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(lim21xxxx 洛必达
2 (7pts). Find derivative of 1sin)(212xexfx
3 (7pts). Compute dxxx122
4(10pts). Calculate dyand)0(x provided that two
variablesxandysatisfy the equationxyyxarctan122with.0)1(y
5 (8pts). Evaluatedxxxx41)1(
6 (10pts). FindAandBgiven that the derivative
of2,2,2)(22xABxxBxAxxf
is continuous for all real x.
7 (10pts).Find the area of the region bounded by cures0,3yxyand
the equation of the tangent to the graph3xyat 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 wherenp2110and the cost of producing narticles is
210600nndollars. 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 )(lim2xfcxexists implies )(limxfcxexists?
Justify your answer.