绝密★启用前
2017年宁夏大学成人继续教育函授班考试
高等数学（一）
答案必须答在答题卡上指定的位置，答在试卷上无效。
一、选择题：1～10小题，每题5分，共40分。在每小题给出的四个选项中，只有一项是符合题目要求的。
1. ![](https://wkrtcs.bdimg.com/rtcs/image?w=109.33&md5sum=80d5ea75d2a3fd3df9e3cb455b74ddd5&sign=440cf5e296&rtcs_flag=2&rtcs_ver=3.2&l=webapp&bucketNum=84&ipr={"t":"img","w":"109.33","h":"44.00","dataType":"gif","c":"word/media/image1.gif"})
A. ![](https://wkrtcs.bdimg.com/rtcs/image?w=13.33&md5sum=80d5ea75d2a3fd3df9e3cb455b74ddd5&sign=440cf5e296&rtcs_flag=2&rtcs_ver=3.2&l=webapp&bucketNum=84&ipr={"t":"img","r":"r_1","w":"13.33","h":"20.00","dataType":"gif","c":"word/media/image2.gif"})
B. C. D.
2.设![](https://wkrtcs.bdimg.com/rtcs/image?w=44.00&md5sum=80d5ea75d2a3fd3df9e3cb455b74ddd5&sign=440cf5e296&rtcs_flag=2&rtcs_ver=3.2&l=webapp&bucketNum=84&ipr={"t":"img","w":"44.00","h":"24.00","dataType":"gif","c":"word/media/image6.gif"})
，则
A. ![](https://wkrtcs.bdimg.com/rtcs/image?w=29.33&md5sum=80d5ea75d2a3fd3df9e3cb455b74ddd5&sign=440cf5e296&rtcs_flag=2&rtcs_ver=3.2&l=webapp&bucketNum=84&ipr={"t":"img","r":"r_1","w":"29.33","h":"41.33","dataType":"gif","c":"word/media/image8.gif"})
B. C. D.
3.设![](https://wkrtcs.bdimg.com/rtcs/image?w=76.00&md5sum=80d5ea75d2a3fd3df9e3cb455b74ddd5&sign=440cf5e296&rtcs_flag=2&rtcs_ver=3.2&l=webapp&bucketNum=84&ipr={"t":"img","w":"76.00","h":"21.33","dataType":"gif","c":"word/media/image12.gif"})
，则
A. ![](https://wkrtcs.bdimg.com/rtcs/image?w=65.33&md5sum=80d5ea75d2a3fd3df9e3cb455b74ddd5&sign=440cf5e296&rtcs_flag=2&rtcs_ver=3.2&l=webapp&bucketNum=84&ipr={"t":"img","r":"r_1","w":"65.33","h":"24.00","dataType":"gif","c":"word/media/image14.gif"})
B.
C. ![](https://wkrtcs.bdimg.com/rtcs/image?w=33.33&md5sum=80d5ea75d2a3fd3df9e3cb455b74ddd5&sign=440cf5e296&rtcs_flag=2&rtcs_ver=3.2&l=webapp&bucketNum=84&ipr={"t":"img","r":"r_1","w":"33.33","h":"41.33","dataType":"gif","c":"word/media/image16.gif"})
D.
4.设![](https://wkrtcs.bdimg.com/rtcs/image?w=60.00&md5sum=80d5ea75d2a3fd3df9e3cb455b74ddd5&sign=440cf5e296&rtcs_flag=2&rtcs_ver=3.2&l=webapp&bucketNum=84&ipr={"t":"img","w":"60.00","h":"21.33","dataType":"gif","c":"word/media/image18.gif"})
，则
A. ![](https://wkrtcs.bdimg.com/rtcs/image?w=45.33&md5sum=80d5ea75d2a3fd3df9e3cb455b74ddd5&sign=440cf5e296&rtcs_flag=2&rtcs_ver=3.2&l=webapp&bucketNum=84&ipr={"t":"img","r":"r_1","w":"45.33","h":"20.00","dataType":"gif","c":"word/media/image20.gif"})
B.
C. ![](https://wkrtcs.bdimg.com/rtcs/image?w=48.00&md5sum=80d5ea75d2a3fd3df9e3cb455b74ddd5&sign=440cf5e296&rtcs_flag=2&rtcs_ver=3.2&l=webapp&bucketNum=84&ipr={"t":"img","r":"r_1","w":"48.00","h":"14.67","dataType":"gif","c":"word/media/image22.gif"})
D.
5. ![](https://wkrtcs.bdimg.com/rtcs/image?w=58.67&md5sum=80d5ea75d2a3fd3df9e3cb455b74ddd5&sign=440cf5e296&rtcs_flag=2&rtcs_ver=3.2&l=webapp&bucketNum=84&ipr={"t":"img","w":"58.67","h":"29.33","dataType":"gif","c":"word/media/image24.gif"})
A. ![](https://wkrtcs.bdimg.com/rtcs/image?w=45.33&md5sum=80d5ea75d2a3fd3df9e3cb455b74ddd5&sign=440cf5e296&rtcs_flag=2&rtcs_ver=3.2&l=webapp&bucketNum=84&ipr={"t":"img","r":"r_1","w":"45.33","h":"21.33","dataType":"gif","c":"word/media/image25.gif"})
B. C. D.
6. ![](https://wkrtcs.bdimg.com/rtcs/image?w=64.00&md5sum=80d5ea75d2a3fd3df9e3cb455b74ddd5&sign=440cf5e296&rtcs_flag=2&rtcs_ver=3.2&l=webapp&bucketNum=84&ipr={"t":"img","w":"64.00","h":"34.67","dataType":"gif","c":"word/media/image29.gif"})
A. ![](https://wkrtcs.bdimg.com/rtcs/image?w=16.00&md5sum=80d5ea75d2a3fd3df9e3cb455b74ddd5&sign=440cf5e296&rtcs_flag=2&rtcs_ver=3.2&l=webapp&bucketNum=84&ipr={"t":"img","r":"r_1","w":"16.00","h":"41.33","dataType":"gif","c":"word/media/image30.gif"})
B.
C. ![](https://wkrtcs.bdimg.com/rtcs/image?w=14.67&md5sum=80d5ea75d2a3fd3df9e3cb455b74ddd5&sign=440cf5e296&rtcs_flag=2&rtcs_ver=3.2&l=webapp&bucketNum=84&ipr={"t":"img","r":"r_1","w":"14.67","h":"41.33","dataType":"gif","c":"word/media/image32.gif"})
D.
7.在空间直角坐标系中，方程![](https://wkrtcs.bdimg.com/rtcs/image?w=70.67&md5sum=80d5ea75d2a3fd3df9e3cb455b74ddd5&sign=440cf5e296&rtcs_flag=2&rtcs_ver=3.2&l=webapp&bucketNum=84&ipr={"t":"img","w":"70.67","h":"24.00","dataType":"gif","c":"word/media/image33.gif"})
表示的曲面是
A. 柱面 B. 球面 C. 锥面 D. 旋转抛物面
8.设![](https://wkrtcs.bdimg.com/rtcs/image?w=74.67&md5sum=80d5ea75d2a3fd3df9e3cb455b74ddd5&sign=440cf5e296&rtcs_flag=2&rtcs_ver=3.2&l=webapp&bucketNum=84&ipr={"t":"img","w":"74.67","h":"24.00","dataType":"gif","c":"word/media/image34.gif"})
，则
A. ![](https://wkrtcs.bdimg.com/rtcs/image?w=81.33&md5sum=80d5ea75d2a3fd3df9e3cb455b74ddd5&sign=440cf5e296&rtcs_flag=2&rtcs_ver=3.2&l=webapp&bucketNum=84&ipr={"t":"img","r":"r_1","w":"81.33","h":"21.33","dataType":"gif","c":"word/media/image36.gif"})
B.
C. ![](https://wkrtcs.bdimg.com/rtcs/image?w=73.33&md5sum=80d5ea75d2a3fd3df9e3cb455b74ddd5&sign=440cf5e296&rtcs_flag=2&rtcs_ver=3.2&l=webapp&bucketNum=84&ipr={"t":"img","r":"r_1","w":"73.33","h":"21.33","dataType":"gif","c":"word/media/image38.gif"})
D.
二、填空题：9～13小题，每小题5分，共30分。
9. ![](https://wkrtcs.bdimg.com/rtcs/image?w=86.67&md5sum=80d5ea75d2a3fd3df9e3cb455b74ddd5&sign=440cf5e296&rtcs_flag=2&rtcs_ver=3.2&l=webapp&bucketNum=84&ipr={"t":"img","w":"86.67","h":"41.33","dataType":"gif","c":"word/media/image40.gif"})
______.
10.设![](https://wkrtcs.bdimg.com/rtcs/image?w=48.00&md5sum=80d5ea75d2a3fd3df9e3cb455b74ddd5&sign=440cf5e296&rtcs_flag=2&rtcs_ver=3.2&l=webapp&bucketNum=84&ipr={"t":"img","w":"48.00","h":"24.00","dataType":"gif","c":"word/media/image41.gif"})
，则______.
11.函数![](https://wkrtcs.bdimg.com/rtcs/image?w=78.67&md5sum=80d5ea75d2a3fd3df9e3cb455b74ddd5&sign=440cf5e296&rtcs_flag=2&rtcs_ver=3.2&l=webapp&bucketNum=84&ipr={"t":"img","w":"78.67","h":"41.33","dataType":"gif","c":"word/media/image43.gif"})
的二阶导数为______.
12.11.向量![](https://wkrtcs.bdimg.com/rtcs/image?w=80.00&md5sum=80d5ea75d2a3fd3df9e3cb455b74ddd5&sign=440cf5e296&rtcs_flag=2&rtcs_ver=3.2&l=webapp&bucketNum=84&ipr={"t":"img","w":"80.00","h":"21.33","dataType":"gif","c":"word/media/image44.gif"})
的模为______.
13. ![](https://wkrtcs.bdimg.com/rtcs/image?w=61.33&md5sum=80d5ea75d2a3fd3df9e3cb455b74ddd5&sign=440cf5e296&rtcs_flag=2&rtcs_ver=3.2&l=webapp&bucketNum=84&ipr={"t":"img","w":"61.33","h":"34.67","dataType":"gif","c":"word/media/image45.gif"})
______.
三、解答题：14～16题，共30分。
14.（本题满分5分）
求幂级数![](https://wkrtcs.bdimg.com/rtcs/image?w=41.33&md5sum=80d5ea75d2a3fd3df9e3cb455b74ddd5&sign=440cf5e296&rtcs_flag=2&rtcs_ver=3.2&l=webapp&bucketNum=84&ipr={"t":"img","w":"41.33","h":"46.67","dataType":"gif","c":"word/media/image46.gif"})
的收敛半径.
15.（本题满分5分）
求![](https://wkrtcs.bdimg.com/rtcs/image?w=76.00&md5sum=80d5ea75d2a3fd3df9e3cb455b74ddd5&sign=440cf5e296&rtcs_flag=2&rtcs_ver=3.2&l=webapp&bucketNum=84&ipr={"t":"img","w":"76.00","h":"24.00","dataType":"gif","c":"word/media/image47.gif"})
的偏导数.
16.（本题满分20分，每小题5分）
计算下列函数的三阶导数.
（1）![](https://wkrtcs.bdimg.com/rtcs/image?w=48.00&md5sum=80d5ea75d2a3fd3df9e3cb455b74ddd5&sign=440cf5e296&rtcs_flag=2&rtcs_ver=3.2&l=webapp&bucketNum=84&ipr={"t":"img","w":"48.00","h":"24.00","dataType":"gif","c":"word/media/image48.gif"})
（2）（3）（4）
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