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.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question
No 8
![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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8bbe1e1f-18dc-4f53-84a9-dc3dae6a4844%2Fa856941b-269e-4de7-8f1f-fe53916d74f3%2Fk74tn0t_processed.jpeg&w=3840&q=75)
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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