Activities
Student Organizations
Math Club
BingAWM
Actuarial Association
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\large Peeling an orange changes its volume V. What does $\Delta V$ represent?
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\begin{enumerate}[a)]
\item the volume of the rind.
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\item the surface area of the orange.
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\item the volume of the "edible part" of the orange.
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\item $-1\times $(the volume of the rind).
\end{enumerate}
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\large Imagine that you increase the dimensions of a square with side $x_1$
to a square with side length $x_2$. The change in the area of the square,
$\Delta A$, is approximated by the differential $dA$. Find $dA$:
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\begin{enumerate}[a)]
\item $2x_1(x_2-x_1)$
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\item $2x_2(x_2-x_1)$
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\item $x_1^2-x_2^2$
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\item $(x_2-x_1)^2$
\end{enumerate}
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\begin{frame}
\large Imagine that you increase the dimensions of a square with side $x_1$
to a square with side length $x_2$. The change in the area of the square,
$\Delta A$, is approximated by the differential $$dA=2x_1(x_2-x_1)$$
This approximation will result in an
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\begin{enumerate}[a)]
\item overestimate
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\item underestimate
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\item exactly equal
\end{enumerate}
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Find the differential of each function:
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\begin{itemize}
\item[\bf a)] $y=\sqrt{1+x^2}$
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\item[\bf b)] $y=x^2\sin(x)$
\end{itemize}
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\begin{itemize}
\item[\bf c)] $y=\sec\left(\sqrt{7x}\right)$
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\item[\bf d)] $y=\dfrac{3-t^2}{3+t^2}$
\end{itemize}
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\large The radius of a sphere is measured to be $84$ inches with a possible
error of $0.5$ inches.
\begin{itemize}
\item[\bf a)] Use differentials to estimate the maximum error in
the calculated surface area. What is the relative error?
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\item[\bf b)] Use differentials to estimate the maximum error in the
calculated volume. What is the relative error?
\end{itemize}
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\large Use differentials to estimate the amount of paint needed to apply a coat
of paint $0.1$ cm thick to hemispherical dome with diameter $50$ meters.
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\large A window has the shape of a square surmounted by a semicircle.
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The base of the window is measured as having width $50$ inches with a possible
error in measurement of $0.1$ inches.
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Use differentials to estimate the maximum error possible in computing the area
of the window. What is the maximum relative error?
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