exam2_math2500

# exam2_math2500 - f ( x, y, z ) = x 2 y 2 z 2 on the sphere...

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

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

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

View Full Document
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
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

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

View Full Document
3. (10 points) Find the maximum value of the function

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

View Full Document
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 Z 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 gure 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 / 3 radians with the z-axis. (Hint: Integrate in spherical coordinates.) x y z / 3 6...
View Full Document

## This note was uploaded on 03/12/2012 for the course MATH 2500 taught by Professor Staff during the Spring '08 term at University of Georgia Athens.

### Page1 / 6

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

This preview shows document pages 1 - 6. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online