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18.02 Pset 4

18.02 Pset 4 - (After Oct 5(10 pts Find the minimum value...

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18.02 HOMEWORK #4, DUE OCTOBER 14, 2010 BJORN POONEN In the Lagrange multiplier problems, don’t forget to check all the things you are supposed to check. 1. Part A (After Oct. 5) 2I-1b, 2I-3 (After Oct. 5) p .924: 36* (15 pts.) (Heron’s formula should read A = s ( s - x )( s - y )( s - z )), 38* (15 pts.) (After Oct. 7) 2J-3b, 2J-4b, 2J-5, 2J-7, 2J-10* (15 pts.), 2J-12a* (10 pts.) (After Oct. 8) 2K-1, 2K-3b* (10 pts.), 2K-4, 2K-5 (After Oct. 12) p. 946: 31 (After Oct. 12) p. 953: 1, 23, 31 (After Oct. 12) p. 959: 26* (5 pts.), 37 (After Oct. 12) 3A-2d* (10 pts.) (just set it up, don’t evaluate!), 3A-6 2. Part B B.1)
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Unformatted text preview: (After Oct. 5) (10 pts.) Find the minimum value of x 2 y , where x and y are positive real numbers satisfying xy 2 = 5. (Warning: This question is misleadingly stated.) B.2) (After Oct. 8) (10 pts.) Show that the solutions f ( x, y ) to the PDE ∂ 2 f ∂x 2 = y are exactly the functions of the form f ( x, y ) := y 2 x 2 + g ( y ) x + h ( y ) for some functions g ( y ) and h ( y ). 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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