课程名称︰微积分乙上 课程性质︰系定必修 课程教师︰李聪成 开课学院：管院 开课系所︰数学系 考试日期（年月日）︰2009/01/15 考试时限（分钟）：(10:20~1:00) 是否需发放奖励金：是 （如未明确表示，则不予发放） 试题 : 请将每一步骤表达清楚, 不可以只写答案 1. Evaluate the indefinite integral(不定积分). __ cos√t ∫--------- dt __ √t 2. Find the area(面积) of the region(区域) enclosed by the curves y=sinx, y=cos2x, x=0, and x=π/2. 3. Evaluate the limit. n π iπ lim Σ ---- tan ----- n→+∞ i=1 4n 4n 4. Evaluate the definite integral(定积分). 2 1 ∫ _ ----------------- dt √2 ______ t^3 √t^2 -1 5. Find the value of the positive constant c such that x+c lim (-----)^x =9 n→+∞ x-c 6. Find the volume(体积) of a right circular cone(圆锥) with height h and base radius γ. 7. Find an equation for the tangle line to the curve y=e^x that passes through the origion(原点). 8. Use logarithmic differentiation to find the derivative of the function (sinx)^2 (tanx)^4 y = -------------------- (x^2 + 1)^2 , where x € (0,π/2) (我找不到属於的符号/3\bbb) 9. Show that x ______ ƒ(x)=∫ √1+t^3 dt 1 is one-to-one on (-1,+∞) and find (ƒ^-1)'(0). 10. Evaluate the limit. x 1 lim (----- - ------) n→1+ x-1 ㏑x 其实期末考题都在老师勾的习题里啦…作课本比较实际。 --

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