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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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題組內容
2. Determine if the given series converges or diverges. Explain your reasoning.
a.
(6分)
其他申論題
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
b. (6分)
#482791
3. Find the maximum value of dy, where C is any circle in the xy-plane, oriented counterclockwise.
#482792
1. How many critical points does the function f(x) =|x2 - 1|have? Answer :________
#482793
2.If = 1, then a-b=? Answer :_________
#482794
3. Suppose f" is continuous on [0,1], f(1) = 2, f'(1) = 2 and the average value of f on [0, 1] is 2. Evaluate dx. Answer :__________
#482795
4. Find g', where g(x) is the inverse of f(x) = . Answer :___________
#482796
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(6分)