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Chapter 13: Problem 15
Find the distance between the two points. $$ (-1,-5,7),(-3,4,-4) $$
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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. $$ \int_{0}^{4} \int_{\sqrt{x}}^{2} d y d x $$
Evaluate the double integral. $$ \int_{0}^{1} \int_{0}^{y}(x+y) d x d y $$
Plot the points and determine whether the data have positive, negative, or no linear correlation (see figures below). Then use a graphing utility to find the value of \(r\) and confirm your result. The number \(r\) is called the correlation coefficient. It is a measure of how well the model fits the data. Correlation coefficients vary between \(-1\) and 1, and the closer \(|r|\) is to 1, the better the model. $$ (1,7.5),(2,7),(3,7),(4,6),(5,5),(6,4.9) $$
Evaluate the partial integral. $$ \int_{-\sqrt{1-y^{2}}}^{\sqrt{1-y^{2}}}\left(x^{2}+y^{2}\right) d x $$
Sketch the region of integration and evaluate the double integral. $$ \int_{0}^{3} \int_{0}^{1}(2 x+6 y) d y d x $$
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