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\problemgrouptitle{Calculating Limits Using Limit Laws}

\begin{problemblock}[2]{Evaluate the following limits.}

\addtoanswerkey{\begin{multicols}{4}}

\item $\displaystyle \lim_{x\to 3}\frac{x^2+4}{x+2}$
\answer{$\displaystyle \frac{13}{5}$}

\item $\displaystyle \lim_{x\to -2}\frac{x^2+4x+4}{x+2}$
\answer{$\displaystyle 0$}

\item $\displaystyle\lim_{x\to0}\frac{2-\sqrt{4-x}}{x}$
\answer{$\displaystyle\frac{1}{4}$}

\item $\displaystyle\lim_{x\to3}|x-3|$
\answer{$0$}

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

\item $\displaystyle\lim_{x\to3}\frac{\frac{1}{x}-\frac{1}{3}}{x-3}$
\answer{$\displaystyle-\frac{1}{9}$}

\item $\displaystyle\lim_{t\to1}\frac{t-\sqrt{t}}{\sqrt{t}-1}$
\answer{$1$}

\item $\displaystyle \lim_{x\to 1}\frac{x^3-2x+1}{x-1}$
\answer{$\displaystyle 1$}

\item $\displaystyle \lim_{t\to 4}\frac{\sqrt{t}-2}{t-4}$
\answer{$\displaystyle \frac{1}{4}$}

\item $\displaystyle \lim_{y\to 3}\frac{2-\sqrt{y^2-5}}{y^2-y-6}$
\answer{$\displaystyle -\frac{3}{10}$}

\item $\displaystyle \lim_{x\to -4}\frac{\left(x+1\right)^2-9}{x+4}$
\answer{$\displaystyle -6$}

\item $\displaystyle \lim_{u\to -5}\frac{\frac{1}{u}+\frac{1}{5}}{u+5}$
\answer{$\displaystyle -\frac{1}{25}$}

\item $\displaystyle \lim_{t\to 2}\frac{t^2+t-6}{\frac{2}{t}-1}$
\answer{$-10$}

\item $\displaystyle \lim_{x\to 4}\frac{x^3-4x^2-4x+16}{x-4}$
\answer{$\displaystyle 12$}

\item $\displaystyle \lim_{t\to 1}\frac{t^3+4t-5}{t^3-1}$
\answer{$\displaystyle \frac{7}{3}$}

\addtoanswerkey{\end{multicols}}

\end{problemblock}
