Assignment 7 - f x,y = 4 x 2-3 y 2 2 xy show that f x,y...

Info icon This preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
Math222 Assignment 7 due Friday Nov. 23, 2007 1. Compute double integral R R D xdA where D is the finite region bounded by y = 2 x 2 and y = 1 + x 2 . 2. Compute double integral R R D ( x 2 + y 2 ) dA where D is the finite region between y = x and y = x 2 . Integrate with respect to x first. 3. By reversing the order of integration evaluate Z 9 0 Z 3 y sin πx 3 dxdy. 4. Evaluate R 2 - 2 R 4 - x 2 - 4 - x 2 R 1 ( x 2 + y 2 ) 2 x 2 dzdydx . 5. Evaluate using polar coordinates: R D ydA , if D is the region in the first quadrant bounded by the circle x 2 + y 2 = 9 and the lines y = 0 and y = x . 6. Let Ω be the solid region bounded above by the plane y + z = 4 , below by the xy plane and on the sides by the cylinder x 2 + y 2 = 16. Evaluate Z Ω p x 2 + y 2 dV . 7. Let
Image of page 1
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: f ( x,y ) = 4 x 2-3 y 2 + 2 xy , show that f ( x,y ) does not have a local max or local min anywhere in the plane. Does it have a saddle point? (Justify your answer.) Find the max and min of f ( x,y ) on the square { ( x,y ) | ≤ x ≤ 1 , ≤ y ≤ 1 } , naming the points at which these extrema occur. 8. Use the method of Lagrange multipliers (or otherwise) to find maxima and minima of f ( x,y,z ) = x 2 + y 2 + z 2 on the ellipse formed by intersection of the cone z 2 = x 2 + y 2 by the plane x-2 z = 3....
View Full Document

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern