Tukukkk

For example, this is what I am looking for:

Usually for limits where the value is 0 or 1 of a particular expression (e^x) in this case, you might see something like a tilted 45 degrees equal sign, and the value of that expression.

Not sure how to do it here.

Maybe something like a overbrace without the actual overbrace visible?

If you only want to draw one of those, this might be a bit of an overkill, but if you plan to do several annotations of that kind and wish to have access to more fancy features, this might be a reasonable way to go.

documentclass{article}

usepackage{amsmath}

usepackage{tikz}

usetikzlibrary{tikzmark}

begin{document}

[lim_{xto0}tikzmarknode{ex}{mathrm{e}^x}left(2+4xright)~=~2]

begin{tikzpicture}[overlay,remember picture]

path[red] ([xshift=1pt,yshift=1pt]ex.north east) -- ++(45:{width("=")*1pt-1pt})

node[midway,sloped]{$=$} node[above right=-2pt]{$1$};

end{tikzpicture}

end{document}

Arguably somewhat clearer alternatives include

documentclass{article}

usepackage{mathtools}

usepackage{tikz}

usetikzlibrary{tikzmark}

begin{document}

[lim_{xto0}tikzmarknode{ex}{mathrm{e}^x}left(2+4xright)~=~2]

begin{tikzpicture}[overlay,remember picture]

draw[red,->] ([xshift=1pt,yshift=1pt]ex.north east) --

++(45:{width("$scriptstyle xto0$")*1pt})

node[midway,sloped,above]{$scriptstyle xto0$} node[above right=-1pt]{$1$};

end{tikzpicture}

end{document}

which illustrates what I mean by "more fancy options".