# a3f08s - HINTS TO ASSIGNMENT#3 1(a Use Th 3.11 to write x y...

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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 ) ( θ f r = , then the parametric equation is θ θ θ θ sin ) ( , cos ) ( f y f x = = , and use problem # 1 above. 3. The parametrization is ) sin sin , cos sin , ( ) , ( θ θ θ x x x x = f , π θ π 2 , 2 ≤ ≤ ≤ ≤ x . Investigate f f θ ∂ × ∂ 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...
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