23 Sample Exam 2B

23 Sample Exam 2B - by the lines x = 0, y = 0, x + y = 1....

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

View Full Document Right Arrow Icon
Sample Second Exam from 2005 1. Calculate the following for the function f ( x, y ) = x ln xy . (a) f x ( x, y ) (b) f y ( x, y ) (c) f xy ( x, y ) 2. Let f be the function f ( x, y ) = 5 - 2 xy . Find the rate of change of f at the point (2 , - 1) in the direction of < 4 , - 3 > . Find the maximal rate of increase of f at the point (2 , - 1) and the direction in which it occurs. 3. Find the tangent plane to the level surface 2 xy + 3 xz 2 = 4 at the point (1 , - 4 , - 2). 4. Find the local maximum and local minimum values and saddle points of - x 2 y + x 2 + 2 y 3 + 3 y 2 . 5. Use the method of Lagrange multipliers to find the maximum and minimum values of f ( x, y ) = x 2 + 2 x - y 2 on 2 x 2 + y 2 = 2. 6. Find the volume of the solid under z = x 2 + y 2 and above the triangular region bounded
Background image of page 1
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: by the lines x = 0, y = 0, x + y = 1. 7. Use polar coordinates to find the surface area of the part of the surface z = x 2 + y 2 above the region in the first quadrant bounded by x 2 + y 2 = 1. 8. Evaluate the triple integral R R R E xdV , where E lies under the plane z = 1 + x + 2 y and above the region in the xy-plane bounded by y = √ x , y = 0, x = 1. NOTE: These problems do not cover all the material that you will be held responsible for on Exam 2. You should look at examples from 15.5, 15.6, and 15.8 as well....
View Full Document

This note was uploaded on 02/09/2008 for the course MATH 23 taught by Professor Yukich during the Spring '06 term at Lehigh University .

Ask a homework question - tutors are online