HW.tex

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\newtheorem{cor}{Corollary}
\newtheorem*{rmk}{Remark}
\newtheorem{lem}{Lemma}
\newtheorem*{joke}{Joke}
\newtheorem{ex}{Example}
\newtheorem*{soln}{Solution}
\newtheorem{prop}{Proposition}

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\begin{document}
%\begin{flushleft}
%Name:\underline{\hspace{13cm}}Date:\underline{\hspace{2cm}}
%\end{flushleft}
\begin{center}
{\Large Math 1041-012 \hspace{0.5cm} Warm-Up}
\end{center}
\vspace{0.2 cm}
\subsection*{Problem 1} Sketch the graph given the information:
\begin{itemize}
    \item $\displaystyle \lim_{x\rightarrow 0}f(x)=1$,
    \item $\displaystyle \lim_{x\rightarrow 3^-}f(x)=-2$,
    \item $\displaystyle \lim_{x\rightarrow 3^+}f(x)=2$,
    \item $f(0)=-1$ and $f(3)=1$.
\end{itemize}
\vspace{3cm}
\begin{center}
{\Large Math 1041-012 \hspace{0.5cm} Warm-Up}
\end{center}
\vspace{0.2 cm}
\subsection*{Problem 1} Sketch the graph given the information:
\begin{itemize}
    \item $\displaystyle \lim_{x\rightarrow 0}f(x)=1$,
    \item $\displaystyle \lim_{x\rightarrow 3^-}f(x)=-2$,
    \item $\displaystyle \lim_{x\rightarrow 3^+}f(x)=2$,
    \item $f(0)=-1$ and $f(3)=1$.
\end{itemize}
\pagebreak
\subsection*{Problem 2} In the theory of relativity, the mass of a particle with velocity $v$ is given by
\[
m=\frac{m_0}{\sqrt{1-v^2/c^2}}
\]
where $m_0$ is the mass of the particle at rest and $c$ is the speed of light. What happens as $v\rightarrow c^-$?
\vspace{7cm}
\subsection*{Problem 2} In the theory of relativity, the mass of a particle with velocity $v$ is given by
\[
m=\frac{m_0}{\sqrt{1-v^2/c^2}}
\]
where $m_0$ is the mass of the particle at rest and $c$ is the speed of light. What happens as $v\rightarrow c^-$?
%\subsection*{Problem 2} Determine the infinite limits and state the vertical asymptotes
%\begin{enumerate}[label=(\alph*)]
%    \item $\displaystyle \lim_{x\rightarrow 2^-}\frac{x^2-2x}{x^2-4x+4}$\\ \vspace{1cm}
%    \item $\displaystyle \lim_{x\rightarrow 0^+}\left(\frac{1}{x}-\ln x\right)$
%\end{enumerate}
%\vspace{7cm}
%\subsection*{Problem 2} Determine the infinite limits and state the vertical asymptotes
%\begin{enumerate}[label=(\alph*)]
%    \item $\displaystyle \lim_{x\rightarrow 2^-}\frac{x^2-2x}{x^2-4x+4}$\\ \vspace{1cm}
%    \item $\displaystyle \lim_{x\rightarrow 0^+}\left(\frac{1}{x}-\ln x\right)$
%\end{enumerate}
\end{document}