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\title{Assignment Week 11}
\author{COMP 150}
\date{Spring, 2021}
\begin{document}
\maketitle
\begin{lstlisting}
# Your name here
\end{lstlisting}
\begin{lstlisting}
\end{lstlisting}

{{An exponential function $f(x) = b^x$, where $b > 1$, is ``eventually bigger than'' a power function $g(x) = x^p$, where $p>0$. }}

\begin{lstlisting}
\end{lstlisting}

{{(1)  Define the exponential function $f(x) = 2^x$ and the power function $g(x) = x^9$ in Sage for use throughout this assignment.}}


\begin{lstlisting}
\end{lstlisting}

{{(2) What are the limits of $f(x)$ and $g(x)$ as $x$ approaches infinity?  Use Sage to support your claim. Explain your work.}}


\begin{lstlisting}
\end{lstlisting}

{{(3) Which function is larger at $x=0$?  Use Sage to support your claim. Explain your work.}}


\begin{lstlisting}
\end{lstlisting}

{{(4) At some $x$-value between 1 and 2, the exponential function is overtaken by the power function. Use Sage to support this claim. Use comments to explain your work and conclusions.}}


\begin{lstlisting}
\end{lstlisting}

{{(5) At some $x$-value between 51 and 52 the functions intersect each other again. Use Sage to support this claim. Use comments to explain your work and conclusions.}}


\end{document}
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