Align enumeration list containing math items with tabular

Question

I'm trying to have the following horizontal alignment of (enumerated) questions, but for some reason there is a misalignment in all the columns except for the first. Or maybe it is the first that is misaligned, I can't understand. Is there an easy way for a rookie like me to fix this? If it can be done with another environment, other than tabular, or even with a new package, I would much appreciate it.

\documentclass[a4paper,12pt]{article}

\usepackage{amsmath}
\usepackage{amsfonts}
\usepackage[utf8]{inputenc}
\usepackage[english,greek]{babel}
\usepackage[inline]{enumitem}



    \begin{document}


    \noindent Να βρείτε το $\underset{x\to x_0}{\textlatin{lim}} f(x)$ όταν:
    \begin{enumerate}[label=(\!\it\roman*\rm)]
    \begin{tabular}{p{0.3\textwidth}p{0.3\textwidth}p{0.3\textwidth}}
        \item $x_0=1$ & \item $x_0=2$ & \item $x_0=3$ \\ \item $x_0=4$ & \item $x_0=5$ & \item $x_0=6$
    \end{tabular}
    \end{enumerate}

    \end{document}

Answer 1

I suggest the tasks package:

\documentclass[a4paper,12pt]{article}

\usepackage{amsmath}
\usepackage{amsfonts}
\usepackage[utf8]{inputenc}
\usepackage[english,greek]{babel}
\usepackage{tasks}

\settasks{
  counter-format=(tsk[r]),
  item-indent=4em,
  label-format=\itshape,
  label-width=3em,
  label-offset=0.5em,
  label-align=right,
}
\begin{document}

\noindent
Να βρείτε το $\lim\limits_{x\to x_0} f(x)$ όταν:
\begin{tasks}(3)
\task $x_0=1$
\task $x_0=2$
\task $x_0=3$
\task $x_0=4$
\task $x_0=5$
\task $x_0=6$
\end{tasks}

\end{document}

Note how the limit operator is input. I'd avoid \limits for in line formulas, though.

If you want upright parentheses

\documentclass[a4paper,12pt]{article}

\usepackage{amsmath}
\usepackage{amsfonts}
\usepackage[utf8]{inputenc}
\usepackage[english,greek]{babel}
\usepackage{tasks}

\NewDocumentCommand{\lparen}{}{\textup(}
\NewDocumentCommand{\rparen}{}{\/\textup)}

\settasks{
  counter-format=\lparen tsk[r]\rparen,
  item-indent=4em,
  label-format=\itshape,
  label-width=3em,
  label-offset=0.5em,
  label-align=right,
}
\begin{document}

\noindent
Να βρείτε το $\lim\limits_{x\to x_0} f(x)$ όταν:
\begin{tasks}(3)
\task $x_0=1$
\task $x_0=2$
\task $x_0=3$
\task $x_0=4$
\task $x_0=5$
\task $x_0=6$
\end{tasks}

\end{document}

Answer 2

There are all kinds of vertical separation/space inserted with the use of \item: \topsep for the first \item, \itemsep for subsequent items, \parsep and \partopsep. Adding the nosep option to your list ensures that no vertical spacing is inserted, resulting in the vertical alignment you seek.

\documentclass{article}

\usepackage{amsmath}
\usepackage{amsfonts}
\usepackage[utf8]{inputenc}
\usepackage[english,greek]{babel}
\usepackage[inline]{enumitem}

\begin{document}

\noindent Να βρείτε το $\underset{x\to x_0}{\textlatin{lim}} f(x)$ όταν:
\begin{enumerate}[label=(\!\itshape\roman*\rmfamily),nosep]
  \begin{tabular}{p{0.3\textwidth}p{0.3\textwidth}p{0.3\textwidth}}
    \item $x_0=1$ & \item $x_0=2$ & \item $x_0=3$ \\ \item $x_0=4$ & \item $x_0=5$ & \item $x_0=6$
  \end{tabular}
\end{enumerate}

\end{document}