\begin{frame}
  \frametitle{Infinite One-Sided Limits}
  
  Like wise we define the one-sided infinite limits:
  \begin{itemize}
    \item[(a)] $\lim_{x \to a^-} f(x) = \infty$
    \item[(b)] $\lim_{x \to a^-} f(x) = -\infty$
    \item[(c)] $\lim_{x \to a^+} f(x) = \infty$
    \item[(d)] $\lim_{x \to a^+} f(x) = -\infty$
  \end{itemize}    
  \begin{center}
    \scalebox{.45}{
    (a)
    \begin{tikzpicture}[default,baseline=-1ex]
      \diagram{-1}{3}{-2}{2}{0}
      \diagramannotatez
      \draw[cblue,ultra thick] plot[smooth,domain=-.5:0.8,samples=20] function{(1/((x-1.3)**2)) -2} node [above] {$f(x)$};
      \node [anchor=north,inner sep=1mm] at (1cm,-2cm) {$a$};
      \draw [dashed,cred] (1cm,-2cm) -- (1cm,2cm);
    \end{tikzpicture}
    }
    \scalebox{.45}{
    (b)
    \begin{tikzpicture}[default,baseline=-1ex]
      \diagram{-1}{3}{-2}{2}{0}
      \diagramannotatez
      \draw[cblue,ultra thick] plot[smooth,domain=-.5:0.8,samples=20] function{-(1/((x-1.3)**2)) +2} node [below left] {$f(x)$};
      \node [anchor=north,inner sep=1mm] at (1cm,-2cm) {$a$};
      \draw [dashed,cred] (1cm,-2cm) -- (1cm,2cm);
    \end{tikzpicture}
    }
    \scalebox{.45}{
    (c)
    \begin{tikzpicture}[default,baseline=-1ex]
      \diagram{-1}{3}{-2}{2}{0}
      \diagramannotatez
      \draw[cblue,ultra thick] plot[smooth,domain=1.2:3,samples=20] function{(1/((x-0.7)**2)) -2} node [below] {$f(x)$};
      \node [anchor=north,inner sep=1mm] at (1cm,-2cm) {$a$};
      \draw [dashed,cred] (1cm,-2cm) -- (1cm,2cm);
    \end{tikzpicture}
    }
    \scalebox{.45}{
    (d)
    \begin{tikzpicture}[default,baseline=-1ex]
      \diagram{-1}{3}{-2}{2}{0}
      \diagramannotatez
      \draw[cblue,ultra thick] plot[smooth,domain=1.2:3,samples=20] function{-(1/((x-0.7)**2)) +2} node [above] {$f(x)$};
      \node [anchor=north,inner sep=1mm] at (1cm,-2cm) {$a$};
      \draw [dashed,cred] (1cm,-2cm) -- (1cm,2cm);
    \end{tikzpicture}
    }
  \end{center}
  \pause
  
  \begin{alertblock}{}
    Note that $\infty$ and $-\infty$ are not considered numbers.
    \bigskip\pause
    
    If $\lim_{x \to a} f(x) = \infty$ then $\lim_{x \to a} f(x)$ does not exist.\\
    It indicates a certain way in which the limit does not exist.
  \end{alertblock}
  
%   \begin{block}{Infinite Left-Limit}
%     \alert{$\lim_{x \to a^-} f(x) = \infty$}
%     if we can make the values of $f(x)$ arbitrarily large
%     by taking $x$ sufficiently close to $a$ with \alert{$x < a$}.
%   \end{block}
% 
%   \begin{block}{Infinite Right-Limit}
%     \alert{$\lim_{x \to a^+} f(x) = \infty$}
%     if we can make the values of $f(x)$ arbitrarily large
%     by taking $x$ sufficiently close to $a$ with \alert{$x > a$}.
%   \end{block}
% 
%   \begin{block}{Negative Infinite Left-Limit}
%     \alert{$\lim_{x \to a^-} f(x) = -\infty$}
%     if we can make the values of $f(x)$ arbitrarily large \alert{negative}
%     by taking $x$ sufficiently close to $a$ with \alert{$x < a$}.
%   \end{block}
% 
%   \begin{block}{Negative Infinite Right-Limit}
%     \alert{$\lim_{x \to a^+} f(x) = -\infty$}
%     if we can make the values of $f(x)$ arbitrarily large \alert{negative}
%     by taking $x$ sufficiently close to $a$ with \alert{$x > a$}.
%   \end{block}
\end{frame}