大学一级高数期末考试题及答案.pdf

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1、1/7 第一学期高等数学期末考试试卷答案一计算题（本题满分35 分，共有5 道小题，每道小题7 分），1求极限xxxxx30sin2cos1lim解：30303012cos1lim12cos12limsin2cos1limxxxxxxxxxxxxxx20302cos1ln032cos1ln02cos1lnlim2cos1lnlim2cos1ln1lim1limxxxxxxxexexxxxxxxx412cos1sinlim0 xxxx 2设0 x时，xf与22x是等价无穷小，30 xdttf与kAx等价无穷小，求常数k与A解：由于当0 x时，30 xdttf与kAx等价无穷小，所以1lim300

2、kxxAxdttf而10132320132323230132300061lim6lim3122lim31limlim3kxkxkxkxkxxAkxAkxxxAkxxxxxfAkxxxfAxdttf所以，161lim10kxAkx因此，61,1Ak3如果不定积分dxxxbaxx22211中不含有对数函数，求常数a与b应满足的条件解：2/7 将22211xxbaxx化为部分分式，有2222211111xDCxxBxAxxbaxx，因此不定积分dxxxbaxx22211中不含有对数函数的充分必要条件是上式中的待定系数0CA即22222222211111111xxxDxBxDxBxxbaxx所以，有D

3、BDxxDBxDxBbaxx2112222比较上式两端的系数，有DBbDaDB,2,1所以，得1b 5计算定积分2502,1mindxx解：1211222,1minxxxx3132221211xxxxxx所以，8132212,1min2522110250dxxdxxdxdxx5设曲线C的极坐标方程为3sin3ar，求曲线C的全长解：曲线3sin3ar一周的定义域为30，即30因此曲线C的全长为adadaadrrs233sin3cos3sin3sin30230242623022文档编码:CK10C6J6B3Z1 HL7R9O1Z4Z2 ZN7T7X5B8X2文档编码:CK10C6J6B3Z1 H

4、L7R9O1Z4Z2 ZN7T7X5B8X2文档编码:CK10C6J6B3Z1 HL7R9O1Z4Z2 ZN7T7X5B8X2文档编码:CK10C6J6B3Z1 HL7R9O1Z4Z2 ZN7T7X5B8X2文档编码:CK10C6J6B3Z1 HL7R9O1Z4Z2 ZN7T7X5B8X2文档编码:CK10C6J6B3Z1 HL7R9O1Z4Z2 ZN7T7X5B8X2文档编码:CK10C6J6B3Z1 HL7R9O1Z4Z2 ZN7T7X5B8X2文档编码:CK10C6J6B3Z1 HL7R9O1Z4Z2 ZN7T7X5B8X2文档编码:CK10C6J6B3Z1 HL7R9O1Z4Z2 ZN

5、7T7X5B8X2文档编码:CK10C6J6B3Z1 HL7R9O1Z4Z2 ZN7T7X5B8X2文档编码:CK10C6J6B3Z1 HL7R9O1Z4Z2 ZN7T7X5B8X2文档编码:CK10C6J6B3Z1 HL7R9O1Z4Z2 ZN7T7X5B8X2文档编码:CK10C6J6B3Z1 HL7R9O1Z4Z2 ZN7T7X5B8X2文档编码:CK10C6J6B3Z1 HL7R9O1Z4Z2 ZN7T7X5B8X2文档编码:CK10C6J6B3Z1 HL7R9O1Z4Z2 ZN7T7X5B8X2文档编码:CK10C6J6B3Z1 HL7R9O1Z4Z2 ZN7T7X5B8X2文档编码

6、:CK10C6J6B3Z1 HL7R9O1Z4Z2 ZN7T7X5B8X2文档编码:CK10C6J6B3Z1 HL7R9O1Z4Z2 ZN7T7X5B8X2文档编码:CK10C6J6B3Z1 HL7R9O1Z4Z2 ZN7T7X5B8X2文档编码:CK10C6J6B3Z1 HL7R9O1Z4Z2 ZN7T7X5B8X2文档编码:CK10C6J6B3Z1 HL7R9O1Z4Z2 ZN7T7X5B8X2文档编码:CK10C6J6B3Z1 HL7R9O1Z4Z2 ZN7T7X5B8X2文档编码:CK10C6J6B3Z1 HL7R9O1Z4Z2 ZN7T7X5B8X2文档编码:CK10C6J6B3Z1

7、 HL7R9O1Z4Z2 ZN7T7X5B8X2文档编码:CK10C6J6B3Z1 HL7R9O1Z4Z2 ZN7T7X5B8X2文档编码:CK10C6J6B3Z1 HL7R9O1Z4Z2 ZN7T7X5B8X2文档编码:CK10C6J6B3Z1 HL7R9O1Z4Z2 ZN7T7X5B8X2文档编码:CK10C6J6B3Z1 HL7R9O1Z4Z2 ZN7T7X5B8X2文档编码:CK10C6J6B3Z1 HL7R9O1Z4Z2 ZN7T7X5B8X2文档编码:CK10C6J6B3Z1 HL7R9O1Z4Z2 ZN7T7X5B8X2文档编码:CK10C6J6B3Z1 HL7R9O1Z4Z2

8、ZN7T7X5B8X2文档编码:CK10C6J6B3Z1 HL7R9O1Z4Z2 ZN7T7X5B8X2文档编码:CK10C6J6B3Z1 HL7R9O1Z4Z2 ZN7T7X5B8X2文档编码:CK10C6J6B3Z1 HL7R9O1Z4Z2 ZN7T7X5B8X2文档编码:CK10C6J6B3Z1 HL7R9O1Z4Z2 ZN7T7X5B8X2文档编码:CK10C6J6B3Z1 HL7R9O1Z4Z2 ZN7T7X5B8X2文档编码:CK10C6J6B3Z1 HL7R9O1Z4Z2 ZN7T7X5B8X2文档编码:CK10C6J6B3Z1 HL7R9O1Z4Z2 ZN7T7X5B8X2文档

9、编码:CK10C6J6B3Z1 HL7R9O1Z4Z2 ZN7T7X5B8X2文档编码:CK10C6J6B3Z1 HL7R9O1Z4Z2 ZN7T7X5B8X2文档编码:CK10C6J6B3Z1 HL7R9O1Z4Z2 ZN7T7X5B8X2文档编码:CK10C6J6B3Z1 HL7R9O1Z4Z2 ZN7T7X5B8X2文档编码:CK10C6J6B3Z1 HL7R9O1Z4Z2 ZN7T7X5B8X2文档编码:CK10C6J6B3Z1 HL7R9O1Z4Z2 ZN7T7X5B8X2文档编码:CK10C6J6B3Z1 HL7R9O1Z4Z2 ZN7T7X5B8X2文档编码:CK10C6J6B3

10、Z1 HL7R9O1Z4Z2 ZN7T7X5B8X2文档编码:CK10C6J6B3Z1 HL7R9O1Z4Z2 ZN7T7X5B8X2文档编码:CK10C6J6B3Z1 HL7R9O1Z4Z2 ZN7T7X5B8X23/7 二（本题满分45 分，共有5 道小题，每道小题9 分），6求出函数nnxxxf221sinlim的所有间断点，并指出这些间断点的类型解：2102121212121sin21sinlim2xxxxxxxxfnn因此211x与212x是函数xf的间断点00limlim2121xxxf，1sinlimlim2121xxfxx，因此21x是函数xf的第一类可去型间断点1sinlim

11、lim2121xxfxx，00limlim2121xxxf，因此21x是函数xf的第一类可去型间断点7设是函数xxfarcsin在区间b,0上使用Lagrange（拉格朗日）中值定理中的“中值”，求极限bb0lim解：xxfarcsin在区间b,0上应用 Lagrange 中值定理，知存在b,0，使得0110arcsinarcsin2bb所以，22arcsin1bb因此，22220220220arcsinarcsinlimarcsin1limlimbbbbbbbbbbb令btarcsin，则有文档编码:CK10C6J6B3Z1 HL7R9O1Z4Z2 ZN7T7X5B8X2文档编码:CK10C

12、6J6B3Z1 HL7R9O1Z4Z2 ZN7T7X5B8X2文档编码:CK10C6J6B3Z1 HL7R9O1Z4Z2 ZN7T7X5B8X2文档编码:CK10C6J6B3Z1 HL7R9O1Z4Z2 ZN7T7X5B8X2文档编码:CK10C6J6B3Z1 HL7R9O1Z4Z2 ZN7T7X5B8X2文档编码:CK10C6J6B3Z1 HL7R9O1Z4Z2 ZN7T7X5B8X2文档编码:CK10C6J6B3Z1 HL7R9O1Z4Z2 ZN7T7X5B8X2文档编码:CK10C6J6B3Z1 HL7R9O1Z4Z2 ZN7T7X5B8X2文档编码:CK10C6J6B3Z1 HL7R9

13、O1Z4Z2 ZN7T7X5B8X2文档编码:CK10C6J6B3Z1 HL7R9O1Z4Z2 ZN7T7X5B8X2文档编码:CK10C6J6B3Z1 HL7R9O1Z4Z2 ZN7T7X5B8X2文档编码:CK10C6J6B3Z1 HL7R9O1Z4Z2 ZN7T7X5B8X2文档编码:CK10C6J6B3Z1 HL7R9O1Z4Z2 ZN7T7X5B8X2文档编码:CK10C6J6B3Z1 HL7R9O1Z4Z2 ZN7T7X5B8X2文档编码:CK10C6J6B3Z1 HL7R9O1Z4Z2 ZN7T7X5B8X2文档编码:CK10C6J6B3Z1 HL7R9O1Z4Z2 ZN7T7X

14、5B8X2文档编码:CK10C6J6B3Z1 HL7R9O1Z4Z2 ZN7T7X5B8X2文档编码:CK10C6J6B3Z1 HL7R9O1Z4Z2 ZN7T7X5B8X2文档编码:CK10C6J6B3Z1 HL7R9O1Z4Z2 ZN7T7X5B8X2文档编码:CK10C6J6B3Z1 HL7R9O1Z4Z2 ZN7T7X5B8X2文档编码:CK10C6J6B3Z1 HL7R9O1Z4Z2 ZN7T7X5B8X2文档编码:CK10C6J6B3Z1 HL7R9O1Z4Z2 ZN7T7X5B8X2文档编码:CK10C6J6B3Z1 HL7R9O1Z4Z2 ZN7T7X5B8X2文档编码:CK1

15、0C6J6B3Z1 HL7R9O1Z4Z2 ZN7T7X5B8X2文档编码:CK10C6J6B3Z1 HL7R9O1Z4Z2 ZN7T7X5B8X2文档编码:CK10C6J6B3Z1 HL7R9O1Z4Z2 ZN7T7X5B8X2文档编码:CK10C6J6B3Z1 HL7R9O1Z4Z2 ZN7T7X5B8X2文档编码:CK10C6J6B3Z1 HL7R9O1Z4Z2 ZN7T7X5B8X2文档编码:CK10C6J6B3Z1 HL7R9O1Z4Z2 ZN7T7X5B8X2文档编码:CK10C6J6B3Z1 HL7R9O1Z4Z2 ZN7T7X5B8X2文档编码:CK10C6J6B3Z1 HL7

16、R9O1Z4Z2 ZN7T7X5B8X2文档编码:CK10C6J6B3Z1 HL7R9O1Z4Z2 ZN7T7X5B8X2文档编码:CK10C6J6B3Z1 HL7R9O1Z4Z2 ZN7T7X5B8X2文档编码:CK10C6J6B3Z1 HL7R9O1Z4Z2 ZN7T7X5B8X2文档编码:CK10C6J6B3Z1 HL7R9O1Z4Z2 ZN7T7X5B8X2文档编码:CK10C6J6B3Z1 HL7R9O1Z4Z2 ZN7T7X5B8X2文档编码:CK10C6J6B3Z1 HL7R9O1Z4Z2 ZN7T7X5B8X2文档编码:CK10C6J6B3Z1 HL7R9O1Z4Z2 ZN7T

17、7X5B8X2文档编码:CK10C6J6B3Z1 HL7R9O1Z4Z2 ZN7T7X5B8X2文档编码:CK10C6J6B3Z1 HL7R9O1Z4Z2 ZN7T7X5B8X2文档编码:CK10C6J6B3Z1 HL7R9O1Z4Z2 ZN7T7X5B8X2文档编码:CK10C6J6B3Z1 HL7R9O1Z4Z2 ZN7T7X5B8X2文档编码:CK10C6J6B3Z1 HL7R9O1Z4Z2 ZN7T7X5B8X2文档编码:CK10C6J6B3Z1 HL7R9O1Z4Z2 ZN7T7X5B8X2文档编码:CK10C6J6B3Z1 HL7R9O1Z4Z2 ZN7T7X5B8X2文档编码:C

18、K10C6J6B3Z1 HL7R9O1Z4Z2 ZN7T7X5B8X2文档编码:CK10C6J6B3Z1 HL7R9O1Z4Z2 ZN7T7X5B8X2文档编码:CK10C6J6B3Z1 HL7R9O1Z4Z2 ZN7T7X5B8X24/7 422022220220sinlimsinsinlimlimtttttttbttb3122sin2lim612cos1lim61122cos22lim42sin2lim0202030ttttttttttttt所以，31lim0bb8设xyydyexf102，求10dxxf解：101010dxxf xxxfdxxf在方程xyydyexf102中，令1x，得0

19、10021102dyedyefyyyy再在方程xyydyexf102两端对x求导，得21xexf，因此，10101010dxxf xdxxf xxxfdxxf121211010101222eeedxxeedxxexxx9研究方程2xaex0a在区间,内实根的个数解：设函数12xeaxxf，xxxexaxeaxaxexf222令0 xf，得函数xf的驻点2,021xx由于0a，所以1limlim2xxxeaxxf，112lim12lim1lim1limlim22xxxxxxxxxeaexaexaeaxxf文档编码:CK10C6J6B3Z1 HL7R9O1Z4Z2 ZN7T7X5B8X2文档编码:

20、CK10C6J6B3Z1 HL7R9O1Z4Z2 ZN7T7X5B8X2文档编码:CK10C6J6B3Z1 HL7R9O1Z4Z2 ZN7T7X5B8X2文档编码:CK10C6J6B3Z1 HL7R9O1Z4Z2 ZN7T7X5B8X2文档编码:CK10C6J6B3Z1 HL7R9O1Z4Z2 ZN7T7X5B8X2文档编码:CK10C6J6B3Z1 HL7R9O1Z4Z2 ZN7T7X5B8X2文档编码:CK10C6J6B3Z1 HL7R9O1Z4Z2 ZN7T7X5B8X2文档编码:CK10C6J6B3Z1 HL7R9O1Z4Z2 ZN7T7X5B8X2文档编码:CK10C6J6B3Z1

21、HL7R9O1Z4Z2 ZN7T7X5B8X2文档编码:CK10C6J6B3Z1 HL7R9O1Z4Z2 ZN7T7X5B8X2文档编码:CK10C6J6B3Z1 HL7R9O1Z4Z2 ZN7T7X5B8X2文档编码:CK10C6J6B3Z1 HL7R9O1Z4Z2 ZN7T7X5B8X2文档编码:CK10C6J6B3Z1 HL7R9O1Z4Z2 ZN7T7X5B8X2文档编码:CK10C6J6B3Z1 HL7R9O1Z4Z2 ZN7T7X5B8X2文档编码:CK10C6J6B3Z1 HL7R9O1Z4Z2 ZN7T7X5B8X2文档编码:CK10C6J6B3Z1 HL7R9O1Z4Z2 Z

22、N7T7X5B8X2文档编码:CK10C6J6B3Z1 HL7R9O1Z4Z2 ZN7T7X5B8X2文档编码:CK10C6J6B3Z1 HL7R9O1Z4Z2 ZN7T7X5B8X2文档编码:CK10C6J6B3Z1 HL7R9O1Z4Z2 ZN7T7X5B8X2文档编码:CK10C6J6B3Z1 HL7R9O1Z4Z2 ZN7T7X5B8X2文档编码:CK10C6J6B3Z1 HL7R9O1Z4Z2 ZN7T7X5B8X2文档编码:CK10C6J6B3Z1 HL7R9O1Z4Z2 ZN7T7X5B8X2文档编码:CK10C6J6B3Z1 HL7R9O1Z4Z2 ZN7T7X5B8X2文档编

23、码:CK10C6J6B3Z1 HL7R9O1Z4Z2 ZN7T7X5B8X2文档编码:CK10C6J6B3Z1 HL7R9O1Z4Z2 ZN7T7X5B8X2文档编码:CK10C6J6B3Z1 HL7R9O1Z4Z2 ZN7T7X5B8X2文档编码:CK10C6J6B3Z1 HL7R9O1Z4Z2 ZN7T7X5B8X2文档编码:CK10C6J6B3Z1 HL7R9O1Z4Z2 ZN7T7X5B8X2文档编码:CK10C6J6B3Z1 HL7R9O1Z4Z2 ZN7T7X5B8X2文档编码:CK10C6J6B3Z1 HL7R9O1Z4Z2 ZN7T7X5B8X2文档编码:CK10C6J6B3Z

24、1 HL7R9O1Z4Z2 ZN7T7X5B8X2文档编码:CK10C6J6B3Z1 HL7R9O1Z4Z2 ZN7T7X5B8X2文档编码:CK10C6J6B3Z1 HL7R9O1Z4Z2 ZN7T7X5B8X2文档编码:CK10C6J6B3Z1 HL7R9O1Z4Z2 ZN7T7X5B8X2文档编码:CK10C6J6B3Z1 HL7R9O1Z4Z2 ZN7T7X5B8X2文档编码:CK10C6J6B3Z1 HL7R9O1Z4Z2 ZN7T7X5B8X2文档编码:CK10C6J6B3Z1 HL7R9O1Z4Z2 ZN7T7X5B8X2文档编码:CK10C6J6B3Z1 HL7R9O1Z4Z2

25、 ZN7T7X5B8X2文档编码:CK10C6J6B3Z1 HL7R9O1Z4Z2 ZN7T7X5B8X2文档编码:CK10C6J6B3Z1 HL7R9O1Z4Z2 ZN7T7X5B8X2文档编码:CK10C6J6B3Z1 HL7R9O1Z4Z2 ZN7T7X5B8X2文档编码:CK10C6J6B3Z1 HL7R9O1Z4Z2 ZN7T7X5B8X2文档编码:CK10C6J6B3Z1 HL7R9O1Z4Z2 ZN7T7X5B8X2文档编码:CK10C6J6B3Z1 HL7R9O1Z4Z2 ZN7T7X5B8X2文档编码:CK10C6J6B3Z1 HL7R9O1Z4Z2 ZN7T7X5B8X2文

26、档编码:CK10C6J6B3Z1 HL7R9O1Z4Z2 ZN7T7X5B8X2文档编码:CK10C6J6B3Z1 HL7R9O1Z4Z2 ZN7T7X5B8X2文档编码:CK10C6J6B3Z1 HL7R9O1Z4Z2 ZN7T7X5B8X25/7 因此，得函数xf的性态x0,02,02,2xf00 xf1142ae1 若0142ae，即42ea时，函数12xeaxxf在0,、2,0、,2内各有一个零点，即方程2xaex在,内有 3个实根 若0142ae，即42ea时，函数12xeaxxf在0,、,0内各有一个零点，即方程2xaex在,内有 2 个实根 若0142ae，即42ea时，函数12

27、xeaxxf在0,有一个零点，即方程2xaex在,内有 1个实根10 设函数xf可导，且满足1xfxxf，00f试求函数xf的极值解：在方程1xfxxf中令xt，得1tfttf，即1xfxxf在方程组xxfxf xxxf xxf中消去xf，得221xxxxf积分，注意00f，得xdttttfxf02210即xxxdttttxfxarctan1ln2112022文档编码:CK10C6J6B3Z1 HL7R9O1Z4Z2 ZN7T7X5B8X2文档编码:CK10C6J6B3Z1 HL7R9O1Z4Z2 ZN7T7X5B8X2文档编码:CK10C6J6B3Z1 HL7R9O1Z4Z2 ZN7T7X5

28、B8X2文档编码:CK10C6J6B3Z1 HL7R9O1Z4Z2 ZN7T7X5B8X2文档编码:CK10C6J6B3Z1 HL7R9O1Z4Z2 ZN7T7X5B8X2文档编码:CK10C6J6B3Z1 HL7R9O1Z4Z2 ZN7T7X5B8X2文档编码:CK10C6J6B3Z1 HL7R9O1Z4Z2 ZN7T7X5B8X2文档编码:CK10C6J6B3Z1 HL7R9O1Z4Z2 ZN7T7X5B8X2文档编码:CK10C6J6B3Z1 HL7R9O1Z4Z2 ZN7T7X5B8X2文档编码:CK10C6J6B3Z1 HL7R9O1Z4Z2 ZN7T7X5B8X2文档编码:CK10

29、C6J6B3Z1 HL7R9O1Z4Z2 ZN7T7X5B8X2文档编码:CK10C6J6B3Z1 HL7R9O1Z4Z2 ZN7T7X5B8X2文档编码:CK10C6J6B3Z1 HL7R9O1Z4Z2 ZN7T7X5B8X2文档编码:CK10C6J6B3Z1 HL7R9O1Z4Z2 ZN7T7X5B8X2文档编码:CK10C6J6B3Z1 HL7R9O1Z4Z2 ZN7T7X5B8X2文档编码:CK10C6J6B3Z1 HL7R9O1Z4Z2 ZN7T7X5B8X2文档编码:CK10C6J6B3Z1 HL7R9O1Z4Z2 ZN7T7X5B8X2文档编码:CK10C6J6B3Z1 HL7R

30、9O1Z4Z2 ZN7T7X5B8X2文档编码:CK10C6J6B3Z1 HL7R9O1Z4Z2 ZN7T7X5B8X2文档编码:CK10C6J6B3Z1 HL7R9O1Z4Z2 ZN7T7X5B8X2文档编码:CK10C6J6B3Z1 HL7R9O1Z4Z2 ZN7T7X5B8X2文档编码:CK10C6J6B3Z1 HL7R9O1Z4Z2 ZN7T7X5B8X2文档编码:CK10C6J6B3Z1 HL7R9O1Z4Z2 ZN7T7X5B8X2文档编码:CK10C6J6B3Z1 HL7R9O1Z4Z2 ZN7T7X5B8X2文档编码:CK10C6J6B3Z1 HL7R9O1Z4Z2 ZN7T7

31、X5B8X2文档编码:CK10C6J6B3Z1 HL7R9O1Z4Z2 ZN7T7X5B8X2文档编码:CK10C6J6B3Z1 HL7R9O1Z4Z2 ZN7T7X5B8X2文档编码:CK10C6J6B3Z1 HL7R9O1Z4Z2 ZN7T7X5B8X2文档编码:CK10C6J6B3Z1 HL7R9O1Z4Z2 ZN7T7X5B8X2文档编码:CK10C6J6B3Z1 HL7R9O1Z4Z2 ZN7T7X5B8X2文档编码:CK10C6J6B3Z1 HL7R9O1Z4Z2 ZN7T7X5B8X2文档编码:CK10C6J6B3Z1 HL7R9O1Z4Z2 ZN7T7X5B8X2文档编码:CK

32、10C6J6B3Z1 HL7R9O1Z4Z2 ZN7T7X5B8X2文档编码:CK10C6J6B3Z1 HL7R9O1Z4Z2 ZN7T7X5B8X2文档编码:CK10C6J6B3Z1 HL7R9O1Z4Z2 ZN7T7X5B8X2文档编码:CK10C6J6B3Z1 HL7R9O1Z4Z2 ZN7T7X5B8X2文档编码:CK10C6J6B3Z1 HL7R9O1Z4Z2 ZN7T7X5B8X2文档编码:CK10C6J6B3Z1 HL7R9O1Z4Z2 ZN7T7X5B8X2文档编码:CK10C6J6B3Z1 HL7R9O1Z4Z2 ZN7T7X5B8X2文档编码:CK10C6J6B3Z1 HL

33、7R9O1Z4Z2 ZN7T7X5B8X2文档编码:CK10C6J6B3Z1 HL7R9O1Z4Z2 ZN7T7X5B8X2文档编码:CK10C6J6B3Z1 HL7R9O1Z4Z2 ZN7T7X5B8X2文档编码:CK10C6J6B3Z1 HL7R9O1Z4Z2 ZN7T7X5B8X2文档编码:CK10C6J6B3Z1 HL7R9O1Z4Z2 ZN7T7X5B8X2文档编码:CK10C6J6B3Z1 HL7R9O1Z4Z2 ZN7T7X5B8X2文档编码:CK10C6J6B3Z1 HL7R9O1Z4Z2 ZN7T7X5B8X2文档编码:CK10C6J6B3Z1 HL7R9O1Z4Z2 ZN7

34、T7X5B8X2文档编码:CK10C6J6B3Z1 HL7R9O1Z4Z2 ZN7T7X5B8X26/7 由221xxxxf得函数xf的驻点1,021xx而222121xxxxf所以，010f，0211f所以，00f是函数xf极小值；42ln2111f是函数xf极大值三应用题与证明题（本题满分20 分，共有2 道小题，每道小题10 分），11求曲线xy的一条切线，使得该曲线与切线l及直线0 x和2x所围成的图形绕x轴旋转的旋转体的体积为最小解：设切点坐标为tt,，由ty21，可知曲线xy在tt,处的切线方程为txtty21，或txty21因此所求旋转体的体积为ttdxxtxtV24384212

35、022所以，023842tdtdV得驻点32t，舍去32t由于031643223222tttdtVd，因而函数V在32t处达到极小值，而且也是最小值因此所求切线方程为2143xy 12 设函数xf在闭区间10，上连续，在开区间10，内可导，且21arctan20 xdxexf，01f证明：至少存在一点10，使得arctan112f解：文档编码:CK10C6J6B3Z1 HL7R9O1Z4Z2 ZN7T7X5B8X2文档编码:CK10C6J6B3Z1 HL7R9O1Z4Z2 ZN7T7X5B8X2文档编码:CK10C6J6B3Z1 HL7R9O1Z4Z2 ZN7T7X5B8X2文档编码:CK10

36、C6J6B3Z1 HL7R9O1Z4Z2 ZN7T7X5B8X2文档编码:CK10C6J6B3Z1 HL7R9O1Z4Z2 ZN7T7X5B8X2文档编码:CK10C6J6B3Z1 HL7R9O1Z4Z2 ZN7T7X5B8X2文档编码:CK10C6J6B3Z1 HL7R9O1Z4Z2 ZN7T7X5B8X2文档编码:CK10C6J6B3Z1 HL7R9O1Z4Z2 ZN7T7X5B8X2文档编码:CK10C6J6B3Z1 HL7R9O1Z4Z2 ZN7T7X5B8X2文档编码:CK10C6J6B3Z1 HL7R9O1Z4Z2 ZN7T7X5B8X2文档编码:CK10C6J6B3Z1 HL7R

37、9O1Z4Z2 ZN7T7X5B8X2文档编码:CK10C6J6B3Z1 HL7R9O1Z4Z2 ZN7T7X5B8X2文档编码:CK10C6J6B3Z1 HL7R9O1Z4Z2 ZN7T7X5B8X2文档编码:CK10C6J6B3Z1 HL7R9O1Z4Z2 ZN7T7X5B8X2文档编码:CK10C6J6B3Z1 HL7R9O1Z4Z2 ZN7T7X5B8X2文档编码:CK10C6J6B3Z1 HL7R9O1Z4Z2 ZN7T7X5B8X2文档编码:CK10C6J6B3Z1 HL7R9O1Z4Z2 ZN7T7X5B8X2文档编码:CK10C6J6B3Z1 HL7R9O1Z4Z2 ZN7T7

38、X5B8X2文档编码:CK10C6J6B3Z1 HL7R9O1Z4Z2 ZN7T7X5B8X2文档编码:CK10C6J6B3Z1 HL7R9O1Z4Z2 ZN7T7X5B8X2文档编码:CK10C6J6B3Z1 HL7R9O1Z4Z2 ZN7T7X5B8X2文档编码:CK10C6J6B3Z1 HL7R9O1Z4Z2 ZN7T7X5B8X2文档编码:CK10C6J6B3Z1 HL7R9O1Z4Z2 ZN7T7X5B8X2文档编码:CK10C6J6B3Z1 HL7R9O1Z4Z2 ZN7T7X5B8X2文档编码:CK10C6J6B3Z1 HL7R9O1Z4Z2 ZN7T7X5B8X2文档编码:CK

39、10C6J6B3Z1 HL7R9O1Z4Z2 ZN7T7X5B8X2文档编码:CK10C6J6B3Z1 HL7R9O1Z4Z2 ZN7T7X5B8X2文档编码:CK10C6J6B3Z1 HL7R9O1Z4Z2 ZN7T7X5B8X2文档编码:CK10C6J6B3Z1 HL7R9O1Z4Z2 ZN7T7X5B8X2文档编码:CK10C6J6B3Z1 HL7R9O1Z4Z2 ZN7T7X5B8X2文档编码:CK10C6J6B3Z1 HL7R9O1Z4Z2 ZN7T7X5B8X2文档编码:CK10C6J6B3Z1 HL7R9O1Z4Z2 ZN7T7X5B8X2文档编码:CK10C6J6B3Z1 HL

40、7R9O1Z4Z2 ZN7T7X5B8X2文档编码:CK10C6J6B3Z1 HL7R9O1Z4Z2 ZN7T7X5B8X2文档编码:CK10C6J6B3Z1 HL7R9O1Z4Z2 ZN7T7X5B8X2文档编码:CK10C6J6B3Z1 HL7R9O1Z4Z2 ZN7T7X5B8X2文档编码:CK10C6J6B3Z1 HL7R9O1Z4Z2 ZN7T7X5B8X2文档编码:CK10C6J6B3Z1 HL7R9O1Z4Z2 ZN7T7X5B8X2文档编码:CK10C6J6B3Z1 HL7R9O1Z4Z2 ZN7T7X5B8X2文档编码:CK10C6J6B3Z1 HL7R9O1Z4Z2 ZN7

41、T7X5B8X2文档编码:CK10C6J6B3Z1 HL7R9O1Z4Z2 ZN7T7X5B8X2文档编码:CK10C6J6B3Z1 HL7R9O1Z4Z2 ZN7T7X5B8X2文档编码:CK10C6J6B3Z1 HL7R9O1Z4Z2 ZN7T7X5B8X2文档编码:CK10C6J6B3Z1 HL7R9O1Z4Z2 ZN7T7X5B8X2文档编码:CK10C6J6B3Z1 HL7R9O1Z4Z2 ZN7T7X5B8X2文档编码:CK10C6J6B3Z1 HL7R9O1Z4Z2 ZN7T7X5B8X2文档编码:CK10C6J6B3Z1 HL7R9O1Z4Z2 ZN7T7X5B8X2文档编码:

42、CK10C6J6B3Z1 HL7R9O1Z4Z2 ZN7T7X5B8X27/7 因为xf在闭区间1,0上连续，所以由积分中值定理，知存在2,0，使得arctan2arctan20fxfexdxe由于21arctan20 xdxexf，所以，21arctan2fe再由01f，得1arctan4arctan1ffee作函数xexgxfarctan，则函数在区间1,01,上连续，在区间1,内可导所以由Rolle 中值定理，存在1,01,，使得0g而21arctanxexxfexgxfxf所以存在1,01,，使得01arctan2ffefe由于0fe，所以011arctan2f，即arctan112f

43、文档编码:CK10C6J6B3Z1 HL7R9O1Z4Z2 ZN7T7X5B8X2文档编码:CK10C6J6B3Z1 HL7R9O1Z4Z2 ZN7T7X5B8X2文档编码:CK10C6J6B3Z1 HL7R9O1Z4Z2 ZN7T7X5B8X2文档编码:CK10C6J6B3Z1 HL7R9O1Z4Z2 ZN7T7X5B8X2文档编码:CK10C6J6B3Z1 HL7R9O1Z4Z2 ZN7T7X5B8X2文档编码:CK10C6J6B3Z1 HL7R9O1Z4Z2 ZN7T7X5B8X2文档编码:CK10C6J6B3Z1 HL7R9O1Z4Z2 ZN7T7X5B8X2文档编码:CK10C6J6

44、B3Z1 HL7R9O1Z4Z2 ZN7T7X5B8X2文档编码:CK10C6J6B3Z1 HL7R9O1Z4Z2 ZN7T7X5B8X2文档编码:CK10C6J6B3Z1 HL7R9O1Z4Z2 ZN7T7X5B8X2文档编码:CK10C6J6B3Z1 HL7R9O1Z4Z2 ZN7T7X5B8X2文档编码:CK10C6J6B3Z1 HL7R9O1Z4Z2 ZN7T7X5B8X2文档编码:CK10C6J6B3Z1 HL7R9O1Z4Z2 ZN7T7X5B8X2文档编码:CK10C6J6B3Z1 HL7R9O1Z4Z2 ZN7T7X5B8X2文档编码:CK10C6J6B3Z1 HL7R9O1Z

45、4Z2 ZN7T7X5B8X2文档编码:CK10C6J6B3Z1 HL7R9O1Z4Z2 ZN7T7X5B8X2文档编码:CK10C6J6B3Z1 HL7R9O1Z4Z2 ZN7T7X5B8X2文档编码:CK10C6J6B3Z1 HL7R9O1Z4Z2 ZN7T7X5B8X2文档编码:CK10C6J6B3Z1 HL7R9O1Z4Z2 ZN7T7X5B8X2文档编码:CK10C6J6B3Z1 HL7R9O1Z4Z2 ZN7T7X5B8X2文档编码:CK10C6J6B3Z1 HL7R9O1Z4Z2 ZN7T7X5B8X2文档编码:CK10C6J6B3Z1 HL7R9O1Z4Z2 ZN7T7X5B8

46、X2文档编码:CK10C6J6B3Z1 HL7R9O1Z4Z2 ZN7T7X5B8X2文档编码:CK10C6J6B3Z1 HL7R9O1Z4Z2 ZN7T7X5B8X2文档编码:CK10C6J6B3Z1 HL7R9O1Z4Z2 ZN7T7X5B8X2文档编码:CK10C6J6B3Z1 HL7R9O1Z4Z2 ZN7T7X5B8X2文档编码:CK10C6J6B3Z1 HL7R9O1Z4Z2 ZN7T7X5B8X2文档编码:CK10C6J6B3Z1 HL7R9O1Z4Z2 ZN7T7X5B8X2文档编码:CK10C6J6B3Z1 HL7R9O1Z4Z2 ZN7T7X5B8X2文档编码:CK10C6

47、J6B3Z1 HL7R9O1Z4Z2 ZN7T7X5B8X2文档编码:CK10C6J6B3Z1 HL7R9O1Z4Z2 ZN7T7X5B8X2文档编码:CK10C6J6B3Z1 HL7R9O1Z4Z2 ZN7T7X5B8X2文档编码:CK10C6J6B3Z1 HL7R9O1Z4Z2 ZN7T7X5B8X2文档编码:CK10C6J6B3Z1 HL7R9O1Z4Z2 ZN7T7X5B8X2文档编码:CK10C6J6B3Z1 HL7R9O1Z4Z2 ZN7T7X5B8X2文档编码:CK10C6J6B3Z1 HL7R9O1Z4Z2 ZN7T7X5B8X2文档编码:CK10C6J6B3Z1 HL7R9O

48、1Z4Z2 ZN7T7X5B8X2文档编码:CK10C6J6B3Z1 HL7R9O1Z4Z2 ZN7T7X5B8X2文档编码:CK10C6J6B3Z1 HL7R9O1Z4Z2 ZN7T7X5B8X2文档编码:CK10C6J6B3Z1 HL7R9O1Z4Z2 ZN7T7X5B8X2文档编码:CK10C6J6B3Z1 HL7R9O1Z4Z2 ZN7T7X5B8X2文档编码:CK10C6J6B3Z1 HL7R9O1Z4Z2 ZN7T7X5B8X2文档编码:CK10C6J6B3Z1 HL7R9O1Z4Z2 ZN7T7X5B8X2文档编码:CK10C6J6B3Z1 HL7R9O1Z4Z2 ZN7T7X5B8X2文档编码:CK10C6J6B3Z1 HL7R9O1Z4Z2 ZN7T7X5B8X2文档编码:CK10C6J6B3Z1 HL7R9O1Z4Z2 ZN7T7X5B8X2文档编码:CK10C6J6B3Z1 HL7R9O1Z4Z2 ZN7T7X5B8X2文档编码:CK10C6J6B3Z1 HL7R9O1Z4Z2 ZN7T7X5B8X2