[轉錄][試題] 94上張秀瑜微積分乙上期末

看板NTUIB99作者Thitta (胖胖 )時間19年前 (2007/01/14 15:16)推噓18(19推 1噓 7→)

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※ [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% -- ※ 發信站: 批踢踢實業坊(ptt.cc) ◆ From: 219.81.183.84 -- ※ 發信站: 批踢踢實業坊(ptt.cc) ◆ From: 140.112.240.101

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