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

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

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

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

\item Differentiate $f(x) = x^2 \sin x$ using the product rule.
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\item Evaluate $\displaystyle\lim_{x \to 0} \frac{1 - \cos x}{x^2}$.
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\item Find the equation of the tangent line to $y = x^3 - 2x$ at the point
$(1, -1)$.
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\item A function satisfies $g'(x) = 3x^2$ and $g(0) = 5$. Find $g(2)$.
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\item Use the chain rule to differentiate $h(x) = \ln\bigl(1 + x^2\bigr)$.
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\end{enumerate}

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