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\begin{frame}
  \frametitle{Computing Limits: Function Replacement}
  
  Function replacement for one-sided limits:
  \begin{block}{}
    If $f(x) = g(x)$ for all $x < a$, then $\lim_{x \to a^-} f(x) = \lim_{x \to a^-} g(x)$.
  \end{block}
  \pause
  \begin{block}{}
    If $f(x) = g(x)$ for all $x > a$, then $\lim_{x \to a^+} f(x) = \lim_{x \to a^+} g(x)$.
  \end{block}
  \pause\bigskip
  
  \begin{exampleblock}{}
    Find $\lim_{x\to 2^-} g(x)$ where
    \begin{talign}
      g(x) = \begin{cases}
        x^2 &\text{for $x < 2$}\\
        5x+1 &\text{for $x \ge 2$}
      \end{cases}
    \end{talign}
    \pause
    We have 
    \begin{talign}
      g(x) = x^2 \quad \text{for all $x < 2$}
    \end{talign}
    \pause
    Hence:
    \begin{talign}
      \lim_{x \to 2^-} g(x) = \lim_{x \to 2^-}  x^2 \mpause[1]{ = 4}
    \end{talign}
  \end{exampleblock}
  \vspace{10cm}
\end{frame}