※ [本文轉錄自 NTU-Exam 看板]
作者: diep (隱藏人物) 看板: NTU-Exam
標題: [試題] 94上 張秀瑜 微積分乙上 期末
時間: Mon Jan 16 11:00:05 2006
課程名稱︰微積分乙上
課程性質︰共同必修
課程教師︰張秀瑜
開課系所︰管院、地理、經濟
考試時間︰94/1/10
試題 :
1. A honeybee population starts with 100 bees and increases at a rate of
15
n'(t) bees per week. What does 100 + ∫ n'(t)dt represent? 7%
0
2. If a and b are positive numbers, show that
1 a b 1 b a
∫ x (1－x) dx = ∫ x (1－x) dx. 10%
0 0
1 3
3. Evaluate the interal ∫ ∣x － x∣dx and interpret it as the area of
-1
a region. Sketch the region. 10%
4. Find the volume of the solid obtained by rotating the region bounded
2 2
by y = 4x－x and y = 8x－2x about the line x = -2. 15%
-1 2
xsin x cosx 3 ＿＿＿
5. Find y': (a) y = e , (b) y = ∫ √1－t^3 dt,
1
2 2
(c) y = ln(x ＋ y ). 15%
x
6. Evaluate the limit: (a) lim x ,(b) lim [ln(2＋x)－ln(1＋x)].
+ x→∞
x→0 10%
7. Evaluate the integral.
x ＿＿＿
(a)∫e √2＋e^x dx, (b)∫lnx dx
6 π/2 5
(c)∫ dx/xlnx, (d)∫ cos xdx.
e 0 20%
8. State the Fundamental Theorem of Calculus Part 1, and find an
2 2
antiderivative F of f(x) = x sinx such tha F(1) = 0. 13%
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