{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

# 237t3 - 1 Let S be the portion of the cone z 2 = x 2 y 2...

This preview shows pages 1–6. Sign up to view the full content.

1. Let S be the portion of the cone 2 2 2 y x z + = with 2 0 z and 0 x . (a) [2 marks] Parametrize the surface S using cylindrical coordinates. (b) [6 marks] Compute dS x y x S ) ( 2 2 + + ∫ ∫ 2

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

View Full Document
2. [8 marks] Evaluate dS curl S n F ∫ ∫ ) ( , where k i F xy yz + - = and S is the part of the paraboloid 2 2 z y x + = between the planes 1 = x and 4 = x , n pointing away from the x -axis . 3
3. [9 marks] Find the flux of ) 1 , , ( ) , , ( 2 2 2 + - = z ye xe z y x z z F across the part of the sphere 2 2 2 2 = + + z y x with 0 , 0 z y , n pointing out of the origin. HINT: Direct calculation might be a failure, close the surface. 4

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

View Full Document
4. (a) [2 marks] Determine the largest set(s) 2 R D on which the vector field j i F 3 2 2 2 1 y x y xy x + - + = is conservative. (b) [4 marks] Determine a potential function for F . (c) [4 marks] Find the work done by F in moving the particle along the curve C parametrized by g ( t ) = ) cos 2 3 , cos 1 ( t t + - , π t 0 . Argue that your answer is correct. 5
5. (a) [2 marks] Formulate all the assumptions of Green’s Theorem.

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.

{[ snackBarMessage ]}

### Page1 / 8

237t3 - 1 Let S be the portion of the cone z 2 = x 2 y 2...

This preview shows document pages 1 - 6. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online