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Unformatted text preview: D f = - + + =- = 7. Verify that ( , ) sin( ) u x t x at =-, satisfies 2 2 2 2 2 u u a t x -= . 8. The gas law for a fixed mass m of an ideal gas at absolute temperature T , pressure P and volume V is given by PV mRT = where R is the gas constant. Show that P V T mR T T = . 9. Determine the dimensions of a rectangular box, open at the top, having a volume of 32 cubic feet, and requiring the least amount of material for its construction. Answer: (4,4,2) 10. Find the points on the sphere 2 2 2 36 x y z + + = that are closest to and farthest from the point (1, 2, 2). Use Lagrange multiplier method. Answer: Closest (2,4,4) and furthest (-2,-4,-4) . You may look at your text book for calculation and work....
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This note was uploaded on 05/09/2008 for the course MAT 272 taught by Professor Firoz during the Spring '08 term at ASU.
- Spring '08