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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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4. Find the slope of the surface f(x, y) = (x
3
+y
3
)
1/3
at the point (0, 0) in the y-direction.
Answer :___________
其他申論題
3. 某交易人欲透過二項樹（Binomial Tree）模型評價歐式股票選擇權，該契約為2 個月後到期。若令S(T)代 表到期日時標的資產價格，T 為選擇權到期日，K 為履約價格，此歐式股票選擇權到期報酬為Max[K-S(T), S(T)-K]。假設市場價格為100 元，履約價格為100 元，股價每期上漲及下跌幅度分別為u=1.2 及d=0.8， 無風險利率為0%，以一個月為一期（N=2），請求算該歐式股票選擇權目前合理價格（10 分）
#482779
1. Find the critical number of y = .Answer:________
#482780
2. Determine the limits of integration where a ≤ b such thatdx has minimal value. Answer:________
#482781
3. Evaluate dx. Answer:_______
#482782
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
6. Find an equation of the tangent plane to the paraboloid r(u,u) = ui + uj + (u2 +u2)k at the point (1,2,5), Answer :____________
#482785
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
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