6. Note that z = f(x,y) where f is differentiable, x = g(t), and y = h(t). It is known that g(3)=2,g'(3)=5,h(3)=7,h'(3)=4,fx(2,7)=6,and fy(2,7)=-8. Determine the value of dz/dt at t = 3. (A)62(B) 30 (C)32 (D)-2 (E)1。

6. Note that z = f(x,y) where f is differentiable, x = g(t), and y = h(t). It is known that g(3)=2,g'(3)=5,h(3)=7,h'(3)=4,f_x(2,7)=6,and fy(2,7)=-8. Determine the value of dz/dt at t = 3.
(A)62
(B) 30
(C)32
(D)-2
(E)1。

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複選題11. Let A be the region bounded above by the graph of y = sin(πx) and below by the graph of y = x3 - 4x. (A)(2.1,0.8) falls into the region A. (B) The area of A can be represented bydx. (C) The area of A is equal to 4. (D)The region A is the base of a solid. For this solid, each cross section per- pendicular to the a-axis is a square.The volume of this solid is equal to dx. (E)The region A models the surface of a small pond. At all points in A tance :i from the y-axis, the depth of the water is given by h(x) = 3-x. The yolume of water in the pond is equal todx.

6. Note that z = f(x,y) where f is differentiable, x = g(t), and y = h(t). It is known that g(3)=2,g'(3)=5,h(3)=7,h'(3)=4,fx(2,7)=6,and fy(2,7)=-8. Determine the value of dz/dt at t = 3. (A)62(B) 30 (C)32 (D)-2 (E)1。

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6. Note that z = f(x,y) where f is differentiable, x = g(t), and y = h(t). It is known that g(3)=2,g'(3)=5,h(3)=7,h'(3)=4,f_x(2,7)=6,and fy(2,7)=-8. Determine the value of dz/dt at t = 3.
(A)62
(B) 30
(C)32
(D)-2
(E)1。