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2022年1998考研数二真题及解析 .pdf

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1、1998 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 小题,每小题 3 分,满分 15 分,把答案填在题中横线上.)(1)20112limxxxx .(2)曲线322yxxx与x轴所围成的图形的面积A .(3)2ln sinsinxdxx .(4)设()f x连续,则220()xdtf xtdtdx .(5)曲线1ln()(0)yxexx的渐近线方程为 .二、选择题(本题共 5小题,每小题 3分,共15分.在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)设数列nx与ny满足lim0nnnx y,则下列断言正确的是 ()(A)若nx发散

2、,则ny发散 (B)若nx无界,则ny必有界(C)若nx有界,则ny必为无穷小 (D)若1nx为无穷小,则ny必为无穷小(2)函数23()(2)f xxxxx的不可导点的个数是 ()(A)0 (B)1 (C)2 (D)3(3)已知函数()yy x在任意点x处的增量2,1y xyx其中是比(0)xx高阶的无穷小,且(0),y,则(1)y ()(A)4e (B)2 (C)(D)4e(4)设函数()f x在xa的某个邻域内连续,且()f a为其极大值,则存在0,当(,)xaa时,必有 ()(A)()()()0 xaf xf a (B)()()()0 xaf xf a(C)2()()lim0()()t

3、af tf xxatx (D)2()()lim0()()taf tfxxatx(5)设A是任一(3)n n阶方阵,A是其伴随矩阵,又k为常数,且0,1k,则必有()kA ()(A)kA (B)1nkA (C)nk A (D)1kA三、(本题满分 5分)求函数tan()4()(1)xxf xx在区间(0,2)内的间断点,并判断其类型.四、(本题满分 5分)确定常数,a b c的值,使30sinlim(0).ln(1)xxbaxxc ctdtt五、(本题满分 5分)利用代换cosuyx将方程cos2sin3 cosxyxyxyxe化简,并求出原方程的通解.六、(本题满分 6分)计算积分32122d

4、xxx.七、(本题满分 6分)从船上向海中沉放某种探测仪器,按探测要求,需确定仪器的下沉深度y(从海平面算起)与下沉速度v之间的函数关系.设仪器在重力作用下,从海平面由静止开始铅直下沉,在下沉过程中还受到阻力和浮力的作用.设仪器的质量为m,体积为B,海水比重为,仪器所受的阻力与下沉速度成正比,比例系数为(0)k k.试建立y与v所满足的微分方程,并求出函数关系式y=fv.八、(本题满分 8分)设()yfx是区间0,1上的任一非负连续函数.(1)试证存在0(0,1)x,使得在区间00,x上以0()f x为高的矩形面积,等于在0,1x上以()yf x为曲边的梯形面积.(2)又设()f x在区间(0

5、,1)内可导,且2()()fxfxx,证明(1)中的0 x是唯一的.文档编码:CL5R6J9J7S6 HH3I1Q3K3H3 ZF5A2U5Q8R6文档编码:CL5R6J9J7S6 HH3I1Q3K3H3 ZF5A2U5Q8R6文档编码:CL5R6J9J7S6 HH3I1Q3K3H3 ZF5A2U5Q8R6文档编码:CL5R6J9J7S6 HH3I1Q3K3H3 ZF5A2U5Q8R6文档编码:CL5R6J9J7S6 HH3I1Q3K3H3 ZF5A2U5Q8R6文档编码:CL5R6J9J7S6 HH3I1Q3K3H3 ZF5A2U5Q8R6文档编码:CL5R6J9J7S6 HH3I1Q3K3

6、H3 ZF5A2U5Q8R6文档编码:CL5R6J9J7S6 HH3I1Q3K3H3 ZF5A2U5Q8R6文档编码:CL5R6J9J7S6 HH3I1Q3K3H3 ZF5A2U5Q8R6文档编码:CL5R6J9J7S6 HH3I1Q3K3H3 ZF5A2U5Q8R6文档编码:CL5R6J9J7S6 HH3I1Q3K3H3 ZF5A2U5Q8R6文档编码:CL5R6J9J7S6 HH3I1Q3K3H3 ZF5A2U5Q8R6文档编码:CL5R6J9J7S6 HH3I1Q3K3H3 ZF5A2U5Q8R6文档编码:CL5R6J9J7S6 HH3I1Q3K3H3 ZF5A2U5Q8R6文档编码:C

7、L5R6J9J7S6 HH3I1Q3K3H3 ZF5A2U5Q8R6文档编码:CL5R6J9J7S6 HH3I1Q3K3H3 ZF5A2U5Q8R6文档编码:CL5R6J9J7S6 HH3I1Q3K3H3 ZF5A2U5Q8R6文档编码:CL5R6J9J7S6 HH3I1Q3K3H3 ZF5A2U5Q8R6文档编码:CL5R6J9J7S6 HH3I1Q3K3H3 ZF5A2U5Q8R6文档编码:CL5R6J9J7S6 HH3I1Q3K3H3 ZF5A2U5Q8R6文档编码:CL5R6J9J7S6 HH3I1Q3K3H3 ZF5A2U5Q8R6文档编码:CL5R6J9J7S6 HH3I1Q3K3

8、H3 ZF5A2U5Q8R6文档编码:CL5R6J9J7S6 HH3I1Q3K3H3 ZF5A2U5Q8R6文档编码:CL5R6J9J7S6 HH3I1Q3K3H3 ZF5A2U5Q8R6文档编码:CL5R6J9J7S6 HH3I1Q3K3H3 ZF5A2U5Q8R6文档编码:CL5R6J9J7S6 HH3I1Q3K3H3 ZF5A2U5Q8R6文档编码:CL5R6J9J7S6 HH3I1Q3K3H3 ZF5A2U5Q8R6文档编码:CL5R6J9J7S6 HH3I1Q3K3H3 ZF5A2U5Q8R6文档编码:CL5R6J9J7S6 HH3I1Q3K3H3 ZF5A2U5Q8R6文档编码:C

9、L5R6J9J7S6 HH3I1Q3K3H3 ZF5A2U5Q8R6文档编码:CL5R6J9J7S6 HH3I1Q3K3H3 ZF5A2U5Q8R6文档编码:CL5R6J9J7S6 HH3I1Q3K3H3 ZF5A2U5Q8R6文档编码:CL5R6J9J7S6 HH3I1Q3K3H3 ZF5A2U5Q8R6文档编码:CL5R6J9J7S6 HH3I1Q3K3H3 ZF5A2U5Q8R6文档编码:CL5R6J9J7S6 HH3I1Q3K3H3 ZF5A2U5Q8R6文档编码:CL5R6J9J7S6 HH3I1Q3K3H3 ZF5A2U5Q8R6文档编码:CL5R6J9J7S6 HH3I1Q3K3

10、H3 ZF5A2U5Q8R6文档编码:CL5R6J9J7S6 HH3I1Q3K3H3 ZF5A2U5Q8R6文档编码:CL5R6J9J7S6 HH3I1Q3K3H3 ZF5A2U5Q8R6文档编码:CL5R6J9J7S6 HH3I1Q3K3H3 ZF5A2U5Q8R6文档编码:CL5R6J9J7S6 HH3I1Q3K3H3 ZF5A2U5Q8R6文档编码:CL5R6J9J7S6 HH3I1Q3K3H3 ZF5A2U5Q8R6文档编码:CL5R6J9J7S6 HH3I1Q3K3H3 ZF5A2U5Q8R6文档编码:CL5R6J9J7S6 HH3I1Q3K3H3 ZF5A2U5Q8R6文档编码:C

11、L5R6J9J7S6 HH3I1Q3K3H3 ZF5A2U5Q8R6文档编码:CL5R6J9J7S6 HH3I1Q3K3H3 ZF5A2U5Q8R6文档编码:CL5R6J9J7S6 HH3I1Q3K3H3 ZF5A2U5Q8R6文档编码:CL5R6J9J7S6 HH3I1Q3K3H3 ZF5A2U5Q8R6九、(本题满分 8分)设有曲线1yx,过原点作其切线,求由此曲线、切线及x轴围成的平面图形绕x轴旋转一周所得到的旋转体的表面积.十、(本题满分 8分)设()yy x是一向上凸的连续曲线,其上任意一点(,)x y处的曲率为211y,且此曲线上点(0,1)处的切线方程为1yx,求该曲线的方程,并

12、求函数()yy x的极值.十一、(本题满分 8分)设(0,1)x,证明：(1)22(1)ln(1);xxx(2)11111.ln 2ln(1)2xx十二、(本题满分 5分)设11(2)TEC B AC,其中E是4阶单位矩阵,TA是4阶矩阵A的转置矩阵,1232120101230120,0012001200010001BC求A.十三、(本题满分 8分)已知123(1,4,0,2),(2,7,1,3),(0,1,1,),(3,10,4)TTTTab,问：(1),a b取何值时,不能由123,线性表示？(2),a b取何值时,可由123,线性表示？并写出此表达式.1998年全国硕士研究生入学统一考试

13、数学二试题解析文档编码:CL5R6J9J7S6 HH3I1Q3K3H3 ZF5A2U5Q8R6文档编码:CL5R6J9J7S6 HH3I1Q3K3H3 ZF5A2U5Q8R6文档编码:CL5R6J9J7S6 HH3I1Q3K3H3 ZF5A2U5Q8R6文档编码:CL5R6J9J7S6 HH3I1Q3K3H3 ZF5A2U5Q8R6文档编码:CL5R6J9J7S6 HH3I1Q3K3H3 ZF5A2U5Q8R6文档编码:CL5R6J9J7S6 HH3I1Q3K3H3 ZF5A2U5Q8R6文档编码:CL5R6J9J7S6 HH3I1Q3K3H3 ZF5A2U5Q8R6文档编码:CL5R6J9J

14、7S6 HH3I1Q3K3H3 ZF5A2U5Q8R6文档编码:CL5R6J9J7S6 HH3I1Q3K3H3 ZF5A2U5Q8R6文档编码:CL5R6J9J7S6 HH3I1Q3K3H3 ZF5A2U5Q8R6文档编码:CL5R6J9J7S6 HH3I1Q3K3H3 ZF5A2U5Q8R6文档编码:CL5R6J9J7S6 HH3I1Q3K3H3 ZF5A2U5Q8R6文档编码:CL5R6J9J7S6 HH3I1Q3K3H3 ZF5A2U5Q8R6文档编码:CL5R6J9J7S6 HH3I1Q3K3H3 ZF5A2U5Q8R6文档编码:CL5R6J9J7S6 HH3I1Q3K3H3 ZF5A

15、2U5Q8R6文档编码:CL5R6J9J7S6 HH3I1Q3K3H3 ZF5A2U5Q8R6文档编码:CL5R6J9J7S6 HH3I1Q3K3H3 ZF5A2U5Q8R6文档编码:CL5R6J9J7S6 HH3I1Q3K3H3 ZF5A2U5Q8R6文档编码:CL5R6J9J7S6 HH3I1Q3K3H3 ZF5A2U5Q8R6文档编码:CL5R6J9J7S6 HH3I1Q3K3H3 ZF5A2U5Q8R6文档编码:CL5R6J9J7S6 HH3I1Q3K3H3 ZF5A2U5Q8R6文档编码:CL5R6J9J7S6 HH3I1Q3K3H3 ZF5A2U5Q8R6文档编码:CL5R6J9J

16、7S6 HH3I1Q3K3H3 ZF5A2U5Q8R6文档编码:CL5R6J9J7S6 HH3I1Q3K3H3 ZF5A2U5Q8R6文档编码:CL5R6J9J7S6 HH3I1Q3K3H3 ZF5A2U5Q8R6文档编码:CL5R6J9J7S6 HH3I1Q3K3H3 ZF5A2U5Q8R6文档编码:CL5R6J9J7S6 HH3I1Q3K3H3 ZF5A2U5Q8R6文档编码:CL5R6J9J7S6 HH3I1Q3K3H3 ZF5A2U5Q8R6文档编码:CL5R6J9J7S6 HH3I1Q3K3H3 ZF5A2U5Q8R6文档编码:CL5R6J9J7S6 HH3I1Q3K3H3 ZF5A

17、2U5Q8R6文档编码:CL5R6J9J7S6 HH3I1Q3K3H3 ZF5A2U5Q8R6文档编码:CL5R6J9J7S6 HH3I1Q3K3H3 ZF5A2U5Q8R6文档编码:CL5R6J9J7S6 HH3I1Q3K3H3 ZF5A2U5Q8R6文档编码:CL5R6J9J7S6 HH3I1Q3K3H3 ZF5A2U5Q8R6文档编码:CL5R6J9J7S6 HH3I1Q3K3H3 ZF5A2U5Q8R6文档编码:CL5R6J9J7S6 HH3I1Q3K3H3 ZF5A2U5Q8R6文档编码:CL5R6J9J7S6 HH3I1Q3K3H3 ZF5A2U5Q8R6文档编码:CL5R6J9J

18、7S6 HH3I1Q3K3H3 ZF5A2U5Q8R6文档编码:CL5R6J9J7S6 HH3I1Q3K3H3 ZF5A2U5Q8R6文档编码:CL5R6J9J7S6 HH3I1Q3K3H3 ZF5A2U5Q8R6文档编码:CL5R6J9J7S6 HH3I1Q3K3H3 ZF5A2U5Q8R6文档编码:CL5R6J9J7S6 HH3I1Q3K3H3 ZF5A2U5Q8R6文档编码:CL5R6J9J7S6 HH3I1Q3K3H3 ZF5A2U5Q8R6文档编码:CL5R6J9J7S6 HH3I1Q3K3H3 ZF5A2U5Q8R6文档编码:CL5R6J9J7S6 HH3I1Q3K3H3 ZF5A

19、2U5Q8R6文档编码:CL5R6J9J7S6 HH3I1Q3K3H3 ZF5A2U5Q8R6文档编码:CL5R6J9J7S6 HH3I1Q3K3H3 ZF5A2U5Q8R6文档编码:CL5R6J9J7S6 HH3I1Q3K3H3 ZF5A2U5Q8R6一、填空题(本题共 5 小题,每小题 3 分,满分 15 分,把答案填在题中横线上.)(1)【答案】14【解析】方法 1：用四则运算将分子化简,再用等价无穷小替换,原式20112112lim112xxxxxxxx220114lim112xxxxxx220211lim4xxx222201112112lim24xxxxx.方法 2：采用洛必达法则.

20、原式02112limxxxx洛0112 12 1lim2xxxx2011lim41xxxxx011lim4xxxx0112 12 1lim4xxx洛011lim12 12 144xxx.方法 3：将分子按佩亚诺余项泰勒公式展开至2x项,1x22111128xxox,1x22211128xxox,从而原式2222122011111122828limxxxoxxxoxx222122014limxxoxoxx14.(2)【答案】3712【分析】求曲线与x轴围成的图形的面积,应分清楚位于x轴上方还是下方,为此,要先求此曲线与x轴交点.【解析】322yxxx与x轴的交点,即322(2)(1)0 xxxx

21、 xx的根文档编码:CL5R6J9J7S6 HH3I1Q3K3H3 ZF5A2U5Q8R6文档编码:CL5R6J9J7S6 HH3I1Q3K3H3 ZF5A2U5Q8R6文档编码:CL5R6J9J7S6 HH3I1Q3K3H3 ZF5A2U5Q8R6文档编码:CL5R6J9J7S6 HH3I1Q3K3H3 ZF5A2U5Q8R6文档编码:CL5R6J9J7S6 HH3I1Q3K3H3 ZF5A2U5Q8R6文档编码:CL5R6J9J7S6 HH3I1Q3K3H3 ZF5A2U5Q8R6文档编码:CL5R6J9J7S6 HH3I1Q3K3H3 ZF5A2U5Q8R6文档编码:CL5R6J9J7S

22、6 HH3I1Q3K3H3 ZF5A2U5Q8R6文档编码:CL5R6J9J7S6 HH3I1Q3K3H3 ZF5A2U5Q8R6文档编码:CL5R6J9J7S6 HH3I1Q3K3H3 ZF5A2U5Q8R6文档编码:CL5R6J9J7S6 HH3I1Q3K3H3 ZF5A2U5Q8R6文档编码:CL5R6J9J7S6 HH3I1Q3K3H3 ZF5A2U5Q8R6文档编码:CL5R6J9J7S6 HH3I1Q3K3H3 ZF5A2U5Q8R6文档编码:CL5R6J9J7S6 HH3I1Q3K3H3 ZF5A2U5Q8R6文档编码:CL5R6J9J7S6 HH3I1Q3K3H3 ZF5A2U

23、5Q8R6文档编码:CL5R6J9J7S6 HH3I1Q3K3H3 ZF5A2U5Q8R6文档编码:CL5R6J9J7S6 HH3I1Q3K3H3 ZF5A2U5Q8R6文档编码:CL5R6J9J7S6 HH3I1Q3K3H3 ZF5A2U5Q8R6文档编码:CL5R6J9J7S6 HH3I1Q3K3H3 ZF5A2U5Q8R6文档编码:CL5R6J9J7S6 HH3I1Q3K3H3 ZF5A2U5Q8R6文档编码:CL5R6J9J7S6 HH3I1Q3K3H3 ZF5A2U5Q8R6文档编码:CL5R6J9J7S6 HH3I1Q3K3H3 ZF5A2U5Q8R6文档编码:CL5R6J9J7S

24、6 HH3I1Q3K3H3 ZF5A2U5Q8R6文档编码:CL5R6J9J7S6 HH3I1Q3K3H3 ZF5A2U5Q8R6文档编码:CL5R6J9J7S6 HH3I1Q3K3H3 ZF5A2U5Q8R6文档编码:CL5R6J9J7S6 HH3I1Q3K3H3 ZF5A2U5Q8R6文档编码:CL5R6J9J7S6 HH3I1Q3K3H3 ZF5A2U5Q8R6文档编码:CL5R6J9J7S6 HH3I1Q3K3H3 ZF5A2U5Q8R6文档编码:CL5R6J9J7S6 HH3I1Q3K3H3 ZF5A2U5Q8R6文档编码:CL5R6J9J7S6 HH3I1Q3K3H3 ZF5A2U

25、5Q8R6文档编码:CL5R6J9J7S6 HH3I1Q3K3H3 ZF5A2U5Q8R6文档编码:CL5R6J9J7S6 HH3I1Q3K3H3 ZF5A2U5Q8R6文档编码:CL5R6J9J7S6 HH3I1Q3K3H3 ZF5A2U5Q8R6文档编码:CL5R6J9J7S6 HH3I1Q3K3H3 ZF5A2U5Q8R6文档编码:CL5R6J9J7S6 HH3I1Q3K3H3 ZF5A2U5Q8R6文档编码:CL5R6J9J7S6 HH3I1Q3K3H3 ZF5A2U5Q8R6文档编码:CL5R6J9J7S6 HH3I1Q3K3H3 ZF5A2U5Q8R6文档编码:CL5R6J9J7S

26、6 HH3I1Q3K3H3 ZF5A2U5Q8R6文档编码:CL5R6J9J7S6 HH3I1Q3K3H3 ZF5A2U5Q8R6文档编码:CL5R6J9J7S6 HH3I1Q3K3H3 ZF5A2U5Q8R6文档编码:CL5R6J9J7S6 HH3I1Q3K3H3 ZF5A2U5Q8R6文档编码:CL5R6J9J7S6 HH3I1Q3K3H3 ZF5A2U5Q8R6文档编码:CL5R6J9J7S6 HH3I1Q3K3H3 ZF5A2U5Q8R6文档编码:CL5R6J9J7S6 HH3I1Q3K3H3 ZF5A2U5Q8R6文档编码:CL5R6J9J7S6 HH3I1Q3K3H3 ZF5A2U

27、5Q8R6文档编码:CL5R6J9J7S6 HH3I1Q3K3H3 ZF5A2U5Q8R6文档编码:CL5R6J9J7S6 HH3I1Q3K3H3 ZF5A2U5Q8R6文档编码:CL5R6J9J7S6 HH3I1Q3K3H3 ZF5A2U5Q8R6为1,0,2.x当10 x时,0y；当02x时,0y,从而0202323210100243432210(2)(2)434311858370(1)(44).43312312Aydxydxxxx dxxxx dxxxxxxx(3)【答案】cotln sincot.xxxxC【解析】因为2cotcscxx21sin x,所以2ln sinsinxdxxl

28、nsincotxxdxln sincotxdxcotln sincotln sinxxxdx分部coscotln sincotsinxxxxdxx22coscotln sinsinxxxdxx221sincotln sinsinxxxdxx2cotln sin1sindxxxdxxcotlnsincotxxxdxxcotln sincotxxxxC.(4)【答案】2()xf x【解析】作积分变量代换22,uxt2:0:0txu x,222dud xttdt12dtdut,220()xtf xtdt22uxt201()2xtf udut220011()()22xxf u duf u du,222

29、001()()2xxddtfxtdtf u dudxdx221()2f xx221()2()2f xxxfx.【相关知识点】1.对积分上限的函数的求导公式：若()()()()ttF tf x dx,()t,()t均一文档编码:CL5R6J9J7S6 HH3I1Q3K3H3 ZF5A2U5Q8R6文档编码:CL5R6J9J7S6 HH3I1Q3K3H3 ZF5A2U5Q8R6文档编码:CL5R6J9J7S6 HH3I1Q3K3H3 ZF5A2U5Q8R6文档编码:CL5R6J9J7S6 HH3I1Q3K3H3 ZF5A2U5Q8R6文档编码:CL5R6J9J7S6 HH3I1Q3K3H3 ZF5

30、A2U5Q8R6文档编码:CL5R6J9J7S6 HH3I1Q3K3H3 ZF5A2U5Q8R6文档编码:CL5R6J9J7S6 HH3I1Q3K3H3 ZF5A2U5Q8R6文档编码:CL5R6J9J7S6 HH3I1Q3K3H3 ZF5A2U5Q8R6文档编码:CL5R6J9J7S6 HH3I1Q3K3H3 ZF5A2U5Q8R6文档编码:CL5R6J9J7S6 HH3I1Q3K3H3 ZF5A2U5Q8R6文档编码:CL5R6J9J7S6 HH3I1Q3K3H3 ZF5A2U5Q8R6文档编码:CL5R6J9J7S6 HH3I1Q3K3H3 ZF5A2U5Q8R6文档编码:CL5R6J9

31、J7S6 HH3I1Q3K3H3 ZF5A2U5Q8R6文档编码:CL5R6J9J7S6 HH3I1Q3K3H3 ZF5A2U5Q8R6文档编码:CL5R6J9J7S6 HH3I1Q3K3H3 ZF5A2U5Q8R6文档编码:CL5R6J9J7S6 HH3I1Q3K3H3 ZF5A2U5Q8R6文档编码:CL5R6J9J7S6 HH3I1Q3K3H3 ZF5A2U5Q8R6文档编码:CL5R6J9J7S6 HH3I1Q3K3H3 ZF5A2U5Q8R6文档编码:CL5R6J9J7S6 HH3I1Q3K3H3 ZF5A2U5Q8R6文档编码:CL5R6J9J7S6 HH3I1Q3K3H3 ZF5

32、A2U5Q8R6文档编码:CL5R6J9J7S6 HH3I1Q3K3H3 ZF5A2U5Q8R6文档编码:CL5R6J9J7S6 HH3I1Q3K3H3 ZF5A2U5Q8R6文档编码:CL5R6J9J7S6 HH3I1Q3K3H3 ZF5A2U5Q8R6文档编码:CL5R6J9J7S6 HH3I1Q3K3H3 ZF5A2U5Q8R6文档编码:CL5R6J9J7S6 HH3I1Q3K3H3 ZF5A2U5Q8R6文档编码:CL5R6J9J7S6 HH3I1Q3K3H3 ZF5A2U5Q8R6文档编码:CL5R6J9J7S6 HH3I1Q3K3H3 ZF5A2U5Q8R6文档编码:CL5R6J9

33、J7S6 HH3I1Q3K3H3 ZF5A2U5Q8R6文档编码:CL5R6J9J7S6 HH3I1Q3K3H3 ZF5A2U5Q8R6文档编码:CL5R6J9J7S6 HH3I1Q3K3H3 ZF5A2U5Q8R6文档编码:CL5R6J9J7S6 HH3I1Q3K3H3 ZF5A2U5Q8R6文档编码:CL5R6J9J7S6 HH3I1Q3K3H3 ZF5A2U5Q8R6文档编码:CL5R6J9J7S6 HH3I1Q3K3H3 ZF5A2U5Q8R6文档编码:CL5R6J9J7S6 HH3I1Q3K3H3 ZF5A2U5Q8R6文档编码:CL5R6J9J7S6 HH3I1Q3K3H3 ZF5

34、A2U5Q8R6文档编码:CL5R6J9J7S6 HH3I1Q3K3H3 ZF5A2U5Q8R6文档编码:CL5R6J9J7S6 HH3I1Q3K3H3 ZF5A2U5Q8R6文档编码:CL5R6J9J7S6 HH3I1Q3K3H3 ZF5A2U5Q8R6文档编码:CL5R6J9J7S6 HH3I1Q3K3H3 ZF5A2U5Q8R6文档编码:CL5R6J9J7S6 HH3I1Q3K3H3 ZF5A2U5Q8R6文档编码:CL5R6J9J7S6 HH3I1Q3K3H3 ZF5A2U5Q8R6文档编码:CL5R6J9J7S6 HH3I1Q3K3H3 ZF5A2U5Q8R6文档编码:CL5R6J9

35、J7S6 HH3I1Q3K3H3 ZF5A2U5Q8R6文档编码:CL5R6J9J7S6 HH3I1Q3K3H3 ZF5A2U5Q8R6文档编码:CL5R6J9J7S6 HH3I1Q3K3H3 ZF5A2U5Q8R6文档编码:CL5R6J9J7S6 HH3I1Q3K3H3 ZF5A2U5Q8R6文档编码:CL5R6J9J7S6 HH3I1Q3K3H3 ZF5A2U5Q8R6文档编码:CL5R6J9J7S6 HH3I1Q3K3H3 ZF5A2U5Q8R6阶可导,则()()()()()F ttfttft.(5)【答案】1yxe【解析】题中未说什么渐近线,所以三类渐近线都要考虑.由曲线方程1ln()

36、yxex知,铅直渐近线可能在两处：1xe及0 x,但题设0 x,所以1xe不予考虑,考虑0 x的情况.当0 x时,01ln()1limln()1limlim0ttxetxextxtet洛,所以无铅直渐近线；因1lim()limln()limln,xxxy xxexex故无水平渐近线.再考虑斜渐近线:1limlim ln()1xxyexx,11limlimln()1limlnln(1)1111limln(1)lim,xxxxxyxxexexexxxexexe(x时,11ln(1)exex)所以有斜渐近线y1xe.【相关知识点】1.铅直渐近线：如函数()yf x在其间断点0 xx处有0lim()x

37、xf x,则0 xx是函数的一条铅直渐近线；水平渐近线：当lim(),(xf xaa为常数）,则ya为函数的水平渐近线.斜渐近线：若有()lim,lim()xxfxabf xaxx存在且不为,则yaxb为斜渐近线.二、选择题(本题共 5小题,每小题 3分,共15分,在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】(D)【解析】方法 1:直接利用无穷小量的性质可以证明(D)是正确的.文档编码:CL5R6J9J7S6 HH3I1Q3K3H3 ZF5A2U5Q8R6文档编码:CL5R6J9J7S6 HH3I1Q3K3H3 ZF5A2U5Q8R6文档编

38、码:CL5R6J9J7S6 HH3I1Q3K3H3 ZF5A2U5Q8R6文档编码:CL5R6J9J7S6 HH3I1Q3K3H3 ZF5A2U5Q8R6文档编码:CL5R6J9J7S6 HH3I1Q3K3H3 ZF5A2U5Q8R6文档编码:CL5R6J9J7S6 HH3I1Q3K3H3 ZF5A2U5Q8R6文档编码:CL5R6J9J7S6 HH3I1Q3K3H3 ZF5A2U5Q8R6文档编码:CL5R6J9J7S6 HH3I1Q3K3H3 ZF5A2U5Q8R6文档编码:CL5R6J9J7S6 HH3I1Q3K3H3 ZF5A2U5Q8R6文档编码:CL5R6J9J7S6 HH3I1Q

39、3K3H3 ZF5A2U5Q8R6文档编码:CL5R6J9J7S6 HH3I1Q3K3H3 ZF5A2U5Q8R6文档编码:CL5R6J9J7S6 HH3I1Q3K3H3 ZF5A2U5Q8R6文档编码:CL5R6J9J7S6 HH3I1Q3K3H3 ZF5A2U5Q8R6文档编码:CL5R6J9J7S6 HH3I1Q3K3H3 ZF5A2U5Q8R6文档编码:CL5R6J9J7S6 HH3I1Q3K3H3 ZF5A2U5Q8R6文档编码:CL5R6J9J7S6 HH3I1Q3K3H3 ZF5A2U5Q8R6文档编码:CL5R6J9J7S6 HH3I1Q3K3H3 ZF5A2U5Q8R6文档编

40、码:CL5R6J9J7S6 HH3I1Q3K3H3 ZF5A2U5Q8R6文档编码:CL5R6J9J7S6 HH3I1Q3K3H3 ZF5A2U5Q8R6文档编码:CL5R6J9J7S6 HH3I1Q3K3H3 ZF5A2U5Q8R6文档编码:CL5R6J9J7S6 HH3I1Q3K3H3 ZF5A2U5Q8R6文档编码:CL5R6J9J7S6 HH3I1Q3K3H3 ZF5A2U5Q8R6文档编码:CL5R6J9J7S6 HH3I1Q3K3H3 ZF5A2U5Q8R6文档编码:CL5R6J9J7S6 HH3I1Q3K3H3 ZF5A2U5Q8R6文档编码:CL5R6J9J7S6 HH3I1Q

41、3K3H3 ZF5A2U5Q8R6文档编码:CL5R6J9J7S6 HH3I1Q3K3H3 ZF5A2U5Q8R6文档编码:CL5R6J9J7S6 HH3I1Q3K3H3 ZF5A2U5Q8R6文档编码:CL5R6J9J7S6 HH3I1Q3K3H3 ZF5A2U5Q8R6文档编码:CL5R6J9J7S6 HH3I1Q3K3H3 ZF5A2U5Q8R6文档编码:CL5R6J9J7S6 HH3I1Q3K3H3 ZF5A2U5Q8R6文档编码:CL5R6J9J7S6 HH3I1Q3K3H3 ZF5A2U5Q8R6文档编码:CL5R6J9J7S6 HH3I1Q3K3H3 ZF5A2U5Q8R6文档编

42、码:CL5R6J9J7S6 HH3I1Q3K3H3 ZF5A2U5Q8R6文档编码:CL5R6J9J7S6 HH3I1Q3K3H3 ZF5A2U5Q8R6文档编码:CL5R6J9J7S6 HH3I1Q3K3H3 ZF5A2U5Q8R6文档编码:CL5R6J9J7S6 HH3I1Q3K3H3 ZF5A2U5Q8R6文档编码:CL5R6J9J7S6 HH3I1Q3K3H3 ZF5A2U5Q8R6文档编码:CL5R6J9J7S6 HH3I1Q3K3H3 ZF5A2U5Q8R6文档编码:CL5R6J9J7S6 HH3I1Q3K3H3 ZF5A2U5Q8R6文档编码:CL5R6J9J7S6 HH3I1Q

43、3K3H3 ZF5A2U5Q8R6文档编码:CL5R6J9J7S6 HH3I1Q3K3H3 ZF5A2U5Q8R6文档编码:CL5R6J9J7S6 HH3I1Q3K3H3 ZF5A2U5Q8R6文档编码:CL5R6J9J7S6 HH3I1Q3K3H3 ZF5A2U5Q8R6文档编码:CL5R6J9J7S6 HH3I1Q3K3H3 ZF5A2U5Q8R6文档编码:CL5R6J9J7S6 HH3I1Q3K3H3 ZF5A2U5Q8R6文档编码:CL5R6J9J7S6 HH3I1Q3K3H3 ZF5A2U5Q8R6文档编码:CL5R6J9J7S6 HH3I1Q3K3H3 ZF5A2U5Q8R6文档编

44、码:CL5R6J9J7S6 HH3I1Q3K3H3 ZF5A2U5Q8R6由1()nnnnyx yx及1lim0,lim0nnnnnx yx可知ny为两个无穷小之积,故ny亦为无穷小,应选(D).方法 2:排除法.(A)的反例:22111,limlimlim0nnnnnnnxn yx ynnnn满足题设,但lim0nny不发散；(B)的反例:21,21,0,21,1,2,0,2,2,2,nnknknkxyknkknk,满足lim0nnnx y,但ny不是有界数列；(C)的反例:1 11:1,2 3nxn有界数列,1(1,2,),nyn满足1limlim0nnnnx yn,但ny不是无穷小；排除

45、掉(A)、(B)、(C),故选(D).(2)【答案】(B)【解析】当函数中出现绝对值号时,就有可能出现不可导的“尖点”,因为这时的函数是分段函数.22()(2)1f xxxx x,当0,1x时()f x可导,因而只需在0,1x处考察()f x是否可导.在这些点我们分别考察其左、右导数.由22222222(2)(1),1,(2)(1),10,()(2)(1),01,(2)(1),1,xxxxxxxx xxf xxxxxxxxx xx22111(2)(1)0(1)limlim011xxfxfxxxxfxx,22111(2)(1)0(1)limlim011xxfxfxxxxfxx,即()f x在1x

46、处可导.又22000(2)(1)0(0)limlim2xxfxfxxx xfxx,22000(2)(1)0(0)limlim2xxfxfxxxxfxx,所以()f x在0 x处不可导.文档编码:CL5R6J9J7S6 HH3I1Q3K3H3 ZF5A2U5Q8R6文档编码:CL5R6J9J7S6 HH3I1Q3K3H3 ZF5A2U5Q8R6文档编码:CL5R6J9J7S6 HH3I1Q3K3H3 ZF5A2U5Q8R6文档编码:CL5R6J9J7S6 HH3I1Q3K3H3 ZF5A2U5Q8R6文档编码:CL5R6J9J7S6 HH3I1Q3K3H3 ZF5A2U5Q8R6文档编码:CL5

47、R6J9J7S6 HH3I1Q3K3H3 ZF5A2U5Q8R6文档编码:CL5R6J9J7S6 HH3I1Q3K3H3 ZF5A2U5Q8R6文档编码:CL5R6J9J7S6 HH3I1Q3K3H3 ZF5A2U5Q8R6文档编码:CL5R6J9J7S6 HH3I1Q3K3H3 ZF5A2U5Q8R6文档编码:CL5R6J9J7S6 HH3I1Q3K3H3 ZF5A2U5Q8R6文档编码:CL5R6J9J7S6 HH3I1Q3K3H3 ZF5A2U5Q8R6文档编码:CL5R6J9J7S6 HH3I1Q3K3H3 ZF5A2U5Q8R6文档编码:CL5R6J9J7S6 HH3I1Q3K3H3

48、 ZF5A2U5Q8R6文档编码:CL5R6J9J7S6 HH3I1Q3K3H3 ZF5A2U5Q8R6文档编码:CL5R6J9J7S6 HH3I1Q3K3H3 ZF5A2U5Q8R6文档编码:CL5R6J9J7S6 HH3I1Q3K3H3 ZF5A2U5Q8R6文档编码:CL5R6J9J7S6 HH3I1Q3K3H3 ZF5A2U5Q8R6文档编码:CL5R6J9J7S6 HH3I1Q3K3H3 ZF5A2U5Q8R6文档编码:CL5R6J9J7S6 HH3I1Q3K3H3 ZF5A2U5Q8R6文档编码:CL5R6J9J7S6 HH3I1Q3K3H3 ZF5A2U5Q8R6文档编码:CL5

49、R6J9J7S6 HH3I1Q3K3H3 ZF5A2U5Q8R6文档编码:CL5R6J9J7S6 HH3I1Q3K3H3 ZF5A2U5Q8R6文档编码:CL5R6J9J7S6 HH3I1Q3K3H3 ZF5A2U5Q8R6文档编码:CL5R6J9J7S6 HH3I1Q3K3H3 ZF5A2U5Q8R6文档编码:CL5R6J9J7S6 HH3I1Q3K3H3 ZF5A2U5Q8R6文档编码:CL5R6J9J7S6 HH3I1Q3K3H3 ZF5A2U5Q8R6文档编码:CL5R6J9J7S6 HH3I1Q3K3H3 ZF5A2U5Q8R6文档编码:CL5R6J9J7S6 HH3I1Q3K3H3

50、 ZF5A2U5Q8R6文档编码:CL5R6J9J7S6 HH3I1Q3K3H3 ZF5A2U5Q8R6文档编码:CL5R6J9J7S6 HH3I1Q3K3H3 ZF5A2U5Q8R6文档编码:CL5R6J9J7S6 HH3I1Q3K3H3 ZF5A2U5Q8R6文档编码:CL5R6J9J7S6 HH3I1Q3K3H3 ZF5A2U5Q8R6文档编码:CL5R6J9J7S6 HH3I1Q3K3H3 ZF5A2U5Q8R6文档编码:CL5R6J9J7S6 HH3I1Q3K3H3 ZF5A2U5Q8R6文档编码:CL5R6J9J7S6 HH3I1Q3K3H3 ZF5A2U5Q8R6文档编码:CL5

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