\documentclass[12pt]{amsart}
\usepackage{amsfonts}
\usepackage{amsthm}
\usepackage[mathscr]{eucal}
\usepackage[all]{xy}
\usepackage{color}
\def\dsp{\displaystyle}


\title{Limit and Continuity}

\begin{document}

\maketitle
\begin{enumerate}
\item[Solutions:]

\item [1.]When x is close to a and x $\neq$ a, f(x) is close to $\it
l.$

\

\item [2.]$\dsp \lim_{x\rightarrow a}f(x)$ exists, and
$\dsp \lim_{x\rightarrow a}f(x)=f(a).$

\

\item [3.](1) 3 \quad (2) $\frac{1}{2}$ \quad (3) does not exist

\

\item [4.](i) (1)2 \quad (2) 2 \quad (3) does not exist

\

\item [] (ii) g is not continuous at 0.

${}^\cdot{}_\cdot{}^\cdot \dsp \lim_{x\rightarrow 0}g(x)$ does not
exist.

\

\item [5.](i) (1) 2 \quad (2) 2 \quad (3) 2

\

\item [] (ii) h is continuous at -1.

${}^\cdot{}_\cdot{}^\cdot \dsp \lim_{x\rightarrow -1}h(x)=h(-1)$

\

\end{enumerate}

\end{document}