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\problemgrouptitle{Infinite Limits and Vertical Asymptotes}


\begin{problemblock}[2]{Determine the following limits.  For any limit that does not exist, identify if it has an infinite trend ($\infty$ or $-\infty$).}

\addtoanswerkey{\begin{multicols}{2}}

\item $\displaystyle\lim_{x\to2^+}\displaystyle\frac{5x+4}{2x-4}$
\answer{$\infty$}

\item $\displaystyle\lim_{x\to3^-}\displaystyle\frac{x^2+2x}{x^2-5x+6}$
\answer{$-\infty$}

\item $\displaystyle\lim_{x\to5}\displaystyle\frac{x^2-4x-5}{x^2-3x-10}$
\answer{$\displaystyle\frac{6}{7}$}

\item $\displaystyle\lim_{x\to0}\displaystyle\frac{\sec x}{x^2}$
\answer{$\infty$}

\end{problemblock}

\addtoanswerkey{\end{multicols}}

\textbook{\clearpage}
\begin{problemblock}[2]{Find the vertical asymptotes of the following functions.}

\item $\displaystyle f(x)=\frac{3x+3}{2x-4}$
\answer{Vertical asymptote: $x=2$}

\item $f(x)=x^3+5x+2$
\answer{No vertical asymptotes}

\item $\displaystyle g(t)=\frac{\sqrt{t^2+3}}{t-2}$
\answer{Vertical asymptote: $t=2$}


\item $\displaystyle f(x)=\frac{x^2-2x+1}{2x^2-2x-12}$
\answer{Vertical asymptotes: $x=-2$, $x=3$}

\item $\displaystyle f(x)=\displaystyle\frac{\cos x}{x}$
\answer{Vertical asymptote: $x=0$}

\item $\displaystyle y=\frac{5x^2-3x+1}{x^2-16}$
\answer{Vertical asymptotes: $x=-4$, $x=4$}


\item $f(x)=\displaystyle\frac{x^3+1}{x^3+x^2}$
\answer{Vertical asymptote: $x=0$}

\item $\displaystyle F(x)=\frac{x}{\sqrt{4x^2+1}}$
\answer{No vertical asymptotes}

\end{problemblock}
