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Problem 10

Let $g(u, v, w)=\left(u e^{v w}+v e^{w w}+w e^{u t}\right) /\left(u^{2}+v^{2}+w^{2}\right)$. Compute \(g(1,2,3)\) and \(g(3,2,1)\).

Expert verified

\(g(1,2,3)=\frac{1\cdot e^{6} + 2\cdot e^{9} + 3\cdot e^{t}}{14}\) and \(g(3,2,1)=\frac{3\cdot e^{2} + 2\cdot e^{1} + 1\cdot e^{3t}}{14}\).

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Chapter 12

Find the first partial derivatives of the function. \(f(x, y)=e^{x y+1}\)

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Chapter 12

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Chapter 12

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Chapter 12

LAND PRICES The rectangular region \(R\) shown in the following figure represents a city's financial district. The price of land within the district is approximated by the function $$p(x, y)=200-10\left(x-\frac{1}{2}\right)^{2}-15(y-1)^{2}$$ where \(p(x, y)\) is the price of land at the point \((x, y)\) in dollars per square foot and \(x\) and \(y\) are measured in miles. Compute $$\frac{\partial p}{\partial x}(0,1) \text { and } \frac{\partial p}{\partial y}(0,1)$$ and interpret your results.

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