1997考研数二真题及解析说课讲解.pdf

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1、此文档仅供收集于网络，如有侵权请联系网站删除只供学习与交流1997 年全国硕士研究生入学统一考试数学二试题一、填空题(本题共 5 分,每小题 3 分,满分 15 分.把答案填在题中横线上.)(1)已知2(cos),0,(),0 xxxf xax在0 x处连续,则a .(2)设21ln1xyx,则0 xy .(3)(4)dxxx .(4)2048dxxx .(5)已知向量组123(1,2,1,1),(2,0,0),(0,4,5,2)t的秩为 2,则t .二、选择题(本题共 5 小题,每小题3 分,满分 15 分.每小题给出的四个选项中,只有一项符合题目要求,把所选项前的字母填在题后的括号内)(1

2、)设0 x时,tan xxee与nx是同阶无穷小,则n为 ()(A)1 (B)2 (C)3 (D)4(2)设在区间,a b上()0,()0,()0,f xfxfx记12(),()()baSf x dx Sf b ba,31()()()2Sf af bba,则 ()(A)123SSS (B)231SSS(C)312SSS (D)213SSS(3)已知函数()yf x对一切x满足2()3()1xxfxx fxe,若00()0(0),fxx则 ()(A)0()f x是()f x的极大值(B)0()f x是()f x的极小值(C)00(,()xfx是曲线()yf x的拐点(D)0()f x不是()f

3、x的极值,00(,()xf x也不是曲线()yf x的拐点(4)2sin()sin,xtxF xetdt设则()F x ()此文档仅供收集于网络，如有侵权请联系网站删除只供学习与交流(A)为正常数 (B)为负常数(C)恒为零 (D)不为常数(5)设22,0,0(),(),()2,0,0 xxxxg xf xg f xxxxx则为 ()(A)22,02,0 xxxx (B)22,02,0 xxxx(C)22,02,0 xxxx (D)22,02,0 xxxx三、(本题共 6 小题,每小题 5 分,满分 30 分.)(1)求极限22411limsinxxxxxx.(2)设()yy x由2arcta

4、n25txtytye所确定,求dydx.(3)计算22(tan1)xexdx.(4)求微分方程222(32)(2)0 xxyydxxxy dy的通解.(5)已知22123,xxxxxxxyxeeyxeeyxeee是某二阶线性非齐次微分方程的三个解,求此微分方程.(6)已知111011001A,且2AABE,其中E是三阶单位矩阵,求矩阵B.四、(本题满分8 分.)取何值时,方程组1231231232124551xxxxxxxxx无解,有惟一解或有无穷多解？并在有无穷多解时写出方程组的通解.五、(本题满分8 分)设曲线L的极坐标方程为()rr,(,)M r为L上任一点,0(2,0)M为L上一定点,

5、若极径0OMOM、与曲线L所围成的曲边扇形面积值等于L上0,MM两点间弧长值的一半,求曲线L的方程.文档编码:CW9T7L1D2N1 HW4D7Y3P6O7 ZG2R8F2W10E9文档编码:CW9T7L1D2N1 HW4D7Y3P6O7 ZG2R8F2W10E9文档编码:CW9T7L1D2N1 HW4D7Y3P6O7 ZG2R8F2W10E9文档编码:CW9T7L1D2N1 HW4D7Y3P6O7 ZG2R8F2W10E9文档编码:CW9T7L1D2N1 HW4D7Y3P6O7 ZG2R8F2W10E9文档编码:CW9T7L1D2N1 HW4D7Y3P6O7 ZG2R8F2W10E9文档编码

6、:CW9T7L1D2N1 HW4D7Y3P6O7 ZG2R8F2W10E9文档编码:CW9T7L1D2N1 HW4D7Y3P6O7 ZG2R8F2W10E9文档编码:CW9T7L1D2N1 HW4D7Y3P6O7 ZG2R8F2W10E9文档编码:CW9T7L1D2N1 HW4D7Y3P6O7 ZG2R8F2W10E9文档编码:CW9T7L1D2N1 HW4D7Y3P6O7 ZG2R8F2W10E9文档编码:CW9T7L1D2N1 HW4D7Y3P6O7 ZG2R8F2W10E9文档编码:CW9T7L1D2N1 HW4D7Y3P6O7 ZG2R8F2W10E9文档编码:CW9T7L1D2N1

7、HW4D7Y3P6O7 ZG2R8F2W10E9文档编码:CW9T7L1D2N1 HW4D7Y3P6O7 ZG2R8F2W10E9文档编码:CW9T7L1D2N1 HW4D7Y3P6O7 ZG2R8F2W10E9文档编码:CW9T7L1D2N1 HW4D7Y3P6O7 ZG2R8F2W10E9文档编码:CW9T7L1D2N1 HW4D7Y3P6O7 ZG2R8F2W10E9文档编码:CW9T7L1D2N1 HW4D7Y3P6O7 ZG2R8F2W10E9文档编码:CW9T7L1D2N1 HW4D7Y3P6O7 ZG2R8F2W10E9文档编码:CW9T7L1D2N1 HW4D7Y3P6O7 Z

8、G2R8F2W10E9文档编码:CW9T7L1D2N1 HW4D7Y3P6O7 ZG2R8F2W10E9文档编码:CW9T7L1D2N1 HW4D7Y3P6O7 ZG2R8F2W10E9文档编码:CW9T7L1D2N1 HW4D7Y3P6O7 ZG2R8F2W10E9文档编码:CW9T7L1D2N1 HW4D7Y3P6O7 ZG2R8F2W10E9文档编码:CW9T7L1D2N1 HW4D7Y3P6O7 ZG2R8F2W10E9文档编码:CW9T7L1D2N1 HW4D7Y3P6O7 ZG2R8F2W10E9文档编码:CW9T7L1D2N1 HW4D7Y3P6O7 ZG2R8F2W10E9文档

9、编码:CW9T7L1D2N1 HW4D7Y3P6O7 ZG2R8F2W10E9文档编码:CW9T7L1D2N1 HW4D7Y3P6O7 ZG2R8F2W10E9文档编码:CW9T7L1D2N1 HW4D7Y3P6O7 ZG2R8F2W10E9文档编码:CW9T7L1D2N1 HW4D7Y3P6O7 ZG2R8F2W10E9文档编码:CW9T7L1D2N1 HW4D7Y3P6O7 ZG2R8F2W10E9文档编码:CW9T7L1D2N1 HW4D7Y3P6O7 ZG2R8F2W10E9文档编码:CW9T7L1D2N1 HW4D7Y3P6O7 ZG2R8F2W10E9文档编码:CW9T7L1D2N

10、1 HW4D7Y3P6O7 ZG2R8F2W10E9文档编码:CW9T7L1D2N1 HW4D7Y3P6O7 ZG2R8F2W10E9文档编码:CW9T7L1D2N1 HW4D7Y3P6O7 ZG2R8F2W10E9文档编码:CW9T7L1D2N1 HW4D7Y3P6O7 ZG2R8F2W10E9文档编码:CW9T7L1D2N1 HW4D7Y3P6O7 ZG2R8F2W10E9文档编码:CW9T7L1D2N1 HW4D7Y3P6O7 ZG2R8F2W10E9文档编码:CW9T7L1D2N1 HW4D7Y3P6O7 ZG2R8F2W10E9文档编码:CW9T7L1D2N1 HW4D7Y3P6O7

11、 ZG2R8F2W10E9文档编码:CW9T7L1D2N1 HW4D7Y3P6O7 ZG2R8F2W10E9文档编码:CW9T7L1D2N1 HW4D7Y3P6O7 ZG2R8F2W10E9文档编码:CW9T7L1D2N1 HW4D7Y3P6O7 ZG2R8F2W10E9文档编码:CW9T7L1D2N1 HW4D7Y3P6O7 ZG2R8F2W10E9文档编码:CW9T7L1D2N1 HW4D7Y3P6O7 ZG2R8F2W10E9此文档仅供收集于网络，如有侵权请联系网站删除只供学习与交流六、(本题满分8 分)设函数()fx在闭区间0,1上连续,在开区间(0,1)内大于零,并满足()()xfx

12、f x232ax(a为常数),又曲线()yf x与1,0 xy所围成的图形S的面积值为2,求函数()yf x,并问a为何值时,图形S绕x轴旋转一周所得的旋转体的体积最小.七、(本题满分8 分.)已知函数()f x连续,且0()lim2xf xx,设10()()xfxt dt,求()x,并讨论()x的连续性.八、(本题满分8 分)就k的不同取值情况,确定方程sin2xxk在开区间(0,)2内根的个数,并证明你的结论.文档编码:CW9T7L1D2N1 HW4D7Y3P6O7 ZG2R8F2W10E9文档编码:CW9T7L1D2N1 HW4D7Y3P6O7 ZG2R8F2W10E9文档编码:CW9T

13、7L1D2N1 HW4D7Y3P6O7 ZG2R8F2W10E9文档编码:CW9T7L1D2N1 HW4D7Y3P6O7 ZG2R8F2W10E9文档编码:CW9T7L1D2N1 HW4D7Y3P6O7 ZG2R8F2W10E9文档编码:CW9T7L1D2N1 HW4D7Y3P6O7 ZG2R8F2W10E9文档编码:CW9T7L1D2N1 HW4D7Y3P6O7 ZG2R8F2W10E9文档编码:CW9T7L1D2N1 HW4D7Y3P6O7 ZG2R8F2W10E9文档编码:CW9T7L1D2N1 HW4D7Y3P6O7 ZG2R8F2W10E9文档编码:CW9T7L1D2N1 HW4D7

14、Y3P6O7 ZG2R8F2W10E9文档编码:CW9T7L1D2N1 HW4D7Y3P6O7 ZG2R8F2W10E9文档编码:CW9T7L1D2N1 HW4D7Y3P6O7 ZG2R8F2W10E9文档编码:CW9T7L1D2N1 HW4D7Y3P6O7 ZG2R8F2W10E9文档编码:CW9T7L1D2N1 HW4D7Y3P6O7 ZG2R8F2W10E9文档编码:CW9T7L1D2N1 HW4D7Y3P6O7 ZG2R8F2W10E9文档编码:CW9T7L1D2N1 HW4D7Y3P6O7 ZG2R8F2W10E9文档编码:CW9T7L1D2N1 HW4D7Y3P6O7 ZG2R8F

15、2W10E9文档编码:CW9T7L1D2N1 HW4D7Y3P6O7 ZG2R8F2W10E9文档编码:CW9T7L1D2N1 HW4D7Y3P6O7 ZG2R8F2W10E9文档编码:CW9T7L1D2N1 HW4D7Y3P6O7 ZG2R8F2W10E9文档编码:CW9T7L1D2N1 HW4D7Y3P6O7 ZG2R8F2W10E9文档编码:CW9T7L1D2N1 HW4D7Y3P6O7 ZG2R8F2W10E9文档编码:CW9T7L1D2N1 HW4D7Y3P6O7 ZG2R8F2W10E9文档编码:CW9T7L1D2N1 HW4D7Y3P6O7 ZG2R8F2W10E9文档编码:CW

16、9T7L1D2N1 HW4D7Y3P6O7 ZG2R8F2W10E9文档编码:CW9T7L1D2N1 HW4D7Y3P6O7 ZG2R8F2W10E9文档编码:CW9T7L1D2N1 HW4D7Y3P6O7 ZG2R8F2W10E9文档编码:CW9T7L1D2N1 HW4D7Y3P6O7 ZG2R8F2W10E9文档编码:CW9T7L1D2N1 HW4D7Y3P6O7 ZG2R8F2W10E9文档编码:CW9T7L1D2N1 HW4D7Y3P6O7 ZG2R8F2W10E9文档编码:CW9T7L1D2N1 HW4D7Y3P6O7 ZG2R8F2W10E9文档编码:CW9T7L1D2N1 HW4

17、D7Y3P6O7 ZG2R8F2W10E9文档编码:CW9T7L1D2N1 HW4D7Y3P6O7 ZG2R8F2W10E9文档编码:CW9T7L1D2N1 HW4D7Y3P6O7 ZG2R8F2W10E9文档编码:CW9T7L1D2N1 HW4D7Y3P6O7 ZG2R8F2W10E9文档编码:CW9T7L1D2N1 HW4D7Y3P6O7 ZG2R8F2W10E9文档编码:CW9T7L1D2N1 HW4D7Y3P6O7 ZG2R8F2W10E9文档编码:CW9T7L1D2N1 HW4D7Y3P6O7 ZG2R8F2W10E9文档编码:CW9T7L1D2N1 HW4D7Y3P6O7 ZG2R

18、8F2W10E9文档编码:CW9T7L1D2N1 HW4D7Y3P6O7 ZG2R8F2W10E9文档编码:CW9T7L1D2N1 HW4D7Y3P6O7 ZG2R8F2W10E9文档编码:CW9T7L1D2N1 HW4D7Y3P6O7 ZG2R8F2W10E9文档编码:CW9T7L1D2N1 HW4D7Y3P6O7 ZG2R8F2W10E9文档编码:CW9T7L1D2N1 HW4D7Y3P6O7 ZG2R8F2W10E9文档编码:CW9T7L1D2N1 HW4D7Y3P6O7 ZG2R8F2W10E9文档编码:CW9T7L1D2N1 HW4D7Y3P6O7 ZG2R8F2W10E9文档编码:

19、CW9T7L1D2N1 HW4D7Y3P6O7 ZG2R8F2W10E9文档编码:CW9T7L1D2N1 HW4D7Y3P6O7 ZG2R8F2W10E9此文档仅供收集于网络，如有侵权请联系网站删除只供学习与交流1997 年全国硕士研究生入学统一考试数学二试题解析一、填空题(本题共 5 分,每小题 3 分,满分 15 分.把答案在题中横线上.)(1)【答案】12e【解析】由于()f x在0 x处连续,故22ln()ln(cos)ln cos0000(0)lim()limlimlimxfxxxxxxxxffxeee22001(sin)ln cosln coscoslimlim20limxxxxx

20、xxxxxeee洛必达0sin1lim2 cos2xxxxee【相关知识点】1.函数()yf x在点0 x连续：设函数()f x在点0 x的某一邻域内有定义,如果00lim()(),xxf xf x则称函数()f x在点0 x连续.2.如果函数在0 x处连续,则有000lim()lim()()xxxxf xf xf x.(2)【答案】32【解析】题目考察复合函数在某点处的高阶导数,按照复合函数求导法则具体计算如下：21ln(1)ln(1)2yxx,221121()2 112(1)1xxyxxxx,2222112(1)(1)xyxx,032xy.【相关知识点】1.复合函数求导法则：如果()ug

21、x在点x可导,而()yf x在点()ug x可导,则复合函数()yfg x在点x可导,且其导数为()()dyfug xdx或dydy dudxdu dx.(3)【答案】2arcsin2xC或2arcsin2xC【解析】题目考察不定积分的计算,分别采用凑微分的方法计算如下：方法 1：原式222()22arcsin224(2)1()2xddxxCxx=.文档编码:CW9T7L1D2N1 HW4D7Y3P6O7 ZG2R8F2W10E9文档编码:CW9T7L1D2N1 HW4D7Y3P6O7 ZG2R8F2W10E9文档编码:CW9T7L1D2N1 HW4D7Y3P6O7 ZG2R8F2W10E9文

22、档编码:CW9T7L1D2N1 HW4D7Y3P6O7 ZG2R8F2W10E9文档编码:CW9T7L1D2N1 HW4D7Y3P6O7 ZG2R8F2W10E9文档编码:CW9T7L1D2N1 HW4D7Y3P6O7 ZG2R8F2W10E9文档编码:CW9T7L1D2N1 HW4D7Y3P6O7 ZG2R8F2W10E9文档编码:CW9T7L1D2N1 HW4D7Y3P6O7 ZG2R8F2W10E9文档编码:CW9T7L1D2N1 HW4D7Y3P6O7 ZG2R8F2W10E9文档编码:CW9T7L1D2N1 HW4D7Y3P6O7 ZG2R8F2W10E9文档编码:CW9T7L1D2

23、N1 HW4D7Y3P6O7 ZG2R8F2W10E9文档编码:CW9T7L1D2N1 HW4D7Y3P6O7 ZG2R8F2W10E9文档编码:CW9T7L1D2N1 HW4D7Y3P6O7 ZG2R8F2W10E9文档编码:CW9T7L1D2N1 HW4D7Y3P6O7 ZG2R8F2W10E9文档编码:CW9T7L1D2N1 HW4D7Y3P6O7 ZG2R8F2W10E9文档编码:CW9T7L1D2N1 HW4D7Y3P6O7 ZG2R8F2W10E9文档编码:CW9T7L1D2N1 HW4D7Y3P6O7 ZG2R8F2W10E9文档编码:CW9T7L1D2N1 HW4D7Y3P6O

24、7 ZG2R8F2W10E9文档编码:CW9T7L1D2N1 HW4D7Y3P6O7 ZG2R8F2W10E9文档编码:CW9T7L1D2N1 HW4D7Y3P6O7 ZG2R8F2W10E9文档编码:CW9T7L1D2N1 HW4D7Y3P6O7 ZG2R8F2W10E9文档编码:CW9T7L1D2N1 HW4D7Y3P6O7 ZG2R8F2W10E9文档编码:CW9T7L1D2N1 HW4D7Y3P6O7 ZG2R8F2W10E9文档编码:CW9T7L1D2N1 HW4D7Y3P6O7 ZG2R8F2W10E9文档编码:CW9T7L1D2N1 HW4D7Y3P6O7 ZG2R8F2W10E

25、9文档编码:CW9T7L1D2N1 HW4D7Y3P6O7 ZG2R8F2W10E9文档编码:CW9T7L1D2N1 HW4D7Y3P6O7 ZG2R8F2W10E9文档编码:CW9T7L1D2N1 HW4D7Y3P6O7 ZG2R8F2W10E9文档编码:CW9T7L1D2N1 HW4D7Y3P6O7 ZG2R8F2W10E9文档编码:CW9T7L1D2N1 HW4D7Y3P6O7 ZG2R8F2W10E9文档编码:CW9T7L1D2N1 HW4D7Y3P6O7 ZG2R8F2W10E9文档编码:CW9T7L1D2N1 HW4D7Y3P6O7 ZG2R8F2W10E9文档编码:CW9T7L1

26、D2N1 HW4D7Y3P6O7 ZG2R8F2W10E9文档编码:CW9T7L1D2N1 HW4D7Y3P6O7 ZG2R8F2W10E9文档编码:CW9T7L1D2N1 HW4D7Y3P6O7 ZG2R8F2W10E9文档编码:CW9T7L1D2N1 HW4D7Y3P6O7 ZG2R8F2W10E9文档编码:CW9T7L1D2N1 HW4D7Y3P6O7 ZG2R8F2W10E9文档编码:CW9T7L1D2N1 HW4D7Y3P6O7 ZG2R8F2W10E9文档编码:CW9T7L1D2N1 HW4D7Y3P6O7 ZG2R8F2W10E9文档编码:CW9T7L1D2N1 HW4D7Y3P

27、6O7 ZG2R8F2W10E9文档编码:CW9T7L1D2N1 HW4D7Y3P6O7 ZG2R8F2W10E9文档编码:CW9T7L1D2N1 HW4D7Y3P6O7 ZG2R8F2W10E9文档编码:CW9T7L1D2N1 HW4D7Y3P6O7 ZG2R8F2W10E9文档编码:CW9T7L1D2N1 HW4D7Y3P6O7 ZG2R8F2W10E9文档编码:CW9T7L1D2N1 HW4D7Y3P6O7 ZG2R8F2W10E9文档编码:CW9T7L1D2N1 HW4D7Y3P6O7 ZG2R8F2W10E9文档编码:CW9T7L1D2N1 HW4D7Y3P6O7 ZG2R8F2W1

28、0E9文档编码:CW9T7L1D2N1 HW4D7Y3P6O7 ZG2R8F2W10E9此文档仅供收集于网络，如有侵权请联系网站删除只供学习与交流方法 2：原式2224()4()dxdxxxx2222arcsin21()2xdxCx.(4)【答案】8【解析】题目考察广义积分的计算,采用凑微分的方法,结合基本微分公式表计算如下：原式20022()1224(2)21()2xddxxx0121arctan()222 248x.(5)【答案】3【解析】方法 1：利用初等变换.以123,为行构成3 4矩阵,对其作初等变换：12122332112111211200042204520452121104220

29、030Attt,t因为1232rAr,所以303t,t.方法 2：利用秩的定义.由于1232rrA,则矩阵A中任一三阶子行列式应等于零.12312112000452t,应有121121121200420420045045003tttt,解得3t.文档编码:CW9T7L1D2N1 HW4D7Y3P6O7 ZG2R8F2W10E9文档编码:CW9T7L1D2N1 HW4D7Y3P6O7 ZG2R8F2W10E9文档编码:CW9T7L1D2N1 HW4D7Y3P6O7 ZG2R8F2W10E9文档编码:CW9T7L1D2N1 HW4D7Y3P6O7 ZG2R8F2W10E9文档编码:CW9T7L1D

30、2N1 HW4D7Y3P6O7 ZG2R8F2W10E9文档编码:CW9T7L1D2N1 HW4D7Y3P6O7 ZG2R8F2W10E9文档编码:CW9T7L1D2N1 HW4D7Y3P6O7 ZG2R8F2W10E9文档编码:CW9T7L1D2N1 HW4D7Y3P6O7 ZG2R8F2W10E9文档编码:CW9T7L1D2N1 HW4D7Y3P6O7 ZG2R8F2W10E9文档编码:CW9T7L1D2N1 HW4D7Y3P6O7 ZG2R8F2W10E9文档编码:CW9T7L1D2N1 HW4D7Y3P6O7 ZG2R8F2W10E9文档编码:CW9T7L1D2N1 HW4D7Y3P6

31、O7 ZG2R8F2W10E9文档编码:CW9T7L1D2N1 HW4D7Y3P6O7 ZG2R8F2W10E9文档编码:CW9T7L1D2N1 HW4D7Y3P6O7 ZG2R8F2W10E9文档编码:CW9T7L1D2N1 HW4D7Y3P6O7 ZG2R8F2W10E9文档编码:CW9T7L1D2N1 HW4D7Y3P6O7 ZG2R8F2W10E9文档编码:CW9T7L1D2N1 HW4D7Y3P6O7 ZG2R8F2W10E9文档编码:CW9T7L1D2N1 HW4D7Y3P6O7 ZG2R8F2W10E9文档编码:CW9T7L1D2N1 HW4D7Y3P6O7 ZG2R8F2W10

32、E9文档编码:CW9T7L1D2N1 HW4D7Y3P6O7 ZG2R8F2W10E9文档编码:CW9T7L1D2N1 HW4D7Y3P6O7 ZG2R8F2W10E9文档编码:CW9T7L1D2N1 HW4D7Y3P6O7 ZG2R8F2W10E9文档编码:CW9T7L1D2N1 HW4D7Y3P6O7 ZG2R8F2W10E9文档编码:CW9T7L1D2N1 HW4D7Y3P6O7 ZG2R8F2W10E9文档编码:CW9T7L1D2N1 HW4D7Y3P6O7 ZG2R8F2W10E9文档编码:CW9T7L1D2N1 HW4D7Y3P6O7 ZG2R8F2W10E9文档编码:CW9T7L

33、1D2N1 HW4D7Y3P6O7 ZG2R8F2W10E9文档编码:CW9T7L1D2N1 HW4D7Y3P6O7 ZG2R8F2W10E9文档编码:CW9T7L1D2N1 HW4D7Y3P6O7 ZG2R8F2W10E9文档编码:CW9T7L1D2N1 HW4D7Y3P6O7 ZG2R8F2W10E9文档编码:CW9T7L1D2N1 HW4D7Y3P6O7 ZG2R8F2W10E9文档编码:CW9T7L1D2N1 HW4D7Y3P6O7 ZG2R8F2W10E9文档编码:CW9T7L1D2N1 HW4D7Y3P6O7 ZG2R8F2W10E9文档编码:CW9T7L1D2N1 HW4D7Y3

34、P6O7 ZG2R8F2W10E9文档编码:CW9T7L1D2N1 HW4D7Y3P6O7 ZG2R8F2W10E9文档编码:CW9T7L1D2N1 HW4D7Y3P6O7 ZG2R8F2W10E9文档编码:CW9T7L1D2N1 HW4D7Y3P6O7 ZG2R8F2W10E9文档编码:CW9T7L1D2N1 HW4D7Y3P6O7 ZG2R8F2W10E9文档编码:CW9T7L1D2N1 HW4D7Y3P6O7 ZG2R8F2W10E9文档编码:CW9T7L1D2N1 HW4D7Y3P6O7 ZG2R8F2W10E9文档编码:CW9T7L1D2N1 HW4D7Y3P6O7 ZG2R8F2W

35、10E9文档编码:CW9T7L1D2N1 HW4D7Y3P6O7 ZG2R8F2W10E9文档编码:CW9T7L1D2N1 HW4D7Y3P6O7 ZG2R8F2W10E9文档编码:CW9T7L1D2N1 HW4D7Y3P6O7 ZG2R8F2W10E9文档编码:CW9T7L1D2N1 HW4D7Y3P6O7 ZG2R8F2W10E9文档编码:CW9T7L1D2N1 HW4D7Y3P6O7 ZG2R8F2W10E9文档编码:CW9T7L1D2N1 HW4D7Y3P6O7 ZG2R8F2W10E9文档编码:CW9T7L1D2N1 HW4D7Y3P6O7 ZG2R8F2W10E9此文档仅供收集于网

36、络，如有侵权请联系网站删除只供学习与交流C a b E D x y O A B 方法 3：利用线性相关性.因为1232r,r A,故123,线性相关,以123TTT,组成的线性齐次方程组1122330TTTxxxBX有非零解,因1231221243132241142212020415102120120044011025003022000TTTtB,t,tt故0BX有非零解3t.二、选择题(本题共 5 小题,每小题3 分,满分 15 分.每小题给出的四个选项中,只有一项符合题目要求,把所选项前的字母填在题后的括号内)(1)【答案】(C)【解析】题目考察无穷小量的性质和无穷小量的比较,采用洛必达法

37、则计算如下：tantan00222311200001limlimtansec1tan1limlimlimlim,33xxxxxnnxxnnnnxxxxeeeexxxxxxxnxnxx洛必达tan xxee与3x同阶,故应选(C).(2)【答案】(D)【解析】方法1：用几何意义.由()0,()0,()0f xfxfx可知,曲线()yf x是上半平面的一段下降的凹弧,()yf x的图形大致如右图.1()baSf x dx是曲边梯形ABCD的面积；2()()Sf b ba是矩形ABCE的面积；31()()()2Sf af bba是梯形ABCD的面积.由图可见213SSS,应选(D).方法2：观察法.

38、因为是要选择对任何满足条件的()f x都成立的结果,故可以取满足条件的特定的()f x来观察结果是什么.例如取21(),1,2f xxx,则2123213211115,248SdxSSSSSx.文档编码:CW9T7L1D2N1 HW4D7Y3P6O7 ZG2R8F2W10E9文档编码:CW9T7L1D2N1 HW4D7Y3P6O7 ZG2R8F2W10E9文档编码:CW9T7L1D2N1 HW4D7Y3P6O7 ZG2R8F2W10E9文档编码:CW9T7L1D2N1 HW4D7Y3P6O7 ZG2R8F2W10E9文档编码:CW9T7L1D2N1 HW4D7Y3P6O7 ZG2R8F2W10

39、E9文档编码:CW9T7L1D2N1 HW4D7Y3P6O7 ZG2R8F2W10E9文档编码:CW9T7L1D2N1 HW4D7Y3P6O7 ZG2R8F2W10E9文档编码:CW9T7L1D2N1 HW4D7Y3P6O7 ZG2R8F2W10E9文档编码:CW9T7L1D2N1 HW4D7Y3P6O7 ZG2R8F2W10E9文档编码:CW9T7L1D2N1 HW4D7Y3P6O7 ZG2R8F2W10E9文档编码:CW9T7L1D2N1 HW4D7Y3P6O7 ZG2R8F2W10E9文档编码:CW9T7L1D2N1 HW4D7Y3P6O7 ZG2R8F2W10E9文档编码:CW9T7L

40、1D2N1 HW4D7Y3P6O7 ZG2R8F2W10E9文档编码:CW9T7L1D2N1 HW4D7Y3P6O7 ZG2R8F2W10E9文档编码:CW9T7L1D2N1 HW4D7Y3P6O7 ZG2R8F2W10E9文档编码:CW9T7L1D2N1 HW4D7Y3P6O7 ZG2R8F2W10E9文档编码:CW9T7L1D2N1 HW4D7Y3P6O7 ZG2R8F2W10E9文档编码:CW9T7L1D2N1 HW4D7Y3P6O7 ZG2R8F2W10E9文档编码:CW9T7L1D2N1 HW4D7Y3P6O7 ZG2R8F2W10E9文档编码:CW9T7L1D2N1 HW4D7Y3

41、P6O7 ZG2R8F2W10E9文档编码:CW9T7L1D2N1 HW4D7Y3P6O7 ZG2R8F2W10E9文档编码:CW9T7L1D2N1 HW4D7Y3P6O7 ZG2R8F2W10E9文档编码:CW9T7L1D2N1 HW4D7Y3P6O7 ZG2R8F2W10E9文档编码:CW9T7L1D2N1 HW4D7Y3P6O7 ZG2R8F2W10E9文档编码:CW9T7L1D2N1 HW4D7Y3P6O7 ZG2R8F2W10E9文档编码:CW9T7L1D2N1 HW4D7Y3P6O7 ZG2R8F2W10E9文档编码:CW9T7L1D2N1 HW4D7Y3P6O7 ZG2R8F2W

42、10E9文档编码:CW9T7L1D2N1 HW4D7Y3P6O7 ZG2R8F2W10E9文档编码:CW9T7L1D2N1 HW4D7Y3P6O7 ZG2R8F2W10E9文档编码:CW9T7L1D2N1 HW4D7Y3P6O7 ZG2R8F2W10E9文档编码:CW9T7L1D2N1 HW4D7Y3P6O7 ZG2R8F2W10E9文档编码:CW9T7L1D2N1 HW4D7Y3P6O7 ZG2R8F2W10E9文档编码:CW9T7L1D2N1 HW4D7Y3P6O7 ZG2R8F2W10E9文档编码:CW9T7L1D2N1 HW4D7Y3P6O7 ZG2R8F2W10E9文档编码:CW9T

43、7L1D2N1 HW4D7Y3P6O7 ZG2R8F2W10E9文档编码:CW9T7L1D2N1 HW4D7Y3P6O7 ZG2R8F2W10E9文档编码:CW9T7L1D2N1 HW4D7Y3P6O7 ZG2R8F2W10E9文档编码:CW9T7L1D2N1 HW4D7Y3P6O7 ZG2R8F2W10E9文档编码:CW9T7L1D2N1 HW4D7Y3P6O7 ZG2R8F2W10E9文档编码:CW9T7L1D2N1 HW4D7Y3P6O7 ZG2R8F2W10E9文档编码:CW9T7L1D2N1 HW4D7Y3P6O7 ZG2R8F2W10E9文档编码:CW9T7L1D2N1 HW4D7

44、Y3P6O7 ZG2R8F2W10E9文档编码:CW9T7L1D2N1 HW4D7Y3P6O7 ZG2R8F2W10E9文档编码:CW9T7L1D2N1 HW4D7Y3P6O7 ZG2R8F2W10E9文档编码:CW9T7L1D2N1 HW4D7Y3P6O7 ZG2R8F2W10E9文档编码:CW9T7L1D2N1 HW4D7Y3P6O7 ZG2R8F2W10E9文档编码:CW9T7L1D2N1 HW4D7Y3P6O7 ZG2R8F2W10E9文档编码:CW9T7L1D2N1 HW4D7Y3P6O7 ZG2R8F2W10E9此文档仅供收集于网络，如有侵权请联系网站删除只供学习与交流【评注】本题

45、也可用分析方法证明如下：由积分中值定理,至少存在一个点,使()()(),baf x dxfba ab成立,再由()0,fx所以()f x是单调递减的,故()(),ff b从而12()()()()()baSf x dxfbaf b baS.为证31SS,令1()()()()(),2xaxf xf axaf t dt则()0,a11()()()()()()2211()()()()2211()()()()()()221()()(),2xfxxaf xf af xfxxafxf afxxafxaaxfxfxa拉格朗日中值定理由于()0fx,所以()fx是单调递增的,故()()fxf,()0 x,即()

46、x在,a b上单调递增的.由于()0,a所以()0,xxa b,从而1()()()()()02babf bf abaf t dt,即31SS.因此,213SSS,应选(D).如果题目改为证明题,则应该用评注所讲的办法去证,而不能用图证.【相关知识点】1.积分中值定理：如果函数()f x在积分区间,a b上连续,则在(,)a b上至少存在一个点,使下式成立：()()()()baf x dxfba ab.这个公式叫做积分中值公式.2.拉格朗日中值定理：如果函数()f x满足在闭区间,a b上连续,在开区间,a b内可导,那么在,a b内至少有一点()ab,使等式()()()()f bf afba成

47、立.(3)【答案】(B)【解析】题目考察函数的极值点与拐点问题,分析如下：由0()0fx知0 xx为()f x的驻点.把0 xx代入恒等式000()1xx fxe,即0001()xefxx.由于分子、分母同号,故0()0fx,因此驻点0 xx为极小值点.应选(B).(4)【答案】(A)【解析】由于函数sinsintet是以2为周期的函数,所以,文档编码:CW9T7L1D2N1 HW4D7Y3P6O7 ZG2R8F2W10E9文档编码:CW9T7L1D2N1 HW4D7Y3P6O7 ZG2R8F2W10E9文档编码:CW9T7L1D2N1 HW4D7Y3P6O7 ZG2R8F2W10E9文档编码

48、:CW9T7L1D2N1 HW4D7Y3P6O7 ZG2R8F2W10E9文档编码:CW9T7L1D2N1 HW4D7Y3P6O7 ZG2R8F2W10E9文档编码:CW9T7L1D2N1 HW4D7Y3P6O7 ZG2R8F2W10E9文档编码:CW9T7L1D2N1 HW4D7Y3P6O7 ZG2R8F2W10E9文档编码:CW9T7L1D2N1 HW4D7Y3P6O7 ZG2R8F2W10E9文档编码:CW9T7L1D2N1 HW4D7Y3P6O7 ZG2R8F2W10E9文档编码:CW9T7L1D2N1 HW4D7Y3P6O7 ZG2R8F2W10E9文档编码:CW9T7L1D2N1

49、HW4D7Y3P6O7 ZG2R8F2W10E9文档编码:CW9T7L1D2N1 HW4D7Y3P6O7 ZG2R8F2W10E9文档编码:CW9T7L1D2N1 HW4D7Y3P6O7 ZG2R8F2W10E9文档编码:CW9T7L1D2N1 HW4D7Y3P6O7 ZG2R8F2W10E9文档编码:CW9T7L1D2N1 HW4D7Y3P6O7 ZG2R8F2W10E9文档编码:CW9T7L1D2N1 HW4D7Y3P6O7 ZG2R8F2W10E9文档编码:CW9T7L1D2N1 HW4D7Y3P6O7 ZG2R8F2W10E9文档编码:CW9T7L1D2N1 HW4D7Y3P6O7 Z

50、G2R8F2W10E9文档编码:CW9T7L1D2N1 HW4D7Y3P6O7 ZG2R8F2W10E9文档编码:CW9T7L1D2N1 HW4D7Y3P6O7 ZG2R8F2W10E9文档编码:CW9T7L1D2N1 HW4D7Y3P6O7 ZG2R8F2W10E9文档编码:CW9T7L1D2N1 HW4D7Y3P6O7 ZG2R8F2W10E9文档编码:CW9T7L1D2N1 HW4D7Y3P6O7 ZG2R8F2W10E9文档编码:CW9T7L1D2N1 HW4D7Y3P6O7 ZG2R8F2W10E9文档编码:CW9T7L1D2N1 HW4D7Y3P6O7 ZG2R8F2W10E9文档