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Sketch the region of integration and then give an equivalent double integral with the order of integration reversed. I S.)dydx.

Sketch the region of integration and then give an equivalent double integral with the order of integration reversed. I S.)dydx.

Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)
Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)
6th Edition
ISBN:9781337111348
Author:Bruce Crauder, Benny Evans, Alan Noell
Publisher:Bruce Crauder, Benny Evans, Alan Noell
ChapterA: Appendix
SectionA.2: Geometric Constructions
Problem 10P: A soda can has a volume of 25 cubic inches. Let x denote its radius and h its height, both in...
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this maximum occur? 4. a) Find all critical points of the function f(x,y) = e"(y² –x') b) Use the second derivatives test to determine if the function has a local maximum, local minimum, or saddle point at each of these critical points. 5. Calculate the iterated integral: ysin(xy)dxdy . 6. Calculate the volume of the solid that lies under the hyperbolic paraboloid x -3y +z=2 and above the rectangle [-1,1]×[1,2]. 7. Evaluate f 2.xydA where D is the triangular region with vertices (0, 0), (1, 2), and (0, 3). 8. Sketch the region of integration and then give an equivalent double integral with the order of integration reversed. SI(x,y)dydx. 9. Evaluate the integral [fe** dA where D is the region to the left of the y-axis that lies between the circles x' +y =1 and x' +y = 4. 10. Find the mass of a lamina that occupies the region bounded by 1- y² and y = 0 if the lamina has density function P(x,y) = kx for some nonzero constant k.
Transcribed Image Text:this maximum occur? 4. a) Find all critical points of the function f(x,y) = e"(y² –x') b) Use the second derivatives test to determine if the function has a local maximum, local minimum, or saddle point at each of these critical points. 5. Calculate the iterated integral: ysin(xy)dxdy . 6. Calculate the volume of the solid that lies under the hyperbolic paraboloid x -3y +z=2 and above the rectangle [-1,1]×[1,2]. 7. Evaluate f 2.xydA where D is the triangular region with vertices (0, 0), (1, 2), and (0, 3). 8. Sketch the region of integration and then give an equivalent double integral with the order of integration reversed. SI(x,y)dydx. 9. Evaluate the integral [fe** dA where D is the region to the left of the y-axis that lies between the circles x' +y =1 and x' +y = 4. 10. Find the mass of a lamina that occupies the region bounded by 1- y² and y = 0 if the lamina has density function P(x,y) = kx for some nonzero constant k.
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