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### Homework9

Course: M 408L, Spring 2008
School: University of Texas
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Word Count: 795

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Homework yp968 9 Radin (58415) This print-out should have 17 questions. Multiple-choice questions may continue on the next column or page find all choices before answering. 001 10.0 points 2. fx = -2 sin(3y - x) - x cos(3y - x) 3. fx = x cos(3y - x) - sin(3y - x) 4. fx = x cos(3y - x) 5. fx = x sin(3y - x) 6. fx = -x sin(3y - x) 7. fx = 2 sin(3y - x) - x cos(3y - x) x 8. fx = - cos(3y - x) - x sin(3y - x) 003...

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Homework yp968 9 Radin (58415) This print-out should have 17 questions. Multiple-choice questions may continue on the next column or page find all choices before answering. 001 10.0 points 2. fx = -2 sin(3y - x) - x cos(3y - x) 3. fx = x cos(3y - x) - sin(3y - x) 4. fx = x cos(3y - x) 5. fx = x sin(3y - x) 6. fx = -x sin(3y - x) 7. fx = 2 sin(3y - x) - x cos(3y - x) x 8. fx = - cos(3y - x) - x sin(3y - x) 003 10.0 points 1 Determine whether the partial derivatives fx , fy of f are positive, negative or zero at the point P on the graph of f shown in z y P Find the slope in the x-direction at the point P (0, 2, f (0, 2)) on the graph of f when f (x, y) = 4(2x + y)e-xy . 1. slope = -10 2. slope = -6 1. fx = 0 , fy < 0 2. fx < 0 , fy = 0 3. fx = 0 , fy > 0 4. fx > 0 , fy = 0 5. fx < 0 , fy > 0 6. fx < 0 , fy < 0 7. fx > 0 , fy > 0 8. fx = 0 , fy = 0 3. slope = -12 4. slope = -8 5. slope = -4 004 10.0 points Determine h = h(x, y) so that h(x, y) f = x (4 x2 + 4 y 2 )2 when f (x, y) = 3x2 y . 4 x2 + 4 y 2 002 10.0 points 1. h(x, y) = 24xy 2 2. h(x, y) = 24x3 y 3. h(x, y) = 12x3 y Determine fx when f (x, y) = cos(3y - x) - x sin(3y - x) . 1. fx = -x cos(3y - x) yp968 Homework 9 Radin (58415) 4. h(x, y) = 12xy 2 5. h(x, y) = 12xy 3 6. h(x, y) = 24xy 3 005 Find fy when x 2 007 (part 1 of 4) 10.0 points The productivity of an automobile manufacturing company is given by the function f (x, y) = 60 xy with the utilization of x units of labor and y units of capital. (i) Find fx and fy . dt . 1. fx = 30 2. fx = 30 3. fx = 60 1 , xy y , x y , x fy = 30 fy = 30 fy = 60 fy = 30 1 xy x y x y x y 10.0 points f (x, y) = y cos t 7 1. fy = 7x6 cos y 7 2. fy = sin y 7 3. fy = - sin y 7 4. fy = cos y 7 4. fx = 30 xy, 5. fx = 30 y , x fy = 30 xy 5. fy = 7x6 sin y 7 6. fy = - cos y 006 7 008 (part 2 of 4) 10.0 points (ii) If the company is now using 160 units of labor and 810 units of capital, find the marginal productivity of labor. 1. marg. prod. labor = 2. marg. prod. labor = 3. marg. prod. labor = 40 3 5 6 135 2 10.0 points Determine z/y when z = z(x, y) is defined by 4x2 + 6xy + yz + 6z 2 = 1 . 6x + z z = - y y + 12z z 6y - x = - y x + 12y 6x - z z = y x + 12y 6x + z z = - y 12z 1. 2. 3. 4. 4. marg. prod. labor = 1080 5. marg. prod. labor = 54 009 (part 3 of 4) 10.0 points (iii) If the company is now using 160 units of labor and 810 units of capital, find marginal the productivity of capital. z 6x - z 5. = y 12z yp968 Homework 9 Radin (58415) 135 1. marg. prod. capital = 2 2. marg. prod. capital = 12 3. marg. prod. capital = 1080 40 4. marg. prod. capital = 3 5. marg. prod. capital = 5 6 7 y is the plane shown in 3 z x 010 (part 4 of 4) 10.0 points (iv) To achieve the greatest increase in productivity when the company is using 160 units of labor and 810 units of capital, should the management encourage increased use of labor or increased use of capital, or neither? 1. increase use of labor 2. increase use of capital 3. increase neither labor nor capital 011 10.0 points A = (x, y) : 0 x 7, 0 y 2 Determine the value of the double integral I = A f (x, y) dxdy over the region in the xy-plane by first identifying it as the volume of a solid below the graph of f . 1. I = 47 cu. units 2. I = 49 cu. units 3. I = 51 cu. units Determine the value of fxy at (1, 0) when f (x, y) = x ye 1. fxy (1, 0) = 3 + e5 2. fxy (1, 0) = 5 3. fxy (1, 0) = 3 4. fxy (1, 0) = 5e3 5. fxy (1, 0) = 3e5 012 10.0 points 2 3x+6y . 4. I = 50 cu. units 5. I = 48 cu. units 013 10.0 points Calculate the value of the double integral I = A 4x sin(x + y) dxdy when A is the rectangle (x, y) : 0 x , 4 0 y 4 . The graph of the function z = f (x, y) = 7 - x yp968 Homework 9 Radin (58415) 1. I = 2. I = 3. I = 4. I = 5. I = 6. I = 1 2 - 4( 2 + 1) 2 1 4( 2 + 1) - (2 + 2) 2 1 4( 2 - 1) - (2 - 2) 2 1 2 + 4( 2 - 1) 2 1 2 - 4( 2 - 1) 2 1 4( 2 - 1) + (2 - 2) 2 014 10.0 points 2. I = 1 3. I = 4. I = 5. I = 4 3 5 3 7 3 016 10.0 points 4 Evaluate the double integral 3 3 y I = 0 6ex dxdy 2 Evaluate the integral 1 x2 0 by reversing the order of integration. 1. I = 3(e9 - 1) 2. I = 1 9 e 2 I = 0 (2x - y) dydx . 1. I = 2. I = 1 2 2 5 3. I = 6(e9 + 1) 4. I = 3(e9 + 1) 5. I = 3e9 6. I = 6(e9 - 1) 017 10.0 points 3 3. I = 10 4. I = 5. I = 1 5 3 5 015 10.0 points Reverse the order of integration in the integral 4 1 Evaluate the double integral I = A I = 2 f (x, y) dy dx, x/2 (x - 3y) dxdy but make no attempt to evaluate either integral. 1 4y 2 when A is the region enclosed by the graphs of x = 1, x + y = 1, y + 1 = 0. 1. I = 2 1. I = f (x, y) dx dy 2/2 2 2y 2 1 2. I = f (x, y) dx dy 2/2 2 yp968 Homework 9 Radin (58415) 1 2 5 3. I = f (x, y) dx dy 2/2 2/2 2y 2 2 4. I = 0 2/2 2 4y 2 f (x, y) dx dy 4x2 5. I = 0 f (x, y) dx dy
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