MultiFinalExam02

MultiFinalExam02 - ae 1. Let z = x 2 e y , where x = u 2 v-...

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Unformatted text preview: ae 1. Let z = x 2 e y , where x = u 2 v- 1 and y = uv- 2. The partial derivative z u at ( u,v ) = (1 , 2) is (1)2 (2)8 (3)10 (4)16 2. For the function f ( x,y ) = x 3- 12 x + y 2 , (1)there are no critical points. (2) f has a saddle point at the critical point (- 2 , 0). (3) f has a local minimum at the critical point (0 , 0). (4) f has a local maximum at the critical point (- 2 , 0). 3. Let f ( x,y ) = (1 + sin(2 x )) y 3 . Using the total differential (or the linearization or standard linear approximation) of f ( x,y ) at the point P (0 , 1), one can approximate the value of (1 + sin(0 . 02))(1 . 01) 3 by (1)1 . 02 (2)1 . 03 (3)1 . 05 (4)1 . 07 4. The tangent plane to the surface z = xy 2 at the point P (1 , 1 , 1) contains the point P (0 , ,k ) when k is (1)- 3 (2)0 (3)- 2 (4)5 5. At the point P (1 , 1 , 1) the function f ( x,y,z ) = 2 x 2 y + z 4 y 2 increases fastest in the direction of the vector (1) i + k (2) i + j + k (3)4 i (4) j- k 6. The value of Z 6 Z 3 y/ 2 e x 2 dxdy...
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This note was uploaded on 04/02/2008 for the course MATH 2224 taught by Professor Mecothren during the Fall '03 term at Virginia Tech.

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MultiFinalExam02 - ae 1. Let z = x 2 e y , where x = u 2 v-...

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