1. If u = ex/y, x = 2r - s, and y = r + 2s for r + 2s non-zero, then, in terms of x and y, the partial derivative of u with respect to r is,

 A. ((2-x)/y)ex/y B. 3ex/y C. (2/y)ex/y D. ((2y-x)/y2)ex/y E. ((2y-x)/y)ex/y
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2. If u = xy z for x, y, and z > 0, then

 A. 3u B. u(1 + z + z2/y) C. u(1 +y ln z +z ln y) D. u(1 + z2/y + y ln z) E. u(1 + z + z ln y)
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3. Let u(x,y,z) = 1/(x2 + y2 + z2)1/2 for x, y, z not all zero. Then

 A. 0 B. 1 C. -(x+y+z)/(x2+y2+z2)1/2 D. (9/2)(x2 + y2 + z2)-5/2 E. (x2 + y2 + z2)-2
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4. Let u(x,y) = (a2x - by2)1/2 for a2x - by2 > 0. Which of the following is equal to

 A. B. C. D. E.
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5. Let f(x,y) = (x2/y) + (y2/x) for x > 0 and y > 0. Then

 A. (2y/x2) - (2x/y2) B. (2x2/y3) + (2/x) C. (2x/y2) - (2y/x2) D. (2/y) + (2y2/x3) E. -(2x/y2)-(2y/x2)
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6. Let f(x,y) = xey/(xy + 3) for xy > 0. What is

 A. ey/y B. -3ey/(xy + 3)2 C. 3ey/(xy + 3)2 D.(2xyey + 3ey)/(xy + 3)2 E. (ey - xyey)/(xy + 3)

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7.

 A. -xy2cos(xy)-2ysin(xy) B. -x2ysin(xy)-2ysin(xy) C. -x2ysin(xy)-2xcos(xy) D. -x2ysin(xy) E. -xy2cos(xy)
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8. Let f(x,y) = 3y2 ln(x3 + 4) + 2y/x for x > 0 and y any real number. What value of y minimizes the partial derivative of f with respect to x, when x = 2?

 A. -1 B. -1/3 C. 0 D. 1/12 E. 1
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