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18.02 Pset 2

18.02 Pset 2 - (Hint An ellipse is the set of points whose...

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18.02 HOMEWORK #2, DUE SEPTEMBER 23, 2010 BJORN POONEN 1. Part A (After Sept. 16) 1E-1, 1E-2, 1E-3, 1E-6, 1E-7* (15 pts.) (assume that the lines are not parallel) (After Sept. 16) p. 650: 34* (15 pts.) (After Sept. 16) p. 802: 37, 39, 57* (10 pts.) (After Sept. 16) 1I-2, 1I-3, 1I-5 (After Sept. 17) 1J-2, 1J-5, 1J-6 (After Sept. 21) p. 858: 27, 37, 53–58 (ignore the labels on the axes in Figures 13.2.39–44, since they are misleading or wrong, depending on your interpretation) (After Sept. 21) 2A-1, 2A-5a (After Sept. 21) 2B-1a, 2B-3, 2B-10* (10 pts.) 2. Part B B.1) (After Sept. 17) Let PQ be the major axis of the elliptical orbit of a planet orbiting a sun. Suppose that the planet is moving at 80 km/s when it is at P , and 20 km/s when it is at Q . (a) (10 pts.) How far is the sun from P ? (Express the answer as a fraction of PQ .) (b) (15 pts.) How fast is the planet moving when it is at an end of the minor axis?
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Unformatted text preview: (Hint: An ellipse is the set of points whose distances from the two foci add to a certain constant.) B.2) (After Sept. 21) (a) (5 pts.) Sketch some level curves of the function max( | x | , | y | ). (b) (10 pts.) Find a function whose level curves are the same as in (a), but rotated 45 ◦ . B.3) (After Sept. 21, 10 pts.) Use the tangent plane approximation formula to estimate the root of x 2-5 . 99 x + 8 . 02 close to 4 without using a calculator . Then use a calculator to ﬁnd the root to 5 places after the decimal point. Reminder: Please write “Sources consulted: none” at the top of your homework, or list your (animate and inanimate) sources. See the course information sheet for details. 1...
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