※ [本文轉錄自 NTU-Exam 看板] 作者: Ying1986316 (仔細思索未來...) 看板: NTU-Exam 標題: [試題]93上 張秀瑜 微乙 期末考題 時間: Sun Jan 16 09:46:52 2005 課程名稱︰微積分乙 課程性質︰ 課程教師︰張秀瑜 開課系所︰管理學院 考試時間︰94.01.11 試題 : 1. Find the derivative of the function 2x -t^2 (1) F(x) =∫ e dt,find f'(x) lnx x^2 y (2) e = x+y,find y' -1 (3) If f(x) = x+x^2+e^x and g(x) = f (x),find g'(1) 1/x^2 2. (1) Evaluate lim (cosx) x→0+ x |x| if x ≠ 0 (2) Let f(x) =﹛ and f(0)=1. Show that f is continuous at 0 1 if x = 0 3. Evaluate the integral -1 1/2 sin x cosx (1) ∫ (2) ∫──── dx 0 ──── dx 2 + sinx ╴╴╴ √1-x^2 sinx 1 (3) ∫ 3 cosx dx (4) ∫ ──── dx ╴╴╴ x √x^2-4 √3 -1 dx (5) ∫ tan (1/x) dx (6) ∫ ───── , a＞0 1 ╴╴╴╴ √x^2-a^2 4. Find the area enclosed by the curves y = 20-x^2, y = x^2-12 5. Find the volume of the solid obtained by rotating about y-axis the region -x^2 bounded by y = e , y = 0, x = 0, and x = 1 6. Let f(x) = ln(ln(lnx)). Differentiate f and find the domain of f --

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