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Unformatted text preview: October 13, 2002 MATH 241—Exam 2 Answer each numbered problem on a separate answer sheet. Show all appropriate work. NO CALCULATORS ARE ALLOWED FOR THIS TEST. (10) 1. a. Let f ( x , y , z ) = z ! x 2 ! y 2 . Find and sketch the domain of f . (10) b. Sketch three level curves of the function f ( x , y ) = e ! ( x 2 + y 2 ) . Label the curves with the value of c . (10) 2. a. Find an equation of the tangent plane to the surface x y 2 z 3 = 12 at the point (3, 2, 1). (18) b. Let f ( x,y,z ) = x y 2 z 3 i. Find the directional derivative of f at the point (3, 2, 1) in the direction from (3, 2, 1) toward the point (5, 1, -1). ii. When is the directional derivative of the function f at (3,2,1) a minimum? iii. When is the directional derivative of the function f at (3,2,1) equal to 0? (12) 3. The base x of a triangle is increasing and the height of the triangle is decreasing. Determine whether the area of the triangle is increasing or decreasing when the base is 50 inches and increasing at a rate of 3...
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This note was uploaded on 04/07/2008 for the course MATH 241 taught by Professor Wolfe during the Fall '08 term at Maryland.
- Fall '08