Chapter 13: Problem 49
Sketch the \(x y\) -trace of the sphere. $$ x^{2}+y^{2}+z^{2}-6 x-10 y+6 z+30=0 $$
Chapter 13: Problem 49
Sketch the \(x y\) -trace of the sphere. $$ x^{2}+y^{2}+z^{2}-6 x-10 y+6 z+30=0 $$
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Get started for freeEvaluate the double integral. $$ \int_{-1}^{1} \int_{-2}^{2}\left(x^{2}-y^{2}\right) d y d x $$
Set up the integral for both orders of integration and use the more convenient order to evaluate the integral over the region \(R\). $$ \begin{aligned} &\int_{R} \int \frac{y}{x^{2}+y^{2}} d A\\\ &R: \text { triangle bounded by } y=x, y=2 x, x=2 \end{aligned} $$
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. $$ \int_{0}^{2} \int_{\sqrt{4-x^{2}}}^{4-x^{2} / 4} \frac{x y}{x^{2}+y^{2}+1} d y d x $$
Use the regression capabilities of a graphing utility or a spreadsheet to find the least squares regression line for the given points. $$ (0,6),(4,3),(5,0),(8,-4),(10,-5) $$
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