a3f08s - HINTS TO ASSIGNMENT #3 1. (a) Use Th. 3.11 to...

Info iconThis preview shows page 1. Sign up to view the full content.

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

Unformatted text preview: HINTS TO ASSIGNMENT #3 1. (a) Use Th. 3.11 to write ) ( x y y = or ) ( y x x = . For both dt dy and dt dx not zero, differentiate using the chain rule. In cases one of the derivatives is zero )) ( ( ) ( t x y t y = investigate that at those points is either max/min or vertical asymptote. (b) Just Calculus I. 2. Note that if ) ( f r = , then the parametric equation is sin ) ( , cos ) ( f y f x = = , and use problem # 1 above. 3. The parametrization is ) sin sin , cos sin , ( ) , ( x x x x = f , 2 , 2 x . Investigate f f x for smoothness. 4. Just introduce a collection of rectangles containing the curve. Compare Q#13, old Assignment #3 . 5. The curve in 2 R that is a graph of the function x x f 1 ) ( = for , ] 1 , ( x ) ( = f does not have content zero in 2 R . Prove that statement! 6. The first part is easy: f is continuous on S , hence it is integrable. For the second part construct the upper and lower Riemann Sums and use the fact that the graph of...
View Full Document

Ask a homework question - tutors are online