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：社科、管院
開課系所︰數學系
考試日期（年月日）︰10/01/12
考試時限（分鐘）：110(0810~1000)
是否需發放獎勵金：是
（如未明確表示，則不予發放）
(範圍：Larson/Edwards Calculus 9th ed. §5.6~§9.10)
(寫出來嚇人的◢▇▆▅▄崩\\\Q皿Q///潰▄▅▆▇◣)
試題 :
1. arctan(1/2)+arctan(1/3)=? (5/50)
y -y
e - e ∞ n
2. x=sinh(y)=----------- , y= sinh^-1(x)=Σ An X =? (5/50)
2 n=0
^
3. Use l'Hopital's rule or any other method to find
2
x - 4x
lim ---------- = ? (5/50)
x→0 2x-1
2 dx
4. ∫ --------- =? (5/50)
0 (x-1)^2
2
x +x+3
5.∫----------- = ? (5/50)
4 2
x +6x +9
1 1 1 1
6.---------+---------+---------+...........+-------------+.....=? (5/50)
1‧2‧3 2‧3‧4 3‧4‧5 n(n+1)(n+2)
7. Find the interval of convergence of the power series
∞ n! (x+1)^n
Σ ------------------ . Be sure to include a check for convergence at
n=1 1‧3‧5‧....(2n-1)
the end point of the interval. (5/50)
8. Find the volume of the solid formed by revolving the region bounded by the
graphs of y=x, y=4 and x=0 about the x-axis. (5/50)
2 2
9. Find the general solution of (x -y )dx+3xydy=0 (5/50)
10. A container of hot liquid is placed in a freeze that is kept at a constant
temperature of 20。F. The initial temperature of the liquid is 160。F.
After 5 minutes, the liquid's temperature is 60。F. How much longer will
it take for its temperature to decrease to 30。F ? (5/50)
--
※ 發信站: 批踢踢實業坊(ptt.cc)
◆ From: 140.112.240.193