Chapter 13: Problem 7
Examine the function for relative extrema and saddle points. $$ f(x, y)=2 x^{2}+2 x y+y^{2}+2 x-3 $$
Chapter 13: Problem 7
Examine the function for relative extrema and saddle points. $$ f(x, y)=2 x^{2}+2 x y+y^{2}+2 x-3 $$
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Get started for freeSketch the region of integration and evaluate the double integral. $$ \int_{0}^{2} \int_{0}^{4-x^{2}} x y^{2} d y d x $$
Sketch the region \(R\) whose area is given by the double integral. Then change the order of integration and show that both orders yield the same area. $$ \int_{0}^{1} \int_{0}^{2} d y d x $$
The population density (in people per square mile) for a coastal town can be modeled by \(f(x, y)=\frac{120,000}{(2+x+y)^{3}}\) where \(x\) and \(y\) are measured in miles. What is the population inside the rectangular area defined by the vertices \((0,0)\), \((2,0),(0,2)\), and \((2,2) ?\)
Use a double integral to find the area of the region bounded by the graphs of the equations. $$ y=9-x^{2}, y=0 $$
Use a symbolic integration utility to evaluate the double integral. $$ \int_{0}^{2} \int_{\sqrt{4-x^{2}}}^{4-x^{2} / 4} \frac{x y}{x^{2}+y^{2}+1} d y d x $$
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