\documentclass[12pt]{article}
\textwidth=16cm
\usepackage{amsfonts}
\usepackage{amsthm}
\usepackage[mathscr]{eucal}
\usepackage[all]{xy}
\usepackage{color}
\def\dsp{\displaystyle}


\begin{document}
\begin{enumerate}

\Huge
\item [\textcolor{blue}{1.}]\textcolor{blue}{Give the $\epsilon - \delta$ definition of $\dsp \lim_{x
\rightarrow a} f(x) = \it{l}$.}

\item [\textcolor{blue}{2.}]\textcolor{blue}{Use $\epsilon - \delta$ definition to prove the following
:}

\textcolor{blue}{
if $ \quad \dsp \lim_{x \rightarrow a} f(x) = \it{l} ,\quad
\dsp
\lim_{x \rightarrow a} g(x) = \it{m} $}

\textcolor{blue}{then $ \quad \dsp \lim_{x
\rightarrow a} f(x)+g(x) = \it{l} + m $}

\item [\textcolor{blue}{3.}]\textcolor{blue}{State the Sandwich Theorem. (i.e. Squeezing Theorem
)}

\item [\textcolor{blue}{4.}]\textcolor{blue}{Give the definition of "f is continuous at
a".}

\item [\textcolor{blue}{5.}]\textcolor{blue}{f(x)=$
\left\{ \begin{array}{ll}
           x^2 + 2  \quad \quad   x<1 \\
           \frac{1}{x + 1} \quad \quad \quad x>1
        \end{array} \right.$.}

\textcolor{blue}{Write down $~~~$ (1) $\dsp \lim_{x\rightarrow 1^-} f(x)$,}

\textcolor{blue}{(2) $\dsp
\lim_{x\rightarrow 1^+} f(x)$,
(3) $\dsp
\lim_{x\rightarrow 1} f(x) \quad$.}}

\end{enumerate}

\end{document}
