Below you will find LaTeX code which will generate a PDF document with a perfect accessibility score according to Canvas’ Ally tool.
Note that the file secant_tangent_lines_by_hand.png is required.
% ------------------------------------------------------------
% Document Preamble Settings for Tagged, Accessible PDF
% ------------------------------------------------------------
% Modern LaTeX document options and metadata (requires TeX Live 2026+ and LuaLaTeX)
\DocumentMetadata{
pdfversion = 2.0, % Use PDF 2.0 for enhanced features and compatibility
lang = en-US, % Specify main document language (improves accessibility)
pdfstandard=ua-2, % Enable PDF/UA-2 conformance for universal accessibility
tagging = on, % Activate structural tagging of document elements
% Uncomment below for custom math tagging and alternate modules if needed:
%tagging-setup = {math/setup=mathml-AF, extra-modules={verbatim-af}}
tagging-setup = {math/setup={mathml-SE}, % Configure Math as Structure Elements
math/alt/use = true, % Embed alternative LaTeX source in math (impacts accessibility)
extra-modules = {verbatim-af} % Add module for verbatim environments
}
}
\documentclass{article} % Basic LaTeX document setup
% ========== Packages for extra features ==========
\usepackage{amsmath,amsthm} % For better math typesetting
\usepackage[colorlinks]{hyperref} % For clickable links and PDF bookmarks
\usepackage{unicode-math} % Maps LaTeX commands for mathematical characters to the Unicode Mathematical Alphanumeric Symbols block.
\usepackage{graphicx} % For including images
\pagestyle{empty} % (Optional) Removes page numbers (nicer for examples)
\usepackage{authblk} % Helps with author names and affiliations
\newtheorem{theorem}{Theorem}[section] % Numbering resets when a section changes
\newtheorem{corollary}{Corollary}[theorem] % Numbering resets when a new theorem happens
\newtheorem{lemma}[theorem]{Lemma} % Uses the same counter as Theorem
\newtheorem{definition}{Definition} % Uses the same counter as Theorem
\newtheorem{example}{Example} % Uses the same counter as Theorem
\usepackage{tikz}
\usetikzlibrary{positioning}
\usepackage[executable=python.exe]{pyluatex} % Because I'm using Python
% ========== Main document begins ==========
\begin{document}
\title{Limits}
\date{19 July 2026}
\author{Keith E Emmert}
\affil{Tarleton State University Mathematics Department}
\pagestyle{headings}
\maketitle
\section{Best Practices for Maximum Accessibility}
\begin{definition}
The \textbf{secant line} of the function $f(x)$ through the points $(a,f(a))$ and $(x,f(x))$ is the line passing through these two points whose slope is given by $m_{sec} = \dfrac{f(x)-f(a)}{x-a}$ provided that $x \not= a$.
\end{definition}
\begin{definition}
The \textbf{slope of a tangent line} is found by letting $m_{tan} = \lim_{x\to a} \dfrac{f(x)-f(a)}{x-a}$.
\end{definition}
\begin{example}
Consider the function $f(x) = -x^3 + 4 x^2 - x - 6$ and suppose that $a=\frac{3}{2}$. Consider three points $x=-\frac{3}{2}, -\frac{1}{2}, \frac{1}{2}$ where we wish to draw secant lines. A figure illustrating these ideas where the three secant lines drawn in red, green and brown, and the tangent line drawn in black are shown on the graph of $f(x)$ drawn in blue. See Figures~\ref{fig-sec-tan} or~\ref{fig-sec-tan-2}.
\end{example}
% --- Figure with embedded alternative text (accessibility for images) ---
\begin{figure}[h]
\centering
% Use the 'alt' key directly within \includegraphics
\includegraphics[width=\linewidth, alt={The graph of $f(x)$ with its tangent line and several secant lines.}]{secant_tangent_lines_by_hand.png}
\caption{The graph of $f(x)$ with its tangent line and several secant lines.}\label{fig-sec-tan}
\end{figure}
\begin{python}
import numpy as np
import matplotlib.pyplot as plt
x = np.linspace(-4, 6, 1000)
f = -x**3 + 4*x**2 - x - 6
l1 = -13*x/4 + 3
l2 = 5*x/4 - 15/4
l3 = 15*x/4 - 15/2
l4 = 17*x/4 - 33/4
fig, ax = plt.subplots(figsize=(8, 3))
ax.plot(x, f, color='blue', linewidth=2, label='f(x) = -x^3+4x^2-x-6')
ax.plot(x, l1, '--', color='red', linewidth=1.5, label='y = -13x/4 + 3')
ax.plot(x, l2, '--', color='green', linewidth=1.5, label='y = 5x/4 - 15/4')
ax.plot(x, l3, '--', color='brown', linewidth=1.5, label='y = 15x/4 - 15/2')
ax.plot(x, l4, color='black', linewidth=1.5, label='y = 17x/4 - 33/4')
x0, y0 = 3/2, -15/8
ax.plot(x0, y0, 'ko', markersize=6)
ax.plot(-3/2, 63/8, 'ro')
ax.plot(-1/2, -35/8, 'go', markersize=6)
ax.plot(1/2, -45/8, 'o', color = 'brown', markersize=6)
ax.set_xlim(x.min(), x.max())
ax.set_ylim(-10, 10)
ax.axhline(0, color='gray', lw=0.6)
ax.axvline(0, color='gray', lw=0.6)
ax.set_xlabel('x')
ax.set_ylabel('y')
ax.legend(loc='best', fontsize=9)
ax.grid(alpha=0.3)
fig.savefig('secant-tangent-python.pdf')
plt.close()
\end{python}
% Display the figure.
\begin{figure}[ht]
\centering
\includegraphics[width=\linewidth, alt={The graph of $f(x)$ with its tangent line and several secant lines.}]{secant-tangent-python.pdf}
\caption{The graph of $f(x)$ with its tangent line and several secant lines. Generated by Python embedded in the \LaTeX\ document.}\label{fig-sec-tan-2}
\end{figure}
\begin{example}
Below is a table illustrating how the secant line slopes change. See Table~\ref{tab-sec-slope}.
\begin{table}[h]
\centering
\caption{Slopes of three different secant lines.}\label{tab-sec-slope}
\tagpdfsetup{table/header-rows={1}} % This identifies the header row as the first row
\begin{tabular}{c|c}
\hline
$x$ & $m_{sec} = \dfrac{f(x)-f(a)}{x-a}$ \\\hline
$-\dfrac{3}{2}$ & $-\dfrac{13}{4}$ \\
$\dfrac{1}{2}$ & $\dfrac{5}{4}$ \\
$\dfrac{1}{2}$ & $\dfrac{17}{4}$
\end{tabular}
\end{table}
\end{example}
Maybe we need to indicate that we have a header row for a data table without a caption.
\tagpdfsetup{table/header-rows={1}} % This identifies the header row as the first row
\begin{tabular}{|l|c|c|}
\hline
Fruit & Calories & Fiber (g) \\
\hline
Apple & 52 & 2.4 \\
Banana & 89 & 2.6 \\
Orange & 47 & 2.4 \\
\hline
\end{tabular}
Maybe you need to have two header rows indicated. If you need a caption then you can utilize \verb+\begin{table}+ and \verb+\end{table}+ with all of the associated things between.
\begin{center}
\tagpdfsetup{table/header-rows={1,2}} % This identifies the header rows as the first two rows
\begin{tabular}{l|r}
\multicolumn{2}{c}{Example}\\
Name & Value\\
This & 11 \\
That & 2
\end{tabular}
\end{center}
What about including columns as well?
\begin{center}
% Define the structural header matrix
\tagpdfsetup{
table/header-rows={1,2}, % Rows 1 & 2 contain structural time headers
table/header-columns={1,2} % Columns 1 & 2 contain product categorization headers
}
\begin{tabular}{ll|cc}
% --- ROW 1 (Header Row) ---
% Cells 1 & 2 are empty corner headers. Cells 3 & 4 span under a 2026 grouping.
& & \multicolumn{2}{c}{\textbf{Fiscal Year 2026}} \\
% --- ROW 2 (Header Row) ---
% Cells 1 & 2 finish the corner. Cells 3 & 4 provide the sub-headers.
\textbf{Division} & \textbf{Product} & \textbf{Q1 Target} & \textbf{Q2 Target} \\ \hline
% --- ROW 3 (Data Row) ---
% Columns 1 & 2 are treated as row headers (<TH>). Columns 3 & 4 are data (<TD>).
Software & Cloud SaaS & \$50k & \$65k \\
% --- ROW 4 (Data Row) ---
Software & On-Premise & \$20k & \$15k \\ \hline
% --- ROW 5 (Data Row) ---
Hardware & Servers & \$80k & \$95k
\end{tabular}
\end{center}
\section{Derivatives}
\begin{definition}
The \textbf{derivative at the point $x = a$} is found by computing $f'(a) = \lim_{x \to a} \dfrac{f(x) - f(a)}{x - a}$.
\end{definition}
\section{Using TikZ}
Often people utilize TikZ to generate figures. See Figure~\ref{fig-myTikZ}.
\begin{figure}[h]
\centering
\begin{tikzpicture}[
roundnode/.style={circle, draw=green!60, fill=green!5, very thick, minimum size=7mm},
squarednode/.style={rectangle, draw=red!60, fill=red!5, very thick, minimum size=5mm},
]{alt=TikZ figure.}
%Nodes
\node[squarednode] (maintopic) {2};
\node[roundnode] (uppercircle) [above=of maintopic] {1};
\node[squarednode] (rightsquare) [right=of maintopic] {3};
\node[roundnode] (lowercircle) [below=of maintopic] {4};
%Lines
\draw[->] (uppercircle.south) -- (maintopic.north);
\draw[->] (maintopic.east) -- (rightsquare.west);
\draw[->] (rightsquare.south) .. controls +(down:7mm) and +(right:7mm) .. (lowercircle.east);
\end{tikzpicture}
\caption{My nice TikZ figure.}\label{fig-myTikZ}
\end{figure}
\end{document}