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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