237q3 - = C C dy x dx y (b) If R d c b a f ] , [ ) , ( : is...

Info iconThis preview shows pages 1–4. Sign up to view the full content.

View Full Document Right Arrow Icon
1. (a) [7] Find the constant 0 k such that 0 ) ( = k r , where r = r , 0 r = ) , , ( z y x . (b) [8] Evaluate C d curl x F ) ( , where ) , , ( ) , , ( z yz y xz z y x - + = F and C is the segment of the curve of intersection of the plane x y = and the paraboloid 2 2 y x z + = from (0,0,0) to (1,1,2). 2
Background image of page 1

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

View Full DocumentRight Arrow Icon
2. (a) [3] Is the set } 4 0 : ) , {( 2 2 + < = y x y x S a regular region in 2 R ? Justify your answer. (b) [10] Evaluate dy x y y x dx x xy C ) 3 3 ( ) 1 ( 2 2 2 4 2 - + + + + where C is the part of the ellipse 1 4 2 2 = + y x that lies to the left of the y -axis ) 0 ( x with counterclockwise orientation. 3
Background image of page 2
3. [4 marks each part] Prove or disprove the statements (giving counterexample if applicable). (a) If C is a simple, closed, piecewise smooth curve, then
Background image of page 3

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

View Full DocumentRight Arrow Icon
Background image of page 4
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: = C C dy x dx y (b) If R d c b a f ] , [ ) , ( : is continuous then the function = d c dy y x f x F ) , ( ) ( is uniformly continuous on ) , ( b a . (c) If a simple curve C having 1 C parametrization n R R b a ] , [ : g has length l and 1 F , then l d C | | x F . Here F denotes a continuous vector field on n R . 4 THIS PAGE IS INTENTIONALLY LEFT BLANK for you to finish/redo any question or for rough work. 5...
View Full Document

Page1 / 4

237q3 - = C C dy x dx y (b) If R d c b a f ] , [ ) , ( : is...

This preview shows document pages 1 - 4. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online