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homework04_w12

# homework04_w12 - Math 215 Homework Set 4 14.514.7 Winter...

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Math 215 Homework Set 4: §§ 14.5–14.7 Winter 2012 Most of the following problems are modiﬁed versions of the problems from your text book, Multivariable Calculus , 7th ed., by James Stewart. Your solution to each problem should be complete, show all work, and be written in complete sentences where appropriate. For Maple problems, include a print-out that shows all of the work and graphs that you generated in Maple to solve the problem, in addition to any work you may have done by hand. 14.5.1: Wheat production W in a given year depends on the average temperature T and the annual rainfall R . Scientists estimate that the average temperature is rising at a rate or 0 . 15 C/year and rainfall is decreasing at a rate of 0 . 2 cm/year. They also estimate that, at current production levels, ∂W/∂T = - 1 and ∂W/∂R = 5 . (a) What is the signiﬁcance of the signs of these partial derivatives? (b) Estimate the current rate of change of wheat production,

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homework04_w12 - Math 215 Homework Set 4 14.514.7 Winter...

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