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Chapter 13: Problem 16
Find the distance between the two points. $$ (8,-2,2),(8,-2,4) $$
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Sketch the region of integration and evaluate the double integral. $$ \int_{-a}^{a} \int_{-\sqrt{a^{2}-x^{2}}}^{\sqrt{a^{2-x^{2}}}} d y d x $$
A company sells two products whose demand functions are given by \(x_{1}=500-3 p_{1}\) and \(x_{2}=750-2.4 p_{2}\) So, the total revenue is given by \(R=x_{1} p_{1}+x_{2} p_{2}\) Estimate the average revenue if the price \(p_{1}\) varies between \(\$ 50\) and \(\$ 75\) and the price \(p_{2}\) varies between \(\$ 100\) and \(\$ 150\).
Evaluate the double integral. $$ \int_{0}^{1} \int_{0}^{2}(x+y) d y d x $$
Evaluate the double integral. $$ \int_{0}^{2} \int_{3 y^{2}-6 y}^{2 y-y^{2}} 3 y d x d y $$
Find the average value of \(f(x, y)\) over the region \(R\). $$ \begin{aligned} &f(x, y)=x^{2}+y^{2}\\\ &R: \text { square with vertices }(0,0),(2,0),(2,2),(0,2) \end{aligned} $$
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