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hmwk4

# hmwk4 - Math 215 Homework Set 4 15.5 15.8 Winter 2008 Most...

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Math 215 Homework Set 4: §§ 15.5 – 15.8 Winter 2008 Most of the following problems are modified 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 field is T ( x, y ) measured in degrees Fahrenheit. 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 satisfies 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 defines 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 G is differentiable and G s , G t , and G u are all nonzero, show that 1 = - u s · s t · t u .
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