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107年 - 107 台灣聯合大學系統(清華、交通、陽明、中央四校聯招)學士班轉學生考試_A3、A4、A7：微積分#112635
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6. Find an equation of the tangent plane to the paraboloid r(u,u) = ui + uj + (u
2
+u
2
)k at the point (1,2,5), Answer :____________
其他申論題
2. Determine the limits of integration where a ≤ b such thatdx has minimal value. Answer:________
#482781
3. Evaluate dx. Answer:_______
#482782
4. Find the slope of the surface f(x, y) = (x3+y3)1/3 at the point (0, 0) in the y-direction. Answer :___________
#482783
5. Find the surface area of the portion of the plane z = 4 - 2x - 2y that lies above the circlex2+y2≤1 in the first quadrant. Answer :__________
#482784
7. Evaluate the integraldxdy. Answer:___________
#482786
8. Use a change of variables to find the volume of the solid region lying below the surface and above the plane region R : region bounded by the parallelogram with vertices (0,0),(1,1), (5,0) and (4, -1): Answer:____________
#482787
(a) (6 分) In what direction from (-1,2) does the temperature increase most rapidly? What is this rate of increase?
#482788
(b) (6 分) Find the path of the particle as it continuously moves in the direction of maximum temperature increase.
#482789
a. (6分)
#482790
b. (6分)
#482791
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