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Chapter 13: Problem 8
Find the coordinates of the point. The point is located seven units in front of the \(y z\) -plane, two units to the left of the \(x z\) -plane, and one unit below the \(x y\) -plane.
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A firm's weekly profit in marketing two products is given by \(P=192 x_{1}+576 x_{2}-x_{1}^{2}-5 x_{2}^{2}-2 x_{1} x_{2}-5000\) where \(x_{1}\) and \(x_{2}\) represent the numbers of units of each product sold weekly. Estimate the average weekly profit if \(x_{1}\) varies between 40 and 50 units and \(x_{2}\) varies between 45 and 50 units.
Sketch the region of integration and evaluate the double integral. $$ \int_{0}^{3} \int_{0}^{1}(2 x+6 y) d y d x $$
Use a symbolic integration utility to evaluate the double integral. $$ \int_{0}^{2} \int_{\sqrt{4-x^{2}}}^{4-x^{2} / 4} \frac{x y}{x^{2}+y^{2}+1} d y d x $$
Evaluate the partial integral. $$ \int_{-\sqrt{1-y^{2}}}^{\sqrt{1-y^{2}}}\left(x^{2}+y^{2}\right) d x $$
Use the regression capabilities of a graphing utility or a spreadsheet to find the least squares regression line for the given points. $$ (1,0),(3,3),(5,6) $$
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