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114Final-2012A

4(a z 2 t =0 p 1 2 4 t 2 dt(b z 2 t =0 p 1 2 4 t 2

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Unformatted text preview: , , 4)? (A) Z 2 t =0 p 1 + ( 2 + 4) t 2 dt (B) Z 2 t =0 p 1 + ( 2 + 4) t 2 dt (C) Z 2 t =0 1 + 2 + 4 t 2 dt (D) Z 2 t =0 1 + 2 + 4 t 2 dt (E) Z 4 t =0 t 1 + 2 + t 2 dt (F) Z 2 t =0 t 1 + 2 + t 2 dt (G) Z 2 t =0 t 1 + 2 + t 2 dt (H) None of the above. Answer to 6: 8 (7) A spaceship flies along the parameterized curve 0 t < x ( t ) = e t ; y ( t ) = ( t- 1) 2 ; z ( t ) = 1 + t The temperature of space is given by ( x,y,z ) = xyz . At the exact point at which the spaceship is coldest along its path, what is the dot product of the spaceships velocity vector v with the gradient vector of temperature? (A) 0 (B) 1 2 (C)- 1 2 (D) 1 (E) 1 e (F) e (G) e 2 (H) None of the above. Answer to 7: 9 (8) Which of the following is the equation of the tangent plane to the surface x 3- xy 2 + 4 xz = 9 when x = 1 and y = 2? (A) 11 x- 4 y + 4 z = 9 (B)- x- 4 y + 4 z = 0 (C) 11 x- 4 y + 4 z = 0 (D) x + 2 y + 3 z = 9 (E) x + 2 y + 3 z = 0 (F) x + 2 y + 3 z = 23 (G) 11 x- 4 y + 4 z = 15 (H) None of the above. Answer to 8: 10 (9) A particle in space accelerates according to ~a ( t ) = 2 i + ( t 2- 1) j + k with initial velocity ~v = 3 i + 4 j and initial position ~ r ( t ) = i + 5 k . Which of the following is its position at time t = 2? (Recall that i = (1 , , 0), j = (0 , 1 , 0) and k = (0 , , 1).) (A) 4 i + 4 j + 5 k (B) 2 i + 3 j + k (C) 11 i + 7 1 3 j + 7 k (D) 3 i + 9 j + 6 k (E) i- 2 j + 5 k (F) i- 2 3 j + k (G) 2 i- 3 j + k (H) None of the above. Answer to 9: 11 (10) Evaluate ZZ R e- y 2 dA , where R is the triangular region with vertices (0 , 0), (0 , 1) and (1 , 1). (A) 3 4 (1- e- 2 ) (B) 1 3 (1- e- 2 ) (C) 1 2 (1- e- 2 ) (D) (1- e- 2 ) (E) 3 2 (1- e- 1 ) (F) 1 2 (1- e- 1 ) (G) 2 3 (1- e- 1 ) (H) 2(1- e- 1 ) Answer to 10 12 (11) Evaluate ZZZ D e x- y + z dV , where D is the parallelepiped bounded by the planes: x- y + z = 2 , x- y + z = 3 , x + 2 y =- 2 , x + 2 y = 1 , x- z = 0 , x- z = 2 ....
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4(A Z 2 t =0 p 1 2 4 t 2 dt(B Z 2 t =0 p 1 2 4 t 2 dt(C Z 2...

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