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homework4 - Math 1120 Fall 2011 Homework 4 — due 9/22 or...

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Math 1120 Homework 4 Due 9/22 or 9/23, 2011 Name: GRADES Book questions / 7 Presentation questions / 30 Print out these pages. Answer the “presentation questions” in the spaces provided. Include full explanations and write your answers in complete, mathematically and grammatically correct sentences. Your answers will be assessed for style and accuracy; you will be given written feedback on these prob- lems. Write your answers to the “book questions” on separate paper and staple to these pages. They will be assessed only for completeness. Always write neatly and legibly. Book questions — 6.3: 6, 10 11.2: 26 6.4: 16, 20, 26, 32 Presentation questions 1. [10 points] (6.3: 20) (a) Find a curve through the point (0 , 1) whose length integral (Equation 4 on page 384) is L = i 2 1 r 1 + 1 y 4 dy. CONTINUE TO THE NEXT PAGE.

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Unformatted text preview: Math 1120, Fall 2011 Homework 4 — due 9/22 or 9/23 2 (b) How many such curves are there? Explain your answer. 2. [10 points] (6.4: 28, adapted) If you cut a spherical loaf of bread into slices of equal width then each will have the same amount of crust. Explain this by showing that if the arc of the semicircle y = √ r 2-x 2 , for a ≤ x ≤ a + h , where a and a + h are between-r and r , is rotated around the x –axis, then the area swept out does not depend on a . CONTINUE TO THE NEXT PAGE. Math 1120, Fall 2011 Homework 4 — due 9/22 or 9/23 3 3. [10 points] Find the area of the surface generated by revolving the parametrized curve x = sin 2 t , y = 2 + cos 2 t , 0 ≤ t ≤ 2 π about the x –axis. THIS IS THE LAST PAGE....
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This note was uploaded on 10/31/2011 for the course MATH 1120 at Cornell.

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homework4 - Math 1120 Fall 2011 Homework 4 — due 9/22 or...

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