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\begin{frame}
  \frametitle{Limits at Infinity}

  \begin{exampleblock}{}
    Evaluate 
    \begin{talign}
      \lim_{x\to \infty} (\sqrt{x^2 - 1} - x )
    \end{talign}
    \pause
    We have
    \begin{talign}
      \lim_{x\to \infty} (\sqrt{x^2 - 1} - x )
      &\mpause[1]{= \lim_{x\to \infty} \left( \frac{\sqrt{x^2 - 1} - x}{1} \cdot \frac{\sqrt{x^2 - 1} + x}{\sqrt{x^2 - 1} + x} \right) } \\
      &\mpause[2]{= \lim_{x\to \infty} \frac{x^2 - 1 - x^2}{\sqrt{x^2 - 1} + x} } \\
      &\mpause[3]{= \lim_{x\to \infty} -\frac{1}{\sqrt{x^2 - 1} + x} } \\
      &\mpause[4]{= \lim_{x\to \infty} -\frac{1}{\sqrt{x^2 - 1} + x} \cdot \frac{\frac{1}{x}}{\frac{1}{x}} } \\
      &\mpause[5]{= \lim_{x\to \infty} -\frac{\frac{1}{x}}{\sqrt{1 - \frac{1}{x^2}} + 1}  } 
      \mpause[6]{= \frac{0}{2} = 0}
    \end{talign}
  \end{exampleblock}
\end{frame}