mathematics beamer problem

Question

I removed slides that worked, checked that they compiled properly and include here all the slides that didn't work (checked individually as well).

\documentclass[17pt]{beamer}
\usepackage{amsmath}
\usepackage{verbatim}
\usepackage[utf8]{inputenc}
\usepackage[OT1]{fontenc}
\usepackage{graphicx}
\usebackgroundtemplate

\begin{document}
\sffamily \bfseries

\begin{frame}
\frametitle{Limit of a Rational Polynomial Function}\pause
begin{itemize}
\item Let us find $\lim_{x \to \2} \frac {3x^{2}-x-10} {x^{2}-4}$
\end{itemize}
\end{frame}

\begin{frame}
\frametitle{Limit of a Rational Polynomial Function}\pause
begin{itemize}
\item To understand limits of functions
\end{itemize}
$\lim_{x \to \2} \frac {3x^{2}-x-10} {x^{2}-4} = 2.75$
\end{frame}

\begin{frame}
\frametitle{Limit of a Discontinuous Function}\pause
Let us find $\lim_{x \to \0} f(x) = \[   \left\{
\begin{array}{11}
          $(2x+3) & x \leq 0$ \\
          $3(x+1) & x $>$ 0$ \\
          \end{array}
          \right. \]
and $\lim_{x \to \1} f(x) = \[   \left\{
\begin{array}{11}
          $(2x+3) & x \leq 0$ \\
          $3(x+1) & x $>$ 0$ \\
          \end{array}
          \right. \]
\end{frame}

\begin{frame}
\frametitle{Limit of a Discontinuous Function}\pause
Let us find $\lim_{x \to \0} f(x) = \[   \left\{
\begin{array}{11}
          $(2x+3) & x \leq 0$ = 3 \\
          $3(x+1) & x $>$ 0$ \\
          \end{array}
          \right. \]
and $\lim_{x \to \1} f(x) = \[   \left\{
\begin{array}{11}
          $(2x+3) & x \leq 0$ = 6 \\
          $3(x+1) & x $>$ 0$ \\
          \end{array}
          \right. \]
\end{frame}

\begin{frame}
\frametitle{Assignment}\pause
\begin{itemize} [<+-|alert@+>] 
\item Find $\lim_{x \to \2} (x^{3}-2x^{2})/(x^{2}-5x+6)$
\item Evaluate $\lim_{x \to \0} \frac {sin 4x} {sin 2x}$
\end{itemize}
\end{frame}

\end{document}

Answer 1

Some of the errors:

• begin{itemize} -> \begin{itemize}

• \2 -> 2, same for \1 and \0

• as David Carlisle already said in his comment, array is already in math mode, you don't need to use $...$.

• the alignment of the array should be ll not 11

• don't nest display math environments (\[...\]) inside math mode

• sin should be \sin

• \usepackage{graphicx} and \usebackgroundtemplate are superfluous

• not a tex error as such, but (2x+3) x≤0=6 looks misleading. Also cases may be better suited as an array

---

\documentclass[17pt]{beamer}
\usepackage{amsmath}
\usepackage{verbatim}
\usepackage[utf8]{inputenc}
\usepackage[OT1]{fontenc}
\usepackage{graphicx}
\usebackgroundtemplate

\begin{document}
\sffamily \bfseries

\begin{frame}
\frametitle{Limit of a Rational Polynomial Function}\pause
\begin{itemize}
\item Let us find $\lim_{x \to 2} \frac {3x^{2}-x-10} {x^{2}-4}$
\end{itemize}
\end{frame}

\begin{frame}
\frametitle{Limit of a Rational Polynomial Function}\pause
\begin{itemize}
\item To understand limits of functions
\end{itemize}
$\lim_{x \to 2} \frac {3x^{2}-x-10} {x^{2}-4} = 2.75$
\end{frame}

\begin{frame}
\frametitle{Limit of a Discontinuous Function}\pause
Let us find \[\lim_{x \to 0} f(x) = \left\{
\begin{array}{ll}
          (2x+3) & x \leq 0 \\
          3(x+1) & x > 0 \\
          \end{array}
          \right. \]
and \[\lim_{x \to 1} f(x) = \left\{
\begin{array}{ll}
          (2x+3) & x \leq 0 \\
          3(x+1) & x > 0 \\
          \end{array}
          \right. \]
\end{frame}

\begin{frame}
\frametitle{Limit of a Discontinuous Function}\pause
Let us find \[\lim_{x \to 0} f(x) = \left\{
\begin{array}{ll}
          (2x+3) & x \leq 0 = 3 \\
          3(x+1) & x > 0 \\
          \end{array}
          \right. \]
and \[\lim_{x \to 1} f(x) = \left\{
\begin{array}{ll}
          (2x+3) & x \leq 0 = 6 \\
          3(x+1) & x > 0 \\
          \end{array}
          \right. \]
\end{frame}

\begin{frame}
\frametitle{Assignment}\pause
\begin{itemize} [<+-|alert@+>] 
\item Find $\lim_{x \to 2} (x^{3}-2x^{2})/(x^{2}-5x+6)$
\item Evaluate $\lim_{x \to 0} \frac {\sin 4x} {\sin 2x}$
\end{itemize}
\end{frame}

\end{document}