# S05fnlansl - 5 Z 1 3 1 9 Z √ y 1 3 f x,y dxdy Z 1 1 3 Z...

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MATH 226 CALCULUS III Prof Baxendale 04/27/05 Answers for Sample Final Exam (Corrected) BEWARE: The following are just the numerical answers. Since the justification is missing, they would not receive full credit on the real exam. 1. (a) r ( t ) = h 1 , 4 , 6 i + t h 3 , - 2 , 1 i ; (b) 5 / 14. 2. R ( u ) = j + 2 k + u ( i + j + k ); at (-2,-1,0). 3. (a)11; (b) 2 x - 6 y + 9 z = 19. 4. Maximum value is 3 3 / 2 / 5 5 / 2 , achieved at the four points ( 1 5 , 1 5 , 3 5 ), ( 1 5 , - 1 5 , - 3 5 ), ( - 1 5 , 1 5 , - 3 5 ) and ( - 1 5 , - 1 5 , 3 5 ).
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Unformatted text preview: 5. Z 1 / 3 1 / 9 Z √ y 1 / 3 f ( x,y ) dxdy + Z 1 1 / 3 Z √ y y f ( x,y ) dxdy . 6. (8 √ 2-2) / 15. 7. 8 πb 4 / 5. 8. (a) f ( x,y ) = x 2 y + xy 3 + 3 y 2 / 2; (b) 105.5. 9.-2/3. 10. div F ( x,y,z ) = xy + 2 y + z 3 ; curl F ( x,y,z ) = xz i + (3 xz 2-yz ) j ; grad(div F )( x,y,z ) = y i + (2 + x ) j + 3 z 2 k . 11. (9 √ 3-8 √ 2 + 1) / 15. 12. 5 π/ 2....
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