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Answer 39-42 only.

ji. =vx Tay ; oz/ax (1, 2), az/ay(1, 2) 32. w = x cosxy; aw/ax (;, n), aw/ay (1. ) 33. Let f(x, y, z) = x2y#23 + xy + z? + 1. Find (a) fx (x, y, z) (b) fy (x, y. z) ( c) f . ( x. y. z ) (d) fx (1, y. z) (e) fy (1, 2, z) (f) f= (1, 2, 3 ). 34. Let w = x2y cos z. Find 2 0 -2 (a) aw/ax(x, y, z) (b) aw/ay(x, y. z) III (c) aw/az(x, y, z) (d) aw/ax(2, y, z) (e) aw/ay(2, 1, z) (f) aw/az(2, 1, 0). of az/ax, azz/ax2, 35-38 Find fx, fy, and fa. in the accompanying 35. f(x, y, z) = z In(x2 y cos z) 36. f(x, y, z) = y-3/2 sec xz y 37. f(x, y, z) = tan-1 V 2 23 38. f(x, y, z) = cosh(z ) sinh?(x2yz) 39-42 Find aw/ax, aw/ay, and aw/az. x2 - y2 Ex-12 39. w = ye' sin xz 40. W = y2 + z2 41. w = vx2 + y2 + z2 42. w = year+3z the statement is true or 43. Let f(x, y, z) = y?etz. Find (a) af/axla,1.1) (b) af/ayla.I.D) (c) af/azlan.1.1). , y) through (4, 2), then 44. Let w = vx2 + 4y2 - z2. Find (a) aw/axl(2,1.-1) (b) aw/ayl(2.1.-1) surface z = f(x, y) in a (c) aw/azl(2.1.-1). 6) and satisfies z = y', 45. Let f(x, y) = ex cos y. Use a graphing utility to graph the functions fr(0, y) and fy(x, it/2). ne in 3-space, then both 46. Let f(x, y) = ed sin y. Use a graphing utility to graph the functions fx(0, y) and fy(x, 0). that satisfies the equa- 47. A point moves along the intersection of the elliptic parab- and fy(x, y) = 2xy + 2y. oloid z = x2 + 3y and the plane y = 1. At what rate is z changing with respect to x when the point is at (2, 1, 7)? 48. A point moves along the intersection of the elliptic parab- = cos(xsy*) oloid z = x2 + 3yz and the plane x = 2. At what rate is z = exy sin 4y? changing with respect to y when the point is at (2, 1, 7)? x2 y3 49. A point moves along the intersection of the plane y = 3 and = vx+y the surface z = v29 - x2 - y2. At what rate is z changing with respect to x when the point is at (4, 3, 2)? 50. Find the slope of the tangent line at (-1, 1, 5) to the curve f (x, y) = x + y of intersection of the surface z = x2 + 4y2 and (a) the plane x = -1 (b) the plane y = 1. 51. The volume V of a right circular cylinder is given by the formula V = mr2h, where r is the radius and h is the height. (a) Find a formula for the instantaneous rate of change of V with respect to r if r changes and h remains constant. (cont )