exam2_241-f01

exam2_241-f01 - Section 1701 October 11, 2001 MATH 241-EXAM...

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x y θ Section 1701 October 11, 2001 MATH 241—EXAM 2 INSTRUCTIONS: Write your name on each answer sheet. Answer each numbered question on a separate answer sheet. You must show all appropriate work in order to receive credit for an answer. (20) 1. a. For each function given below draw two level curves for the values of c given and choose the best descriptive name for the graph (i.e., z = f ( x,y ) from among the following nouns: plane, cone, sphere, paraboloid, hyperboloid, hemisphere, sheet, ellipsoid, cylinder, parallelepiped, disk, and the adjectives (where appropriate) circular, elliptic, parabolic, hyperbolic. For a hyperboloid state whether it is one sheet or two sheets. i. f ( x , y ) = 2 + y 2 ! 9 . ( c = 0 and c = 4) ii. g ( x , y ) = 2 y 2 ( c = 2, c = 8) (6) b. Sketch the graph of the equation z 2 = 25 x 2 + 4 y 2 2. Let f ( x , y , z ) = ze xy . (10) a. Find the directional derivative of f at (0, 1, 2) in the direction from (0, 1, 2) toward (-1, 3, 0). (10) b. Find the maximum rate of incease in f at the point (0, 1, 2). In which direction does it occur? (10) 3. a. The length x on one side of a triangle is increasing at a rate of 3 inches
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