課程名稱︰微積分乙上
課程性質︰必修
課程教師︰王藹農
開課學院：理學院
開課系所︰數學系
考試日期（年月日）︰2009/11/12
考試時限（分鐘）：110(上課期間1020~1210)
是否需發放獎勵金：是
（如未明確表示，則不予發放）
試題 :
1. A ladder 25 feet long is leaning against the wall. The base of the ladder
is pulled away from the wall at a rate of 2 feet per second. How fast is
the top of the ladder moving down the wall when its base is 15 feet from
the wall? (4/40)
2. Find the tangent lines to the curve y=x^3-9x through the point (x,y)=(1,-9)
(4/40)
3. Determine the slope of the graph 3(x^2+y^2)=100xy at the point (x,y)=(3,1).
(4/40)
4. An offshore oil well is 2km off the coast. The refinery is 4km down the
coast. Laying pipe in the ocean is twise as expensive as on land. What path
should the pipe follow in order to minimize the cost? (4/40)
5. x^3
f(x)=--------, Find intercepts, relative extrema, points of inflection and
x^2-9 asymptotes. Sketch the graph. (4/40)
6. Use differentials to approximate 26^(1/3). (4/40)
7. x^2
F(x)=∫ sinθ^2 dθ. F'(x)=? (4/40)
0
8. 1
lim -----------(√1+√2+√3+........+√n) =? (4/40)
n→∞ n^(3/2)
9. y=x‧lnx-4x. x+y-xy'=? (4/40)
10. e^x + e^(-x)
∫-------------- dx =? (4/40)
e^x - e^(-x)
答案：
1. -3/2
2. (y+9)=-9(x-1) or (y+9)=-(x-1)
3. 13/9
4. Laying pipe among the coast from the refinery for 4-(2/3)√3
than lay from the point to the well.
5. 圖略
intercept of y =(0,0) intercept of x =(0,0)
relative extrema: (0,0) (3√3, (9/2)√3) (-3√3, (-9/2)√3)
point of inflection: (0,0)
asymptotes: x=±3, y=x
6. 2.963
7. sinx^4‧2x
8. 2/3
9. 0
10.ln[e^x-e^(-x)]+C
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◆ From: 140.112.7.59
※ 編輯: RedHerrings 來自: 140.112.7.59 (11/17 09:46)