课程名称︰微积分乙上 课程性质︰必修 课程教师︰王蔼农 开课学院：理学院 开课系所︰数学系 考试日期（年月日）︰2009/11/12 考试时限（分钟）：110(上课期间1020~1210) 是否需发放奖励金：是 （如未明确表示，则不予发放） 试题 : 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. 图略 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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