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Unformatted text preview: MATH 231 Group Work Quiz Related 1. Classify and sketch the following surfaces: (a) z = 2 x 2 + y 2 (b) z 2 = x 2 + 1 3 y 2 (c) 1 + 5 z 2 = 7 x 2 y 2 (d) 4 + z 2 = x 2 + y 2 Answer: (a) Elliptic paraboloid. (b) Cone. (c) Hyperboloid of two sheets. (d) Hyperboloid of one sheet. 1 2. What is the domain of the vector function r ( t ) = D 2 t, ln t, t 2 1 t 1 E ? 3. At what point(s) do the curves r ( t ) = t 2 ,t 2 + 1 , 4 t and s ( t ) = t 4 , 1 2 t, t 2 4 intersect? 4. Find a vector function that represents the curve of intersection of z 2 = x 2 + y 2 and 2 x + 3 y z = 1. Answer: This one is the really ugly one of the bunch. The concepts involved in solving it are more important here than the specific details. For similar problems, look at 13.1 #3638. We know that there are two pieces to the curve of intersection between these two things. One for z > and one for z < 0. Substituting z = 2 x + 3 y 1 into z 2 = x 2 + y 2 and using the quadratic formula, we find that x = 1 3...
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This homework help was uploaded on 04/17/2008 for the course MATH 231 taught by Professor Bociu during the Spring '08 term at UVA.
 Spring '08
 BOCIU
 Calculus, Cone

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