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) --

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