安徽工程学院2018-2019学年第一学期微积分A卷期末考试试卷

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安徽工程学院2018-2019学年第一学期期末考试试卷

课程代码: 12003 课 时:48

课程名称:微积分I(A卷) 适用对象:国际学院05级

1 (7pts). Evaluate 122)sin(lim21xxxx 洛必达

2 (7pts). Find derivative of 1sin)(212xexfx

3 (7pts). Compute dxxx122

4(10pts). Calculate dyand)0(x provided that two

variablesxandysatisfy the equationxyyxarctan122with.0)1(y

5 (8pts). Evaluatedxxxx41)1(

6 (10pts). FindAandBgiven that the derivative

of2,2,2)(22xABxxBxAxxf

is continuous for all real x.

7 (10pts).Find the area of the region bounded by cures0,3yxyand

the equation of the tangent to the graph3xyat the point (1,1).What is the

volume of the solid generated by revolving the region about the x-axis?

8 (12pts). A manufacturing plant has a capacity of 25 articles per week.

Experience has shown that narticles per week can be sold at a price of

pdollars each wherenp2110and the cost of producing narticles is

210600nndollars. How many articles should be made each week to give the largest profit?

9 (15pts). Sketch the graph of the function 2xey

10 (8pts). Let)(xLbe a differentiable function on ),0(such

that

xxL1)(and 0)1(L. Prove that for any two positive numbers aandb,

)()()(bLaLabL.

11 (6pts). Is it true or false that )(lim2xfcxexists implies )(limxfcxexists?

Justify your answer.