Chapter 13: Problem 11
Find the intercepts and sketch the graph of the plane. $$ x+y-z=0 $$
Chapter 13: Problem 11
Find the intercepts and sketch the graph of the plane. $$ x+y-z=0 $$
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Get started for freeUse a double integral to find the volume of the solid bounded by the graphs of the equations. $$ z=x^{2}, z=0, x=0, x=2, y=0, y=4 $$
Use the regression capabilities of a graphing utility or a spreadsheet to find linear and quadratic models for the data. State which model best fits the data. $$ (1,10.3),(2,14.2),(3,18.9),(4,23.7),(5,29.1),(6,35) $$
Set up the integral for both orders of integration and use the more convenient order to evaluate the integral over the region \(R\). $$ \begin{aligned} &\int_{R} \int \frac{y}{1+x^{2}} d A\\\ &R: \text { region bounded by } y=0, y=\sqrt{x}, x=4 \end{aligned} $$
Find the average value of \(f(x, y)\) over the region \(R\). $$ \begin{aligned} &f(x, y)=e^{x+y}\\\ &R: \text { triangle with vertices }(0,0),(0,1),(1,1) \end{aligned} $$
Evaluate the double integral. $$ \int_{0}^{\infty} \int_{0}^{\infty} e^{-(x+y) / 2} d y d x $$
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