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Determine which value best approximates the volume of the solid between the xyx y plane and the function over the region. (Make your selection on the basis of a sketch of the solid and not by performing any calculations.)
f(x,y)=4xf(x, y)=4 x RR : square with vertices (0,0),(4,0),(4,4),(0,4)(0,0),(4,0),(4,4),(0,4)
(a) 200-200 (b) 600600 (c ) 5050 (d) 125125 (e) 10001000


Answered 2 years ago
Answered 2 years ago
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The volume of the region can be approximated as height of the region times the area of the base. Since the area in xyxy plane is a square with the area equal to 1616 and the function f(x,y)=4xf(x,y)=4x is positive over the given region any negative answer can be eliminated. Next, 50 is a bit too small while 600 or 1000 is a bit too much since 4x4x does not grow that rapidly or that slowly. The most educated guess is then d), 125.

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