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\problemgrouptitle{Differentials}

\begin{problemblock}{Find the volume $V$ and the absolute error $\Delta V$ of the following objects.}

\item A cubical cardboard box with side length measurement of $l=5.0\pm0.2$~cm.
\answer{$V\pm\Delta V=125\pm15$ cm$^3$}

\item A spherical cannonball with measured radius of $r=6.0\pm0.5$~cm.
\answer{$V\pm\Delta V=288\pi\pm72\pi$ cm$^3$}

\end{problemblock}

\begin{problemblock}{Find the linear approximation (linearization) $L(x)$ of the function at the given value of $x$.}

\item $\displaystyle f(x)=\sqrt{2x^3-7}$ at $x$-value $a=2$~.
\answer{$L(x)=3+4(x-2)$}

\item $\displaystyle f(x)=\tan(x)$ at $x$-value $a=\pi/4$~.
\answer{$L(x)=1+2(x-\pi/4)$}

\end{problemblock}
