[Tex/LaTex] Displaystyle for “lim” (global) in tabular-environment

displaystylemath-modetables

I want to use a tabular-environment and within it some math formulas (limits). But I want \lim to be in displaystyle (without using display-function each time or defining a new command).

My MWE:

\documentclass[14pt,a4paper,headlines=6,headinclude=true]{scrartcl}

\usepackage[english,ngerman]{babel}         
\usepackage[utf8]{inputenc}                         

\usepackage{amsmath,amssymb,stmaryrd}       
\usepackage{enumitem}                                       
\usepackage{paralist}                                       
\usepackage{scrhack}                                        

\usepackage[left=1.5cm,right=1.5cm,top=4.5cm,bottom=0.5cm,includefoot]{geometry}        
\usepackage[colorlinks, linkcolor = black, citecolor = black, filecolor = black, urlcolor = blue, pdfborder ={0 0 0}, pdfstartview={FitH}]{hyperref} 

\usepackage{mwe}
\usepackage{scrlayer-scrpage}

\usepackage[compact,explicit]{titlesec}% http://ctan.org/pkg/titlesec
\titleformat{\section}[runin]{\large\bfseries}{}{0pt}{#1\quad\thesection}

\begin{document}
\begin{itemize}
    \item 1.) \textbf{Limits}: Calculate the following limits
        \begin{center} \begin{tabular}{ p{5cm} p{5cm} p{5cm} }
        \lim_{x \to -2} (x^2 + 5x) & \lim_{x \to 0} (x^2 + 3x - 4) & \lim_{x \to 2} (2x^2 + 5)^3   \\
        \\
        \lim_{x \to 0} \frac{x^2 - 2x -1}{x^5 - x^2 - 1 } & & \\
        & \lim_{x \to 4} \frac{2x^{\frac{3}{2}} - \sqrt{x}}{x^2 - 15} & \lim_{x \to a} A x^n 
        \end{tabular} \end{center}
\end{itemize}


\begin{align*}
    \lim_{x \to -2} (x^2 + 5x) &= \lim_{x \to -2} (x \cdot x) + \lim_{x \to -2} (5 \cdot x) \\
    &= \left( \lim_{x \to -2} x  \right) \left( \lim_{x \to -2} x  \right) + \left( \lim_{x \to -2} 5  \right) \left( \lim_{x \to -2} x  \right)
\end{align*}
\end{document}

enter image description here

Is there an easy way to set displaymode in tabular? Thank you

(2) Additional question, to the idea in the comments: How can I use this \everymath{\displaystyle} with align-environment? It doesnt work here:

\begin{center} \everymath{\displaystyle}
\begin{align*} 
    \lim_{x \to -2} (x^2 + 5x) &= \lim_{x \to -2} (x \cdot x) + \lim_{x \to -2} (5 \cdot x) \\
    &= \left( \lim_{x \to -2} x  \right) \left( \lim_{x \to -2} x  \right) + \left( \lim_{x \to -2} 5  \right) \left( \lim_{x \to -2} x  \right) \\
    &= (-2) (-2) + 5 \cdot (-2) = -6 \\
    \lim_{x \to 4} \frac{2x^{\frac{3}{2}} - \sqrt{x}}{x^2 - 15} &= \frac{2 \lim_{x \to 4} x^{\frac{2}{3}}- \lim_{x \to 4} \sqrt{x} }{\lim_{x \to 4} x^2 - 15} \\
    &= \frac{2 \cdot 4^{\frac{2}{3}} - \sqrt{4}}{4^2 - \sqrt{15}} = \frac{2 \cdot 8 - 2}{16 -15} = 14
\end{align*}
\end{center}

Thank you for your patience 🙂

(3) I Mean: Even within align-environment there's displaymode only in highest hierarchy (don't know to explain this better). Within a frac (see numerator) the limit is again small. I would like to use full displaymode in specified environment within all "under-layers" (or in the hole document in all under-layers). 

\documentclass{article}

\usepackage{amsmath,array}

\begin{document}
\begin{align*} 
    \lim_{x \to -2} (x^2 + 5x) &= \lim_{x \to -2} (x \cdot x) + \lim_{x \to -2} (5 \cdot x) \\
    &= \left( \lim_{x \to -2} x  \right) \left( \lim_{x \to -2} x  \right) + \left( \lim_{x \to -2} 5  \right) \left( \lim_{x \to -2} x  \right) \\
    &= (-2) (-2) + 5 \cdot (-2) = -6 \\
    \lim_{x \to 4} \frac{2x^{\frac{3}{2}} - \sqrt{x}}{x^2 - 15} &= \frac{2 \lim_{x \to 4} x^{\frac{2}{3}}- \lim_{x \to 4} \sqrt{x} }{\lim_{x \to 4} x^2 - 15} \\
    &= \frac{2 \cdot 4^{\frac{2}{3}} - \sqrt{4}}{4^2 - \sqrt{15}} = \frac{2 \cdot 8 - 2}{16 -15} = 14
\end{align*}

\end{document}

enter image description here

Best Answer

Then use array to adjust the style for the columns you're interested in:

enter image description here

\documentclass{article}

\usepackage{amsmath,array}

\begin{document}

\begin{enumerate}
  \item \textbf{Limits}: Calculate the following limits
    \begin{center}
      \begin{tabular}{ *{3}{>{$\displaystyle}p{5cm}<{$}} }
        \lim_{x \to -2} (x^2 + 5x) & \lim_{x \to 0} (x^2 + 3x - 4) & \lim_{x \to 2} (2x^2 + 5)^3 \\
        \\
        \lim_{x \to 0} \frac{x^2 - 2x -1}{x^5 - x^2 - 1 } & & \\
        & \lim_{x \to 4} \frac{2x^{\frac{3}{2}} - \sqrt{x}}{x^2 - 15} & \lim_{x \to a} A x^n
      \end{tabular}
    \end{center}
\end{enumerate}

\begin{align*}
  \lim_{x \to -2} (x^2 + 5x) &= \lim_{x \to -2} (x \cdot x) + \lim_{x \to -2} (5 \cdot x) \\
  &= \left( \lim_{x \to -2} x  \right) \left( \lim_{x \to -2} x  \right) + \left( \lim_{x \to -2} 5  \right) \left( \lim_{x \to -2} x  \right)
\end{align*}

\end{document}

Insert something before every entry in that column using >{<stuff>} and add something after every entry using <{<stuff>}.

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