\documentclass{article}
\usepackage{amsmath, amssymb}
\textheight=9in
%\textwidth=6.5in
%\evensidemargin=-1in
\topmargin=-1in
\date{}

\title{Quiz the Last}

\begin{document}
\maketitle
\thispagestyle{empty}

\begin{enumerate}
\item Find the third order Fourier approximation to $f(x)=3x$.

\vfill

\item Convert $\{1,x\}$ into an orthogonal set with respect to the inner product $\langle f, g\rangle=\int_0^2 f(x)g(x)dx$.
    
\vfill

\item Let $L\colon P_2(x)\to P_1(x)$ be given by $L(p)=p'+2p''$. Let $\mathcal B=\{1,x,x^2\}$ be a basis for $P_2$, and let $\mathcal B'=\{1, x+1\}$ be a basis for $P_1$. Find the matrix representation of $L$ with respect to $\mathcal B$ and $\mathcal B'$: ${}_{\mathcal B'}[L]_{\mathcal B}$.
    
\vfill


\end{enumerate}
\end{document}