e204k - Exam II and Key MAC 2312 Oct 27, 2004 S Hudson 1)...

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Exam II and Key Oct 27, 2004 MAC 2312 S Hudson 1) (edit) Find the equation of the tangent plane to z = sin πxy 2 at P (3 , 5 , - 1). 2) Use differentials to approximate p (3 . 1) 2 + (4 . 2) 2 + (11 . 7) 2 3) Falling sand forms a conical sandpile. When the sandpile has a height of 5 ft, and its base radius is 2 ft, its height is increasing at 0.4 ft/s and its base radius is increasing at 0.7 ft/s. At what rate is its volume ( V = πr 2 h/ 3) increasing at that moment? 4) Let f ( x, y ) = 2 x 2 + 3 xy + 4 y 2 . Find the maximal directional derivative at P (1 , 1) and the direction in which it occurs. 5) An open-topped box must have a volume of 600 in 3 . The material for the bottom costs 6 cents per in 2 and the sides cost 5 cents per in 2 . Find the dimensions that minimize the total cost. 6) Answer True or False. You do not have to explain. If f x = f y = 0 and f xx = f yy = 1 at (a,b), then f has a local minimum there. At a local maximum, the discriminant is positive.
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This note was uploaded on 12/27/2011 for the course MAC 2313 taught by Professor Grantcharov during the Fall '06 term at FIU.

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e204k - Exam II and Key MAC 2312 Oct 27, 2004 S Hudson 1)...

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