hmwk4 - Math 215 Homework Set 4: §§ 15.5 – 15.8 Winter...

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Unformatted text preview: Math 215 Homework Set 4: §§ 15.5 – 15.8 Winter 2008 Most of the following problems are modiFed versions of homework problems from your text book Multivariable Calculus by James Stewart. 15.5a. Because you will probably actually need to use these equations at some point in your academic career, please do Problems 45, 53, and 53 of § 15.5 of Stewart’s Multivariable Calculus . 15.5b. The temperature at a point ( x, y ) on the Michigan football Feld is T ( x, y ) measured in degrees ¡ahrenheit. Alan Mitchell runs so that his position after t seconds is given by x = 26 + √ 25 + 3 t 2 and y = 14 + t/ 5 where x and y are measured in yards. The temperature function satisFes T x (36 , 15) = . 3 and T y (36 , 15) = . 1 . How fast is the temperature rising along Carter’s path after 5 seconds? 15.5c. Suppose that the equation G ( s, t, u ) = 0 implicitly deFnes each of the three variables s , t , and u as functions of the other two: s = x ( t, u ) , t = y ( s, u ) , and u = z ( s, t ) . If....
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This note was uploaded on 04/01/2008 for the course MATH 215 taught by Professor Fish during the Winter '08 term at University of Michigan.

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