a5f08s - HINTS TO ASSIGNMENT #5 1. Just evaluate both sides...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
HINTS TO ASSIGNMENT #5 1. Just evaluate both sides and see that they are equal (mixed second partials equal!). For notations see formula 5.33 in your text. 2. In all parts it is useful to apply identity 5.28 of your text and simple result r r r = . (a) r r r r r r r r r 12 ) 3 ( 3 ] ) ( ) ( [ 3 3 ) 3 ( 2 3 = + = + = = = r r r r 12 = k (b) 3 2 2 ) 2 ( 1 2 ) 1 ( 2 ) 1 3 1 ( ) ( r r r r r r r r r r r r r = = = = 2 = k (c) k k k k r k r r k r r = = + 3 3 1 ) ( 1 r r r so 3 = k (d) ) 2 ( ) 1 ( ) 1 ( ) ( 3 2 2 2 2 2 r r r r r r r = = = 4 5 4 2 ] 4 3 [ ) 2 ( r r r r = = r r , k . 2 = 3. The area is , here π 80 )] ( 01 . 0 4 [ 2 2 = + ds y x C 2 0 , sin 10 , cos 10 : = = t t y t x C . For both sides the area is 160 . Hence one needs 2 m 6 . 1 liters of paint. 4. (a) 3 2 6 2 sin 4 2 2 )] 2 )(sin 2 cos 2 )( 2 sin [( 4 0 3 4 0 = = = t dt t t t I (b) t dt t s t 2 2 2 2 ) ( 0 = = , that is 2 2 s = t . For 4 , 0 = t we get 2 2 , 0 = s so the arc length parametrization of C is 2 2 0 ), 2 sin , 2 cos 2 , 2 sin ( ) (
Background image of page 1

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

View Full DocumentRight Arrow Icon
Image of page 2
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 10/21/2010 for the course MATHEMATIC MAT237Y1 taught by Professor Romauldstanczak during the Fall '09 term at University of Toronto- Toronto.

Page1 / 3

a5f08s - HINTS TO ASSIGNMENT #5 1. Just evaluate both sides...

This preview shows document pages 1 - 2. Sign up to view the full document.

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