{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

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

This preview shows pages 7–13. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

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 &amp;lt; 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 ....
View Full Document

{[ snackBarMessage ]}

### Page7 / 18

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...

This preview shows document pages 7 - 13. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online