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

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 1

22)sin(lim 21--+→x x x x π 洛必达 2 (7pts). Find derivative of 1sin )(212+=+x e

x f x 3 (7pts). Compute ⎰+dx x x 122 4(10pts). Calculate dy and )0(x '' provided

that two variables x and y satisfy the equation x y

y x arctan 122=-+with .0)1(=y 5 (8pts). Evaluate dx x x x ⎰+41

)1( 6 (10pts). Find A and B given

that the derivative of ⎩

⎨⎧>-≤++=2,2,2)(22x A Bx x Bx Ax x f is continuous for all real x .

7 (10pts).Find the area of the region bounded by cures 0,3==y x y and the equation of the tangent to the graph 3x y =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 n articles per week can be sold at a price of p dollars each where n p 2110-=and the cost of producing n articles is 210600n n ++dollars. How many articles should be made each week to

give the largest profit?

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

x e y -= 10 (8pts). Let )(x L be a differentiable function on ),0(+∞such that x x L 1)(='and 0)1(=L . Prove that for any two positive numbers a and b , )()()(b L a L ab L +=.

11 (6pts). Is it true or false that )(lim 2x f c x →exists implies )(lim x f c x →exists? Justify your answer.