{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

exam2_math2500

exam2_math2500 - f x y z = x 2 y 2 z 2 on the sphere x 2 y...

Info icon This preview shows pages 1–6. Sign up to view the full content.

View Full Document Right Arrow Icon
MATH 2550 Midterm Exam 2 November 8, 2006 NAME (please print legibly): Please complete all 5 questions in the space provided. You may use the backs of the pages for extra space, or ask me for more paper if needed. Work carefully, and try to complete the problems you find easier before going back to the harder ones. Good luck! QUESTION VALUE SCORE 1 10 2 10 3 10 4 10 5 10 TOTAL 50 1
Image of page 1

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
1. (10 points) Find an equation for the tangent plane to the function f ( x, y ) = e x cos y at (0 , 0) in the form z = P ( x, y ) . Use this formula to estimate f (0 . 2 , 0 . 2) . ANSWER: Bonus (5pts): Find the second degree (or quadratic) Taylor approximation to f ( x, y ) and use it to estimate f (0 . 2 , 0 . 2) . ANSWER: 2
Image of page 2
2. (10 points) Find all of the local maxima, local minima, and saddle points of the function f ( x, y ) = 3 y 2 - 2 y 3 - 3 x 2 + 6 xy. ANSWER: 3
Image of page 3

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
3. (10 points) Find the maximum value of the function
Image of page 4
Image of page 5

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Image of page 6
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: f ( x, y, z ) = x 2 y 2 z 2 on the sphere x 2 + y 2 + z 2 = 1 using Lagrange multipliers. ANSWER: 4 4. (10 points) Sketch the region of integration for the integral Z π Z π x sin y y d y d x. Then reverse the order of integration and do the integral. (Hint: You will probably not be able to do the integral without changing the order of integration.) ANSWER: 5 5. (10 points) Find the volume of the solid shown in the figure below. It is bounded on the bottom by the xy plane, on the sides by the sphere centered at the origin of radius 2 and on the top by a cone which makes an angle of π/ 3 radians with the z-axis. (Hint: Integrate in spherical coordinates.) x y z π/ 3 6...
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