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1、更多各科期末考试学习资料答案加QQ146958 2255 全套已整理工程数学二复习题（教师用）一、选择题：1、下列等式中有一个是微分方程，它是（D）A、)(uvvuvuB、vuvvuvu2C、dxeydedxdyxx)(D、043yyy解：选项 A 和 B 是求导公式，选项C 为恒等式，选项D 符合微分方程的定义2、下列方程中有一个是一阶微分方程，它是（C）A、yyxyxy22)(B、0)(5)(7542xyyyC、0)()(2222dyyxdxyxD、043yyyx3、若级数1nna与1nnb都发散，则（C）A、1)(nnnba发散B、1nnnba发散C、1)(nnnba发散D、122)(n
2、nnba发散解：由nnnbaa推知若选项C 收敛，则1nna收敛，与题设矛盾，故选C 4、级数1nna的部分和数列nS有界是该级数收敛的（A）A、必要非充分条件B、充分非必要条件C、充要条件D、既非充分也非必要条件5、级数1nnqa（a 为常数）收敛的充分条件是（A）A、|q|1 B、q=1 C、|q|1 D、q1 时级数收敛6、若级数1nna收敛，那么下列级数中发散的是（B）A、1100nnaB、1)100(nnaC、100+1nnaD、1100nna解：选项 B 中，因为0100)100(limnna，所以该级数发散7、若级数1nna发散，则（D）A、0limnnaB、)(lim21nnn
3、naaaSSC、1nna任意加括号后所成的级数必发散D、1nna任意加括号后所成的级数可能收敛解：选项A 和 B 均为级数发散的充分条件，但非要条件。若级数发散，则任意加括号后所成级数可能收敛也可能发散8、若级数1nna收敛，则下述结论中，不正确的是（C）A、1212)(nnnaa收敛B、1nnka收敛)0(kC、1|nna收敛D、0limnna解：选项 A 中因为14321212)()()(nnnaaaaaa所以 A 正确选项 B 中由级数收敛性质知该级数收敛，所以B 正确选项 D 是级数收敛的必要条件，所以D 正确选项 C 中原级数收敛，1|nna可能收敛也可以发散9、无穷级数1)0()1
4、(nnnnuu收敛的充分条件是（C）文档编码:CG2F3D8B1I1 HT9W1G9C5J4 ZE1Q6R2J10Y2文档编码:CG2F3D8B1I1 HT9W1G9C5J4 ZE1Q6R2J10Y2文档编码:CG2F3D8B1I1 HT9W1G9C5J4 ZE1Q6R2J10Y2文档编码:CG2F3D8B1I1 HT9W1G9C5J4 ZE1Q6R2J10Y2文档编码:CG2F3D8B1I1 HT9W1G9C5J4 ZE1Q6R2J10Y2文档编码:CG2F3D8B1I1 HT9W1G9C5J4 ZE1Q6R2J10Y2文档编码:CG2F3D8B1I1 HT9W1G9C5J4 ZE1Q6R2
5、J10Y2文档编码:CG2F3D8B1I1 HT9W1G9C5J4 ZE1Q6R2J10Y2文档编码:CG2F3D8B1I1 HT9W1G9C5J4 ZE1Q6R2J10Y2文档编码:CG2F3D8B1I1 HT9W1G9C5J4 ZE1Q6R2J10Y2文档编码:CG2F3D8B1I1 HT9W1G9C5J4 ZE1Q6R2J10Y2文档编码:CG2F3D8B1I1 HT9W1G9C5J4 ZE1Q6R2J10Y2文档编码:CG2F3D8B1I1 HT9W1G9C5J4 ZE1Q6R2J10Y2文档编码:CG2F3D8B1I1 HT9W1G9C5J4 ZE1Q6R2J10Y2文档编码:CG2
6、F3D8B1I1 HT9W1G9C5J4 ZE1Q6R2J10Y2文档编码:CG2F3D8B1I1 HT9W1G9C5J4 ZE1Q6R2J10Y2文档编码:CG2F3D8B1I1 HT9W1G9C5J4 ZE1Q6R2J10Y2文档编码:CG2F3D8B1I1 HT9W1G9C5J4 ZE1Q6R2J10Y2文档编码:CG2F3D8B1I1 HT9W1G9C5J4 ZE1Q6R2J10Y2文档编码:CG2F3D8B1I1 HT9W1G9C5J4 ZE1Q6R2J10Y2文档编码:CG2F3D8B1I1 HT9W1G9C5J4 ZE1Q6R2J10Y2文档编码:CG2F3D8B1I1 HT9W
7、1G9C5J4 ZE1Q6R2J10Y2文档编码:CG2F3D8B1I1 HT9W1G9C5J4 ZE1Q6R2J10Y2文档编码:CG2F3D8B1I1 HT9W1G9C5J4 ZE1Q6R2J10Y2文档编码:CG2F3D8B1I1 HT9W1G9C5J4 ZE1Q6R2J10Y2文档编码:CG2F3D8B1I1 HT9W1G9C5J4 ZE1Q6R2J10Y2文档编码:CG2F3D8B1I1 HT9W1G9C5J4 ZE1Q6R2J10Y2文档编码:CG2F3D8B1I1 HT9W1G9C5J4 ZE1Q6R2J10Y2文档编码:CG2F3D8B1I1 HT9W1G9C5J4 ZE1Q6
8、R2J10Y2文档编码:CG2F3D8B1I1 HT9W1G9C5J4 ZE1Q6R2J10Y2文档编码:CG2F3D8B1I1 HT9W1G9C5J4 ZE1Q6R2J10Y2文档编码:CG2F3D8B1I1 HT9W1G9C5J4 ZE1Q6R2J10Y2文档编码:CG2F3D8B1I1 HT9W1G9C5J4 ZE1Q6R2J10Y2文档编码:CG2F3D8B1I1 HT9W1G9C5J4 ZE1Q6R2J10Y2文档编码:CG2F3D8B1I1 HT9W1G9C5J4 ZE1Q6R2J10Y2文档编码:CG2F3D8B1I1 HT9W1G9C5J4 ZE1Q6R2J10Y2文档编码:C
9、G2F3D8B1I1 HT9W1G9C5J4 ZE1Q6R2J10Y2文档编码:CG2F3D8B1I1 HT9W1G9C5J4 ZE1Q6R2J10Y2文档编码:CG2F3D8B1I1 HT9W1G9C5J4 ZE1Q6R2J10Y2文档编码:CG2F3D8B1I1 HT9W1G9C5J4 ZE1Q6R2J10Y2文档编码:CG2F3D8B1I1 HT9W1G9C5J4 ZE1Q6R2J10Y2文档编码:CG2F3D8B1I1 HT9W1G9C5J4 ZE1Q6R2J10Y2文档编码:CG2F3D8B1I1 HT9W1G9C5J4 ZE1Q6R2J10Y2文档编码:CG2F3D8B1I1 HT
10、9W1G9C5J4 ZE1Q6R2J10Y2文档编码:CG2F3D8B1I1 HT9W1G9C5J4 ZE1Q6R2J10Y2文档编码:CG2F3D8B1I1 HT9W1G9C5J4 ZE1Q6R2J10Y2文档编码:CG2F3D8B1I1 HT9W1G9C5J4 ZE1Q6R2J10Y2文档编码:CG2F3D8B1I1 HT9W1G9C5J4 ZE1Q6R2J10Y2A、),2,1(1nuunnB、0limnnuC、),2,1(1nuunn，且0limnnuD、11)()1(nnnnuu收敛解：所给级数为交错级数，选项C 为交错级数判断收敛性的莱布尼茨定理中的条件10、设),2,1(10nn
11、un，则下列级数中必定收敛的是（D）A、1nnuB、1)1(nnnuC、1nnuD、12)1(nnnu11、在球02222zzyx内部的点是（C）A、（0，0，2）B、（0，0，-2）C、)21,21,21(D、)21,21,21(解：球的标准方程为1)1(222zyx，是以（0，0，1）为球心，1 为半径的球面，经验算选项C 中的点到球心的距离为12312、设函数22),(yxxyyxfz，则下列各结论中不正确的是（D）A、22),1(yxxyxyfB、22),1(yxxyyxfC、22)1,1(yxxyyxfD、22),(yxxyyxyxf13、设函数z=f(x,y)在点(x0，y0)处存
12、在对x，y 的偏导数，则f x(x0，y0)=（B）A、xyxfyxxfx),(),2(lim00000B、xyxxfyxfx),(),(lim00000C、xyxfyyxxfx),(),(lim00000D、0000),(),(limxxyxfyxfx解：根据偏导数定义知选项C 和 D 显然错误选项 A 中，xyxfyxxfx),(),2(lim00000=),(22),(),2(lim20000000yxfxyxfyxxfxx选项 B 中，文档编码:CG2F3D8B1I1 HT9W1G9C5J4 ZE1Q6R2J10Y2文档编码:CG2F3D8B1I1 HT9W1G9C5J4 ZE1Q6R
13、2J10Y2文档编码:CG2F3D8B1I1 HT9W1G9C5J4 ZE1Q6R2J10Y2文档编码:CG2F3D8B1I1 HT9W1G9C5J4 ZE1Q6R2J10Y2文档编码:CG2F3D8B1I1 HT9W1G9C5J4 ZE1Q6R2J10Y2文档编码:CG2F3D8B1I1 HT9W1G9C5J4 ZE1Q6R2J10Y2文档编码:CG2F3D8B1I1 HT9W1G9C5J4 ZE1Q6R2J10Y2文档编码:CG2F3D8B1I1 HT9W1G9C5J4 ZE1Q6R2J10Y2文档编码:CG2F3D8B1I1 HT9W1G9C5J4 ZE1Q6R2J10Y2文档编码:CG
14、2F3D8B1I1 HT9W1G9C5J4 ZE1Q6R2J10Y2文档编码:CG2F3D8B1I1 HT9W1G9C5J4 ZE1Q6R2J10Y2文档编码:CG2F3D8B1I1 HT9W1G9C5J4 ZE1Q6R2J10Y2文档编码:CG2F3D8B1I1 HT9W1G9C5J4 ZE1Q6R2J10Y2文档编码:CG2F3D8B1I1 HT9W1G9C5J4 ZE1Q6R2J10Y2文档编码:CG2F3D8B1I1 HT9W1G9C5J4 ZE1Q6R2J10Y2文档编码:CG2F3D8B1I1 HT9W1G9C5J4 ZE1Q6R2J10Y2文档编码:CG2F3D8B1I1 HT9
15、W1G9C5J4 ZE1Q6R2J10Y2文档编码:CG2F3D8B1I1 HT9W1G9C5J4 ZE1Q6R2J10Y2文档编码:CG2F3D8B1I1 HT9W1G9C5J4 ZE1Q6R2J10Y2文档编码:CG2F3D8B1I1 HT9W1G9C5J4 ZE1Q6R2J10Y2文档编码:CG2F3D8B1I1 HT9W1G9C5J4 ZE1Q6R2J10Y2文档编码:CG2F3D8B1I1 HT9W1G9C5J4 ZE1Q6R2J10Y2文档编码:CG2F3D8B1I1 HT9W1G9C5J4 ZE1Q6R2J10Y2文档编码:CG2F3D8B1I1 HT9W1G9C5J4 ZE1Q
16、6R2J10Y2文档编码:CG2F3D8B1I1 HT9W1G9C5J4 ZE1Q6R2J10Y2文档编码:CG2F3D8B1I1 HT9W1G9C5J4 ZE1Q6R2J10Y2文档编码:CG2F3D8B1I1 HT9W1G9C5J4 ZE1Q6R2J10Y2文档编码:CG2F3D8B1I1 HT9W1G9C5J4 ZE1Q6R2J10Y2文档编码:CG2F3D8B1I1 HT9W1G9C5J4 ZE1Q6R2J10Y2文档编码:CG2F3D8B1I1 HT9W1G9C5J4 ZE1Q6R2J10Y2文档编码:CG2F3D8B1I1 HT9W1G9C5J4 ZE1Q6R2J10Y2文档编码:
17、CG2F3D8B1I1 HT9W1G9C5J4 ZE1Q6R2J10Y2文档编码:CG2F3D8B1I1 HT9W1G9C5J4 ZE1Q6R2J10Y2文档编码:CG2F3D8B1I1 HT9W1G9C5J4 ZE1Q6R2J10Y2文档编码:CG2F3D8B1I1 HT9W1G9C5J4 ZE1Q6R2J10Y2文档编码:CG2F3D8B1I1 HT9W1G9C5J4 ZE1Q6R2J10Y2文档编码:CG2F3D8B1I1 HT9W1G9C5J4 ZE1Q6R2J10Y2文档编码:CG2F3D8B1I1 HT9W1G9C5J4 ZE1Q6R2J10Y2文档编码:CG2F3D8B1I1 H
18、T9W1G9C5J4 ZE1Q6R2J10Y2文档编码:CG2F3D8B1I1 HT9W1G9C5J4 ZE1Q6R2J10Y2文档编码:CG2F3D8B1I1 HT9W1G9C5J4 ZE1Q6R2J10Y2文档编码:CG2F3D8B1I1 HT9W1G9C5J4 ZE1Q6R2J10Y2文档编码:CG2F3D8B1I1 HT9W1G9C5J4 ZE1Q6R2J10Y2文档编码:CG2F3D8B1I1 HT9W1G9C5J4 ZE1Q6R2J10Y2文档编码:CG2F3D8B1I1 HT9W1G9C5J4 ZE1Q6R2J10Y2文档编码:CG2F3D8B1I1 HT9W1G9C5J4 ZE
19、1Q6R2J10Y2文档编码:CG2F3D8B1I1 HT9W1G9C5J4 ZE1Q6R2J10Y2文档编码:CG2F3D8B1I1 HT9W1G9C5J4 ZE1Q6R2J10Y2xyxxfyxfx),(),(lim00000=),(),(),(lim0000000yxfxyxfyxxfxx14、二元函数z=f(x,y)的两个偏导数存在，且0,0yzxz，则（D）A、当 y 保持不变时，f(x,y)是随 x 的减少而单调增加的B、当 x 保持不变时，f(x,y)是随 y 的增加而单调增加的C、当 y 保持不变时，f(x,y)是随 x 的增加而单调减少的D、当 x 保持不变时，f(x,y)是
20、随 y 的增加而单调减少的解：由0 xz知当 y 保持不变时，f(x,y)是 x 的单调增加函数；由0yz知当 x 保持不变时，f(x,y)是 y 的单调减少函数；15、函数 z=f(x,y)在点（x0,y0）处可微的充分条件是（D）A、f(x,y)在点(x0,y0)处连续B、f(x,y)在点(x0,y0)处存在偏导数C、0),(),(lim00000yyxfxyxfzyxD、0),(),(lim00000yyxfxyxfzyx，其中22)()(yx解：二元函数在点（x0,y0）连续或偏导数存在均不能保证在此点可微由全徽分的定义知选项D 正确16、已知函数22),(yxyxyxf，则yyxfx
21、yxf),(),(（B）A、2x-2y B、x+y C、2x+2y D、x-y 解：设 u=x+y，v=x-y，则 f(u，v)=uv，从而 f(x，y)=xy yyxfxyxf),(),(17、已知函数xyyxyxxyf22),(，则yyxfxyxf),(,),(分别为（A）A、-1，2y B、2y，-1 C、2x+2y，2y+x D、2y，2x 解：设 u=xy,v=x+y，则 f(u，v)=(x+y)2-xy=v2-u 所以 f(x，y)=y2-x 18、点),(00yx使0),(yxfx且0),(yxfy成立，则（D）文档编码:CG2F3D8B1I1 HT9W1G9C5J4 ZE1Q6
22、R2J10Y2文档编码:CG2F3D8B1I1 HT9W1G9C5J4 ZE1Q6R2J10Y2文档编码:CG2F3D8B1I1 HT9W1G9C5J4 ZE1Q6R2J10Y2文档编码:CG2F3D8B1I1 HT9W1G9C5J4 ZE1Q6R2J10Y2文档编码:CG2F3D8B1I1 HT9W1G9C5J4 ZE1Q6R2J10Y2文档编码:CG2F3D8B1I1 HT9W1G9C5J4 ZE1Q6R2J10Y2文档编码:CG2F3D8B1I1 HT9W1G9C5J4 ZE1Q6R2J10Y2文档编码:CG2F3D8B1I1 HT9W1G9C5J4 ZE1Q6R2J10Y2文档编码:C
23、G2F3D8B1I1 HT9W1G9C5J4 ZE1Q6R2J10Y2文档编码:CG2F3D8B1I1 HT9W1G9C5J4 ZE1Q6R2J10Y2文档编码:CG2F3D8B1I1 HT9W1G9C5J4 ZE1Q6R2J10Y2文档编码:CG2F3D8B1I1 HT9W1G9C5J4 ZE1Q6R2J10Y2文档编码:CG2F3D8B1I1 HT9W1G9C5J4 ZE1Q6R2J10Y2文档编码:CG2F3D8B1I1 HT9W1G9C5J4 ZE1Q6R2J10Y2文档编码:CG2F3D8B1I1 HT9W1G9C5J4 ZE1Q6R2J10Y2文档编码:CG2F3D8B1I1 HT
24、9W1G9C5J4 ZE1Q6R2J10Y2文档编码:CG2F3D8B1I1 HT9W1G9C5J4 ZE1Q6R2J10Y2文档编码:CG2F3D8B1I1 HT9W1G9C5J4 ZE1Q6R2J10Y2文档编码:CG2F3D8B1I1 HT9W1G9C5J4 ZE1Q6R2J10Y2文档编码:CG2F3D8B1I1 HT9W1G9C5J4 ZE1Q6R2J10Y2文档编码:CG2F3D8B1I1 HT9W1G9C5J4 ZE1Q6R2J10Y2文档编码:CG2F3D8B1I1 HT9W1G9C5J4 ZE1Q6R2J10Y2文档编码:CG2F3D8B1I1 HT9W1G9C5J4 ZE1
25、Q6R2J10Y2文档编码:CG2F3D8B1I1 HT9W1G9C5J4 ZE1Q6R2J10Y2文档编码:CG2F3D8B1I1 HT9W1G9C5J4 ZE1Q6R2J10Y2文档编码:CG2F3D8B1I1 HT9W1G9C5J4 ZE1Q6R2J10Y2文档编码:CG2F3D8B1I1 HT9W1G9C5J4 ZE1Q6R2J10Y2文档编码:CG2F3D8B1I1 HT9W1G9C5J4 ZE1Q6R2J10Y2文档编码:CG2F3D8B1I1 HT9W1G9C5J4 ZE1Q6R2J10Y2文档编码:CG2F3D8B1I1 HT9W1G9C5J4 ZE1Q6R2J10Y2文档编码
26、:CG2F3D8B1I1 HT9W1G9C5J4 ZE1Q6R2J10Y2文档编码:CG2F3D8B1I1 HT9W1G9C5J4 ZE1Q6R2J10Y2文档编码:CG2F3D8B1I1 HT9W1G9C5J4 ZE1Q6R2J10Y2文档编码:CG2F3D8B1I1 HT9W1G9C5J4 ZE1Q6R2J10Y2文档编码:CG2F3D8B1I1 HT9W1G9C5J4 ZE1Q6R2J10Y2文档编码:CG2F3D8B1I1 HT9W1G9C5J4 ZE1Q6R2J10Y2文档编码:CG2F3D8B1I1 HT9W1G9C5J4 ZE1Q6R2J10Y2文档编码:CG2F3D8B1I1
27、HT9W1G9C5J4 ZE1Q6R2J10Y2文档编码:CG2F3D8B1I1 HT9W1G9C5J4 ZE1Q6R2J10Y2文档编码:CG2F3D8B1I1 HT9W1G9C5J4 ZE1Q6R2J10Y2文档编码:CG2F3D8B1I1 HT9W1G9C5J4 ZE1Q6R2J10Y2文档编码:CG2F3D8B1I1 HT9W1G9C5J4 ZE1Q6R2J10Y2文档编码:CG2F3D8B1I1 HT9W1G9C5J4 ZE1Q6R2J10Y2文档编码:CG2F3D8B1I1 HT9W1G9C5J4 ZE1Q6R2J10Y2文档编码:CG2F3D8B1I1 HT9W1G9C5J4 Z
28、E1Q6R2J10Y2文档编码:CG2F3D8B1I1 HT9W1G9C5J4 ZE1Q6R2J10Y2文档编码:CG2F3D8B1I1 HT9W1G9C5J4 ZE1Q6R2J10Y2文档编码:CG2F3D8B1I1 HT9W1G9C5J4 ZE1Q6R2J10Y2A、),(00yx是),(yxf的极值点B、),(00yx是),(yxf的最小值点C、),(00yx是),(yxf的最大值点D、),(00yx可能是),(yxf的极值点解：0),(yxfx且0),(yxfy是),(yxf在),(00yx有极值的必要而非充分条件19、设区域D 是单位圆122yx在第一象限的部分，则二重积分Dxyd（
29、C）A、221010 xyxydydxB、21010yxydydxC、21010yxydxdyD、102202sin21drrd解：在直解坐标系下：2210101010 xyDxydydxxydxdyxyd在极坐标系下：103201020cossinsincosdrdrdrrrdxydD20、1010),(xdyyxfdx（D）A、xdxyxfdy1010),(B、1010),(dxyxfdyC、1010),(xdxyxfdyD、1010),(ydxyxfdy解：改变积分次序后，积分区域可记为10,10|),(yxyyxD21、若Ddxdy1，则积分区域D 可以是（C）A、由 x 轴，y 轴及
30、 x+y-2=0 所围成的区域B、由 x=1，x=2 及 y=2，y=4 所围成的区域C、由|x|=1/2，|y|=1/2 所围成的区域D、由|x+y|=1，|x-y|=1 所围成的区域解：由二重积分的几何意义可知 D 的面积为1，画出草图可知选项A、B、D 所给区域面积均为 2，选项 C 所给区域的面积为1 二、填空题：1、微分方程0yyx满足条件1)1(y的解是（xy1）2、微分方程0)1()1(dyxdxy的通解是（Cyx)1)(1(）文档编码:CG2F3D8B1I1 HT9W1G9C5J4 ZE1Q6R2J10Y2文档编码:CG2F3D8B1I1 HT9W1G9C5J4 ZE1Q6R2
31、J10Y2文档编码:CG2F3D8B1I1 HT9W1G9C5J4 ZE1Q6R2J10Y2文档编码:CG2F3D8B1I1 HT9W1G9C5J4 ZE1Q6R2J10Y2文档编码:CG2F3D8B1I1 HT9W1G9C5J4 ZE1Q6R2J10Y2文档编码:CG2F3D8B1I1 HT9W1G9C5J4 ZE1Q6R2J10Y2文档编码:CG2F3D8B1I1 HT9W1G9C5J4 ZE1Q6R2J10Y2文档编码:CG2F3D8B1I1 HT9W1G9C5J4 ZE1Q6R2J10Y2文档编码:CG2F3D8B1I1 HT9W1G9C5J4 ZE1Q6R2J10Y2文档编码:CG2
32、F3D8B1I1 HT9W1G9C5J4 ZE1Q6R2J10Y2文档编码:CG2F3D8B1I1 HT9W1G9C5J4 ZE1Q6R2J10Y2文档编码:CG2F3D8B1I1 HT9W1G9C5J4 ZE1Q6R2J10Y2文档编码:CG2F3D8B1I1 HT9W1G9C5J4 ZE1Q6R2J10Y2文档编码:CG2F3D8B1I1 HT9W1G9C5J4 ZE1Q6R2J10Y2文档编码:CG2F3D8B1I1 HT9W1G9C5J4 ZE1Q6R2J10Y2文档编码:CG2F3D8B1I1 HT9W1G9C5J4 ZE1Q6R2J10Y2文档编码:CG2F3D8B1I1 HT9W
33、1G9C5J4 ZE1Q6R2J10Y2文档编码:CG2F3D8B1I1 HT9W1G9C5J4 ZE1Q6R2J10Y2文档编码:CG2F3D8B1I1 HT9W1G9C5J4 ZE1Q6R2J10Y2文档编码:CG2F3D8B1I1 HT9W1G9C5J4 ZE1Q6R2J10Y2文档编码:CG2F3D8B1I1 HT9W1G9C5J4 ZE1Q6R2J10Y2文档编码:CG2F3D8B1I1 HT9W1G9C5J4 ZE1Q6R2J10Y2文档编码:CG2F3D8B1I1 HT9W1G9C5J4 ZE1Q6R2J10Y2文档编码:CG2F3D8B1I1 HT9W1G9C5J4 ZE1Q6
34、R2J10Y2文档编码:CG2F3D8B1I1 HT9W1G9C5J4 ZE1Q6R2J10Y2文档编码:CG2F3D8B1I1 HT9W1G9C5J4 ZE1Q6R2J10Y2文档编码:CG2F3D8B1I1 HT9W1G9C5J4 ZE1Q6R2J10Y2文档编码:CG2F3D8B1I1 HT9W1G9C5J4 ZE1Q6R2J10Y2文档编码:CG2F3D8B1I1 HT9W1G9C5J4 ZE1Q6R2J10Y2文档编码:CG2F3D8B1I1 HT9W1G9C5J4 ZE1Q6R2J10Y2文档编码:CG2F3D8B1I1 HT9W1G9C5J4 ZE1Q6R2J10Y2文档编码:C
35、G2F3D8B1I1 HT9W1G9C5J4 ZE1Q6R2J10Y2文档编码:CG2F3D8B1I1 HT9W1G9C5J4 ZE1Q6R2J10Y2文档编码:CG2F3D8B1I1 HT9W1G9C5J4 ZE1Q6R2J10Y2文档编码:CG2F3D8B1I1 HT9W1G9C5J4 ZE1Q6R2J10Y2文档编码:CG2F3D8B1I1 HT9W1G9C5J4 ZE1Q6R2J10Y2文档编码:CG2F3D8B1I1 HT9W1G9C5J4 ZE1Q6R2J10Y2文档编码:CG2F3D8B1I1 HT9W1G9C5J4 ZE1Q6R2J10Y2文档编码:CG2F3D8B1I1 HT
36、9W1G9C5J4 ZE1Q6R2J10Y2文档编码:CG2F3D8B1I1 HT9W1G9C5J4 ZE1Q6R2J10Y2文档编码:CG2F3D8B1I1 HT9W1G9C5J4 ZE1Q6R2J10Y2文档编码:CG2F3D8B1I1 HT9W1G9C5J4 ZE1Q6R2J10Y2文档编码:CG2F3D8B1I1 HT9W1G9C5J4 ZE1Q6R2J10Y2文档编码:CG2F3D8B1I1 HT9W1G9C5J4 ZE1Q6R2J10Y2文档编码:CG2F3D8B1I1 HT9W1G9C5J4 ZE1Q6R2J10Y2文档编码:CG2F3D8B1I1 HT9W1G9C5J4 ZE1
37、Q6R2J10Y2文档编码:CG2F3D8B1I1 HT9W1G9C5J4 ZE1Q6R2J10Y2文档编码:CG2F3D8B1I1 HT9W1G9C5J4 ZE1Q6R2J10Y2解：xdxydy11，于是Cxyln)1ln()1ln(8、设yxz，则 dz=(dyyxydxxyxy222)4、yydxyxfdydxyxfdy0202110),(),(交换二次积分的次序为（102),(xxdyyxfdx）5、已知)2,2,1(),4,1,1(ba，则ba（-9），a与b的夹角为（43）6、二元函数yxz的定义域是（222(,)|24,Dx yxyxy）。三、计算题1、求级数7538642xx
38、xx的收敛域，并求和函数。解：122)(nnnxxa212121|2)22(lim)()(limxnxxnxaxannnnnn当1|2x即1|x时收敛，当1|2x即1|x时发散当 x=1 时，原级数为12nn发散，当x=1 时，原级数为1)2(nn发散所收敛域为（1，1）令1122)(nnnxxS，则 S（0）=0 xnxnnnxxxxdtntdttS010122212)1|(|12)()1|(|)1(21)(2222xxxxxxS2、将函数xexxf3)(展开成 x 的幂级数。参考答案：解：1!nnxnxe),(x1!)1(nnnxnxe),(x文档编码:CG2F3D8B1I1 HT9W1G
39、9C5J4 ZE1Q6R2J10Y2文档编码:CG2F3D8B1I1 HT9W1G9C5J4 ZE1Q6R2J10Y2文档编码:CG2F3D8B1I1 HT9W1G9C5J4 ZE1Q6R2J10Y2文档编码:CG2F3D8B1I1 HT9W1G9C5J4 ZE1Q6R2J10Y2文档编码:CG2F3D8B1I1 HT9W1G9C5J4 ZE1Q6R2J10Y2文档编码:CG2F3D8B1I1 HT9W1G9C5J4 ZE1Q6R2J10Y2文档编码:CG2F3D8B1I1 HT9W1G9C5J4 ZE1Q6R2J10Y2文档编码:CG2F3D8B1I1 HT9W1G9C5J4 ZE1Q6R2
40、J10Y2文档编码:CG2F3D8B1I1 HT9W1G9C5J4 ZE1Q6R2J10Y2文档编码:CG2F3D8B1I1 HT9W1G9C5J4 ZE1Q6R2J10Y2文档编码:CG2F3D8B1I1 HT9W1G9C5J4 ZE1Q6R2J10Y2文档编码:CG2F3D8B1I1 HT9W1G9C5J4 ZE1Q6R2J10Y2文档编码:CG2F3D8B1I1 HT9W1G9C5J4 ZE1Q6R2J10Y2文档编码:CG2F3D8B1I1 HT9W1G9C5J4 ZE1Q6R2J10Y2文档编码:CG2F3D8B1I1 HT9W1G9C5J4 ZE1Q6R2J10Y2文档编码:CG2
41、F3D8B1I1 HT9W1G9C5J4 ZE1Q6R2J10Y2文档编码:CG2F3D8B1I1 HT9W1G9C5J4 ZE1Q6R2J10Y2文档编码:CG2F3D8B1I1 HT9W1G9C5J4 ZE1Q6R2J10Y2文档编码:CG2F3D8B1I1 HT9W1G9C5J4 ZE1Q6R2J10Y2文档编码:CG2F3D8B1I1 HT9W1G9C5J4 ZE1Q6R2J10Y2文档编码:CG2F3D8B1I1 HT9W1G9C5J4 ZE1Q6R2J10Y2文档编码:CG2F3D8B1I1 HT9W1G9C5J4 ZE1Q6R2J10Y2文档编码:CG2F3D8B1I1 HT9W
42、1G9C5J4 ZE1Q6R2J10Y2文档编码:CG2F3D8B1I1 HT9W1G9C5J4 ZE1Q6R2J10Y2文档编码:CG2F3D8B1I1 HT9W1G9C5J4 ZE1Q6R2J10Y2文档编码:CG2F3D8B1I1 HT9W1G9C5J4 ZE1Q6R2J10Y2文档编码:CG2F3D8B1I1 HT9W1G9C5J4 ZE1Q6R2J10Y2文档编码:CG2F3D8B1I1 HT9W1G9C5J4 ZE1Q6R2J10Y2文档编码:CG2F3D8B1I1 HT9W1G9C5J4 ZE1Q6R2J10Y2文档编码:CG2F3D8B1I1 HT9W1G9C5J4 ZE1Q6
43、R2J10Y2文档编码:CG2F3D8B1I1 HT9W1G9C5J4 ZE1Q6R2J10Y2文档编码:CG2F3D8B1I1 HT9W1G9C5J4 ZE1Q6R2J10Y2文档编码:CG2F3D8B1I1 HT9W1G9C5J4 ZE1Q6R2J10Y2文档编码:CG2F3D8B1I1 HT9W1G9C5J4 ZE1Q6R2J10Y2文档编码:CG2F3D8B1I1 HT9W1G9C5J4 ZE1Q6R2J10Y2文档编码:CG2F3D8B1I1 HT9W1G9C5J4 ZE1Q6R2J10Y2文档编码:CG2F3D8B1I1 HT9W1G9C5J4 ZE1Q6R2J10Y2文档编码:C
44、G2F3D8B1I1 HT9W1G9C5J4 ZE1Q6R2J10Y2文档编码:CG2F3D8B1I1 HT9W1G9C5J4 ZE1Q6R2J10Y2文档编码:CG2F3D8B1I1 HT9W1G9C5J4 ZE1Q6R2J10Y2文档编码:CG2F3D8B1I1 HT9W1G9C5J4 ZE1Q6R2J10Y2文档编码:CG2F3D8B1I1 HT9W1G9C5J4 ZE1Q6R2J10Y2文档编码:CG2F3D8B1I1 HT9W1G9C5J4 ZE1Q6R2J10Y2文档编码:CG2F3D8B1I1 HT9W1G9C5J4 ZE1Q6R2J10Y2文档编码:CG2F3D8B1I1 HT
45、9W1G9C5J4 ZE1Q6R2J10Y2文档编码:CG2F3D8B1I1 HT9W1G9C5J4 ZE1Q6R2J10Y2文档编码:CG2F3D8B1I1 HT9W1G9C5J4 ZE1Q6R2J10Y2文档编码:CG2F3D8B1I1 HT9W1G9C5J4 ZE1Q6R2J10Y2从而133!)1()(nnnxnxexxf),(x3、级数2ln11nnn是否收敛？如果收敛，是绝对收敛还是条件收敛？参考答案：解：因nnn1ln1|u|，而21nn发散，故2ln1nn发散。因此原级数不是绝对收敛，显然nnln11ln1，,3,2n，且0ln1limnn，故由莱布尼兹判别法知原级数条件收敛。
46、4、已知1,1,4a（），1,2,2b（），求a在b上的投影。参考答案：1 1 1(2)(4)2=-9a b|PrPr3|bba ba bbj aj ab5、设sinuzev，而uxy，vxy求zx。参考答案：zzuz vxuxvxsincosuuyevev(sin()cos()xyeyxyxy6、(2,1)xyze计算函数在点处的全微分。参考答案：22(2,1)(2,1),2,xyxyzzzzyexeeexyxy所求全微分222dze dxe dy文档编码:CG2F3D8B1I1 HT9W1G9C5J4 ZE1Q6R2J10Y2文档编码:CG2F3D8B1I1 HT9W1G9C5J4 ZE1
47、Q6R2J10Y2文档编码:CG2F3D8B1I1 HT9W1G9C5J4 ZE1Q6R2J10Y2文档编码:CG2F3D8B1I1 HT9W1G9C5J4 ZE1Q6R2J10Y2文档编码:CG2F3D8B1I1 HT9W1G9C5J4 ZE1Q6R2J10Y2文档编码:CG2F3D8B1I1 HT9W1G9C5J4 ZE1Q6R2J10Y2文档编码:CG2F3D8B1I1 HT9W1G9C5J4 ZE1Q6R2J10Y2文档编码:CG2F3D8B1I1 HT9W1G9C5J4 ZE1Q6R2J10Y2文档编码:CG2F3D8B1I1 HT9W1G9C5J4 ZE1Q6R2J10Y2文档编码
48、:CG2F3D8B1I1 HT9W1G9C5J4 ZE1Q6R2J10Y2文档编码:CG2F3D8B1I1 HT9W1G9C5J4 ZE1Q6R2J10Y2文档编码:CG2F3D8B1I1 HT9W1G9C5J4 ZE1Q6R2J10Y2文档编码:CG2F3D8B1I1 HT9W1G9C5J4 ZE1Q6R2J10Y2文档编码:CG2F3D8B1I1 HT9W1G9C5J4 ZE1Q6R2J10Y2文档编码:CG2F3D8B1I1 HT9W1G9C5J4 ZE1Q6R2J10Y2文档编码:CG2F3D8B1I1 HT9W1G9C5J4 ZE1Q6R2J10Y2文档编码:CG2F3D8B1I1
49、HT9W1G9C5J4 ZE1Q6R2J10Y2文档编码:CG2F3D8B1I1 HT9W1G9C5J4 ZE1Q6R2J10Y2文档编码:CG2F3D8B1I1 HT9W1G9C5J4 ZE1Q6R2J10Y2文档编码:CG2F3D8B1I1 HT9W1G9C5J4 ZE1Q6R2J10Y2文档编码:CG2F3D8B1I1 HT9W1G9C5J4 ZE1Q6R2J10Y2文档编码:CG2F3D8B1I1 HT9W1G9C5J4 ZE1Q6R2J10Y2文档编码:CG2F3D8B1I1 HT9W1G9C5J4 ZE1Q6R2J10Y2文档编码:CG2F3D8B1I1 HT9W1G9C5J4 Z
50、E1Q6R2J10Y2文档编码:CG2F3D8B1I1 HT9W1G9C5J4 ZE1Q6R2J10Y2文档编码:CG2F3D8B1I1 HT9W1G9C5J4 ZE1Q6R2J10Y2文档编码:CG2F3D8B1I1 HT9W1G9C5J4 ZE1Q6R2J10Y2文档编码:CG2F3D8B1I1 HT9W1G9C5J4 ZE1Q6R2J10Y2文档编码:CG2F3D8B1I1 HT9W1G9C5J4 ZE1Q6R2J10Y2文档编码:CG2F3D8B1I1 HT9W1G9C5J4 ZE1Q6R2J10Y2文档编码:CG2F3D8B1I1 HT9W1G9C5J4 ZE1Q6R2J10Y2文档