Worksheet

\documentclass[11pt]{article}
\usepackage[margin=0.9in]{geometry}
\usepackage{amsmath,amssymb}
\usepackage{lmodern}
\usepackage{xcolor}
\usepackage{enumitem}
\pagestyle{empty}
\setlength{\parindent}{0pt}

\definecolor{accent}{HTML}{0F766E}

% Ruled answer space: #1 = number of lines
\newcommand{\answerlines}[1]{%
  \par\vspace{0.4em}%
  \newcount\wslines \wslines=#1
  \loop
    \noindent\textcolor{accent!35}{\rule{\linewidth}{0.4pt}}\par\vspace{1.7em}%
    \advance\wslines by -1
  \ifnum\wslines>0 \repeat
}

\begin{document}

{\color{accent}\rule{\linewidth}{2.5pt}}

\vspace{0.5em}
{\LARGE\bfseries Worksheet 6: Derivatives and Limits}\\[2pt]
{\large MATH 1210, Calculus I \hfill Section 03}

\vspace{0.6em}
Name: \rule{2.6in}{0.4pt} \hfill Date: \rule{1.4in}{0.4pt}

\vspace{0.4em}
{\color{accent}\rule{\linewidth}{0.8pt}}

\vspace{0.8em}
\textit{Show all work. Answers without supporting steps receive partial credit only.}

\vspace{1em}
\begin{enumerate}[label=\textbf{Q\arabic*.}, leftmargin=2.6em, itemsep=0.4em]

\item Differentiate $f(x) = x^2 \sin x$ using the product rule.
\answerlines{2}

\item Evaluate $\displaystyle\lim_{x \to 0} \frac{1 - \cos x}{x^2}$.
\answerlines{2}

\item Find the equation of the tangent line to $y = x^3 - 2x$ at the point
$(1, -1)$.
\answerlines{2}

\item A function satisfies $g'(x) = 3x^2$ and $g(0) = 5$. Find $g(2)$.
\answerlines{2}

\item Use the chain rule to differentiate $h(x) = \ln\bigl(1 + x^2\bigr)$.
\answerlines{2}

\end{enumerate}

\end{document}