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Chapter 13: Problem 42
Identify the quadric surface. $$ \frac{x^{2}}{9}+\frac{y^{2}}{16}+\frac{z^{2}}{16}=1 $$
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Evaluate the double integral. $$ \int_{1}^{2} \int_{0}^{4}\left(3 x^{2}-2 y^{2}+1\right) d x d y $$
Sketch the region of integration and evaluate the double integral. $$ \int_{0}^{6} \int_{y / 2}^{3}(x+y) d x d y $$
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. $$ (1,3),(2,6),(3,2),(4,3),(5,9),(6,1) $$
Exercises 55 and 56, determine whether the statement is true or false. If it is false, explain why or give an example that shows it is false. $$ \int_{2}^{5} \int_{1}^{6} x d y d x=\int_{1}^{6} \int_{2}^{5} x d x d y $$
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