1. Textbook questions - read sections 4.1, 4.2, 4.3 pg. 128 (Chapter 4) questions 11, 16 11. Use calculus to prove Archimedes' result that the area of a parabolic segment is four-thirds of the area of the inscribed triangle. 16. There is a story about Archimedes that he used a "burning mirror" in the shape of a paraboloid of revolution to set fire to enemy ships in the harbor. What would be the equation of the parabola that one would rotate to form the appropriate paraboloid if it were to be designed to set fire to a ship 100 m from the mirror? How large would the burning mirror need to be? What is the likelihood that this story is true?

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