\documentclass[
paper=A4,
pagesize,
fontsize=11pt,
titlepage=false,
fleqn,
toc=flat,
bibliography=totoc,
index=totoc,
listof=flat]{scrartcl}
\usepackage{scrhack}
\setuptoc{toc}{leveldown}
\usepackage[utf8x]{inputenc}
\usepackage[T1]{fontenc}
\usepackage{xltxtra}
\usepackage[
left=3cm,
right=2cm,
top=2cm,
bottom=2cm,
includeheadfoot]{geometry}
\usepackage[automark,headsepline,ilines,komastyle]{scrpage2}
\pagestyle{scrheadings}
\usepackage{fixltx2e}
\raggedbottom
\usepackage{ellipsis,ragged2e,marginnote}
\usepackage{inconsolata}
\renewcommand{\familydefault}{\sfdefault}
\setkomafont{sectioning}{\normalcolor\bfseries}
\setkomafont{disposition}{\normalcolor\bfseries}
\usepackage{mathtools}
\mathtoolsset{showonlyrefs=true}
\usepackage{amssymb}
\usepackage{sfmath}
\usepackage[USenglish]{babel}
\usepackage{etoolbox}
\usepackage{url}
\usepackage{hyperref}
\usepackage{graphicx}
\usepackage[Export]{adjustbox}
\adjustboxset{max size={\textwidth}{0.7\textheight}}
\usepackage{textcomp}
\def\leftqquote{``}\def\rightqqoute{''}
\catcode`\"=13
\def"{\bgroup\def"{\rightqqoute\egroup}\leftqquote}
\makeatletter
\preto{\@verbatim}{\topsep=0pt \partopsep=0pt }
\makeatother
\usepackage{color}
\definecolor{midgray}{rgb}{0.5,0.5,0.5}
\definecolor{lightyellow}{rgb}{1,1,.92}
\definecolor{dblackcolor}{rgb}{0.0,0.0,0.0}
\definecolor{dbluecolor}{rgb}{.01,.02,0.7}
\definecolor{dredcolor}{rgb}{1,0,0}
\definecolor{dbrowncolor}{rgb}{0.625,0.3125,0}
\definecolor{dgraycolor}{rgb}{0.30,0.3,0.30}
\definecolor{graycolor}{rgb}{0.35,0.35,0.35}
\usepackage{listings}
\lstdefinelanguage{Sage}[]{Python}
{morekeywords={True,False,sage,singular},
sensitive=true}
\lstset{
showtabs=False,
showspaces=False,
showstringspaces=False,
commentstyle={\ttfamily\color{dbrowncolor}},
keywordstyle={\ttfamily\color{dbluecolor}\bfseries},
stringstyle ={\ttfamily\color{dgraycolor}\bfseries},
numberstyle ={\tiny\color{midgray}},
backgroundcolor=\color{lightyellow},
language = Sage,
basicstyle={\ttfamily},
extendedchars=true,
keepspaces=true,
aboveskip=1em,
belowskip=0.1em,
breaklines=true,
prebreak = \raisebox{0ex}[0ex][0ex]{\ensuremath{\backslash}},
}
\newcommand{\Bold}[1]{\mathbb{#1}}
\newcommand{\ZZ}{\Bold{Z}}
\newcommand{\NN}{\Bold{N}}
\newcommand{\RR}{\Bold{R}}
\newcommand{\CC}{\Bold{C}}
\newcommand{\FF}{\Bold{F}}
\newcommand{\QQ}{\Bold{Q}}
\newcommand{\QQbar}{\overline{\QQ}}
\newcommand{\CDF}{\Bold{C}}
\newcommand{\CIF}{\Bold{C}}
\newcommand{\CLF}{\Bold{C}}
\newcommand{\RDF}{\Bold{R}}
\newcommand{\RIF}{\Bold{I} \Bold{R}}
\newcommand{\RLF}{\Bold{R}}
\newcommand{\CFF}{\Bold{CFF}}
\newcommand{\GF}[1]{\Bold{F}_{#1}}
\newcommand{\Zp}[1]{\ZZ_{#1}}
\newcommand{\Qp}[1]{\QQ_{#1}}
\newcommand{\Zmod}[1]{\ZZ/#1\ZZ}
\newcommand{\lt}{<}
\newcommand{\gt}{>}
\newcommand{\lequal}{≤}
\newcommand{\gequal}{≥}
\newcommand{\notequal}{≠}
\lstset{literate=
{á}{{\'a}}1 {é}{{\'e}}1 {í}{{\'i}}1 {ó}{{\'o}}1 {ú}{{\'u}}1
{Á}{{\'A}}1 {É}{{\'E}}1 {Í}{{\'I}}1 {Ó}{{\'O}}1 {Ú}{{\'U}}1
{à}{{\`a}}1 {è}{{\`e}}1 {ì}{{\`i}}1 {ò}{{\`o}}1 {ù}{{\`u}}1
{À}{{\`A}}1 {È}{{\'E}}1 {Ì}{{\`I}}1 {Ò}{{\`O}}1 {Ù}{{\`U}}1
{ä}{{\"a}}1 {ë}{{\"e}}1 {ï}{{\"i}}1 {ö}{{\"o}}1 {ü}{{\"u}}1
{Ä}{{\"A}}1 {Ë}{{\"E}}1 {Ï}{{\"I}}1 {Ö}{{\"O}}1 {Ü}{{\"U}}1
{â}{{\^a}}1 {ê}{{\^e}}1 {î}{{\^i}}1 {ô}{{\^o}}1 {û}{{\^u}}1
{Â}{{\^A}}1 {Ê}{{\^E}}1 {Î}{{\^I}}1 {Ô}{{\^O}}1 {Û}{{\^U}}1
{œ}{{\oe}}1 {Œ}{{\OE}}1 {æ}{{\ae}}1 {Æ}{{\AE}}1 {ß}{{\ss}}1
{ç}{{\c c}}1 {Ç}{{\c C}}1 {ø}{{\o}}1 {å}{{\r a}}1 {Å}{{\r A}}1
{ã}{{\~a}}1 {Ã}{{\~A}}1 {õ}{{\~o}}1 {Õ}{{\~O}}1
{€}{{\EUR}}1 {£}{{\pounds}}1
}
\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}