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Chapter 9: Problem 3
Find the differential \(d y\). \(y=(4 x-1)^{3}\)
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Let \(x=2\) and complete the table for the function. $$ \begin{array}{|c|c|c|c|c|} \hline d x=\Delta x & d y & \Delta y & \Delta y-d y & d y / \Delta y \\ \hline 1.000 & & & & \\ \hline 0.500 & & & & \\ \hline 0.100 & & & & \\ \hline 0.010 & & & & \\ \hline 0.001 & & & & \\ \hline \end{array} $$ \(y=\frac{1}{x}\)
Sketch the graph of the function. Label the intercepts, relative extrema, points of inflection, and asymptotes. Then state the domain of the function. \(y=\frac{x^{4}}{x^{4}-1}\)
The body surface area (BSA) of a 180-centimeter-tall (about six-feet-tall) person is modeled by $$ B=0.1 \sqrt{5 w} $$ where \(B\) is the BSA (in square meters) and \(w\) is the weight (in kilograms). Use differentials to approximate the change in the person's BSA when the person's weight changes from 90 kilograms to 95 kilograms.
The cost \(C\) (in millions of dollars) for the federal government to seize \(p \%\) of a type of illegal drug as it enters the country is modeled by \(C=528 p /(100-p), \quad 0 \leq p<100\) (a) Find the costs of seizing \(25 \%, 50 \%\), and \(75 \%\). (b) Find the limit of \(C\) as \(p \rightarrow 100^{-}\). Interpret the limit in the context of the problem. Use a graphing utility to verify your result.
Sketch the graph of the function. Choose a scale that allows all relative extrema and points of inflection to be identified on the graph. \(y=x^{3}-6 x^{2}+3 x+10\)
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