This preview shows page 1. Sign up to view the full content.
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
 Fall '09
 RomauldStanczak
 Calculus, Chain Rule, Derivative, The Chain Rule

Click to edit the document details