課程名稱︰微積分甲上
課程性質︰共同必修
課程教師︰劉崑山
開課學院：生農學院、管理學院
開課系所︰生工 生機 地質 科管
考試日期（年月日）︰2010/11/22
考試時限（分鐘）：110分鐘(可以超時到寫完為止)
是否需發放獎勵金：是
（如未明確表示，則不予發放）
試題 :
-1 y-1
(1)(2pt) ytan (x)+2y+xe =2
find the equation of the tangent line at (0,1)
2
sin x
(2)(1pt) f(x)=tan(e ),f'(x)=?
lnx
(3)(1pt) f(x)=(secx) ,f'(x)=?
3/4 2 1/2
(x+1) (x +1)
(4)(2pt) f(x)= ──────── ,f'(0)=?
5
(3x+2)
3/x
(5)(1pt) lim x =?
x→∞
x
∫ lntdt
1
(6)(2pt) lim ────── =?
x→1 2
x -2x+1
n + 1 n + 2 n + 3 n + n
(7)(3pt) lim (──── + ──── + ──── + ... + ────)=?
n→∞ 2 2 2 2 2 2 2 2
n + 1 n + 2 n + 3 n + n
2
tan (lnx)
(8)(2pt) ∫────── dx=?
x
2 2
(9)(2pt) ∫sec xtan xdx=?
2/x
2 e
(10)(2pt)∫ ────── dx=?
1 2
x
3 ______
(11)(1pt) Estimate √27.27 by the linear approximation.
(12)(3pt) Show that ｜sina - sinb｜≦｜a - b｜for all a and b.
Show that 3x-1-sinx = 0 has exactly one real root.
(13)(3pt) A right circular cylinder is inscribed in a sphere of radius R.
Find the largest possible volume of such a cylinder.
3
x
(14)(8pt) Sketch the graph of f(x) = ────
2
x + 3
A. The domain.
B. The x- and y- intercepts.
C. The symmetry.
D. All possible asymptotes.
E. The intervals of increase and decrease,
and the maximum and minimum.
D. The intervals of concavity, and the points of inflection.
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※ 編輯: howhao 來自: 111.250.5.215 (11/23 00:00)