delta \tensor*[^{\lower-0.01em \hbox{\scriptstyle T}}_t]{\bigg\lvert \frac{df(t)}{dt}\bigg\rvert}{^2} dt$
\end{document}