山东大学网络远程高起专高等数学1-2-3试题答案
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高等数学模拟卷 1
一 求下列极限 1 1
lim sin n n n
→∞=0(有界量乘无穷小量)
2 求0lim x x x →=1lim 1lim {00x -=-=-+
→→x
x
x x x
3 求10
lim x
x e →=0
lim lim {
1010=∞
=-
+
→→x
x x
x e e
sin 4
lim
sin 5x x x x x
→++
=
31616155sin 5sin lim 55sin 5lim 5sin sin lim sin lim 0000=+=+++=+++→→→→x
x x x x x
x x x x x x x x x x x x x x x x (第一个重要极限)
二
a 取什么值,0
()0
x e x f x a x x ?<=?+≥?连续 答:根据函数在一点处连续的定义,)(lim )(lim 0
x f a x f x x -+→→==,而
)(lim 0
x f x -→=x x e -→0
lim =1
所以 a=1
三 计算下列各题 1
已
知
2sin ln y x x
=?
求
,
y 答:
y ’=2(sin x ·lnx )’=2[(sinx)’(lnx )+(sinx)(lnx)’] =2cosxlnx+2
x
sinx
2 ()
,()x
f x y f e e
y =?已知,求
答:由链式法则,()()()
()dx
dy e e f e e e f dx x f x x f x x +?=dy
所以()()
()
()x f x x f x x e
e f e e f y -=+1'
2 / 5
2
3
x xe dx
?求
答:
c
e dx e x d e x x x +===??2
22
2121222原式
四、若20
2tan()sec x y
x x y tdt ---=
?
,求
dy
dx
另x-y=m, y=x-m, 对两边求导数,得到dy/dx = 1 - dm/dx 将y = x-m 带回原式,再两边对x 求导。可得dm/dx 带回上式可得结果
五 求y x =,2y x =和2
y x =所围平面图形的面积
解
:
3114423014222223224110=?????
? ??-+???? ??-=??? ??-+??? ??-??y y y y dy y y dy y y
高等数学模拟卷 2
一 求下列极限
1 1
lim
cos n n n
→∞=0
2 求22lim 2x x x →--=2222lim 22lim 22lim 2x x x x x x
x x x →→→-??-?-?
--??-?
-+
=1
==-1 3 求10
lim 2x x →=1
10
100lim 2lim 2lim 20x x x x x x +-
→→→?=∞??=??=?? 0
2sin 4lim
3sin x x x x x →++求 0
2sin 3
lim
3sin 4x x x x x →++解
=
sin 0()00
x x f x x
x ?≠?=??=?
二讨论
在 x=0 处的连续性
答:因为f(x)在0点的左右极限都为1,不等于其在0点的函数值,所以f(x)
3 / 5
在0点不连续
三 计算下列各题 1 ,ln[ln(ln )]
y x y =求
,
1111
.[ln(ln )]..[ln(ln )][ln(ln )]ln y x x x x x
'==
2 ,
,y
x
x y y =求
,ln ln .ln .ln 1
.ln ln ..ln ln ln ln y x
x y y x x y
y y x y y x x y
x y y x y y x
y y x y x x y
=='+=+?
?'-=- ??
?-
'∴=
-
解:
2
2
20
100
cos lim
sin x x x t dt
x
→-?四
求
由于分子分母极限都为0,所以可以对分子分母分别求导,得到
Lim( 2x-2xcosx^4)/10sin^9(x)cosx 再对两边求导
五 求2
25y x =-和4y x =-所围平面图形的面积
{
()()225
4
23
2331
131735113
16422623
y x y x y s y dy y y y
=-=---+=+-=-+=?解:
得交点
,-,
六 2
2(1)24dy x xy x dx
++=
222
2
222()ln 11223
23
2
24(1)(1)(1)
1
()4443()43
1
x dx
p x dx
x x dy xy x x dx x x c y ce ce ce x c x x x D
c x x dx x D y x -
--++++=
++??
==
+'=+==
+∴=+?解:两边同除以得
==代入原方程得
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高等数学模拟卷3
一 求下列极限 1 1lim
n tgn n
→∞ 解:不存在 2 求lim x a x a x a →--=lim 1
lim lim 1x a x a x a x a x a x a
a x x a
x a
→→→-??-?-?
--?=-?-?+-== 3 求1
20
lim x
x e
→=1
210
21
20lim lim lim 0x x x
x x x e e
e +-
→→→?=∞??=??=?? 00sin 4
lim
lim sin x x mx mx m
nx nx n →→==
2
0()0
x x f x x
x >?=?≤?二已知
,讨论f (x )在0x =处的导数
()()()()002
0000lim lim 1
00lim lim 0()0x x x x f x f x
x x
f x f x x x
f x x ?→?→?→?→+?-?==??+?-?==??∴=Q +
+--解:在不可导
三 计算下列各题
1、3
,
tan (ln )y x y =已知求
()221
3tan (ln ).sec ln .y x x x
'=解:
2、2
,
()y f x y =已知,求
2().2y f x x ''解: =
四 2
3
2
1()()2a
a x f x dx xf x dx =?
?证明
,(0)a >,其中()f x 在
讨论的区间连续。
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22
3
2
222
0022
32
2
2
20
00
1
()()2
00,111()()()()222a
a
a
a
a a x f x dx x f x d x x u u x a u a x f x dx x f x d x u f u du xf x dx
=====∴
===???
?
??Q 证明
令=当x 时时,
五 计算反常积分2d ;1x
x +∞
-∞+?
ππ
π=+??? ??--=∞++∞-=+++=+???∞+∞-∞
+∞-2
20arctan 0arctan 1dx 1dx 1dx 02
022x x x x x 解:
六 求2
(1)(arctan )y dx y x dy +=-的通解
()()
()()()()()22
2
2
1
(arctan ).11.1111.11
111
ln 1(arctan )ln arctan 1y x u u y y u y y
y u y u
u u
du u u du dx dx u u u u x c
y x y x x c
''''-==
-=++++'++'+=
-==-+-=+---=+解:令则则原方程为=
变量分离两边同时积分得:所以原方程的通解为:+
山大网络教育英语模拟题一含答案
模拟题一 第一部分:交际用语 此部分共有5个未完成的对话,针对每个对话是未完成的部分有4个选项,请从A、B、 C、D四个选项中选出可以填入空白处的最佳选项,并用铅笔将答题卡上的相应字母涂黑。 1. — Hello! May I talk to the manager about the price —. A. Sorry, he is out at the moment B. No, you can’t C. Sorry, y ou can’t D. I don’t know 2. —I’m terribly sorry that I made your table cloth dirty. —______. A. Never mind B. Don’t mention it C. That’s right D. Sorry 3. ― Do you mind if I open the window ―______ I feel a bit cold. A. Of course not. B. I’d rather you didn’t. C. Go ahead. D. Why not 4. —Excuse me, sir. Where is Dr. Smith’s office —. A. You can’t ask me B. Good question C. Please don’t say so D. Sorry I don’t know, but you can as k the man over there 5. — Good morning, sir. May I help you —. A. No, I don’t buy anything B. No, I don’t need your help C. Yes, I need some salt D. Oh, no. That’s Ok 第二部分:阅读理解 此部分共有2篇短文,每篇短文后有5个问题。请从每个问题后的A、B、C、D四个选项中,选出可以填入空白处的最佳选项,并用铅笔将答题卡上的相应字母涂黑。 Passage 1
高等数学2(高起专)
平顶山学院 补考 课程:高等数学2(高起专)总时长:120分钟 1. (判断题) 是阶微分方程. ( )(本题3.0分) A. 正确 B. 错误 答案: B 解析: 无 2. (判断题) 非零向量满足. ( )(本题 3.0分) A. 正确 B. 错误 答案: A 解析: 无 3. (判断题) 若二元函数的两个偏导数都存在并且连续, 则二元函数一定可微. ( )(本题3.0分) A. 正确 B. 错误 答案: A 解析: 无
4. (判断题) 若,则收敛. ( )(本题3.0分) A. 正确 B. 错误 答案: B 解析: 无 5. (判断题) 若级数和都发散,则级数也发散. ( )(本题3.0分) A. 正确 B. 错误 答案: B 解析: 无 6. (填空题) 设是非零向量的方向角, 则___.(本题3.0分) 答案: (1) 1; 得分点:未设置 解析: 无 7. (填空题) 设非零向量满足,向量的位置关系是___.(本题3.0分) 答案: (1) 平行; 得分点:未设置 解析: 无 8. (填空题) 函数的定义域为___.(本题3.0分)
答案: (1) ; 得分点:未设置 解析: 无 9. (填空题) ___.(本题3.0分) 答案: (1) 2; 得分点:未设置 解析: 无 10. (填空题) 函数在点处的全微分___.(本题3.0分) 答案: (1) ; 得分点:未设置 解析: 无 11. (填空题) 设函数, 则___.(本题3.0分) 答案: (1) ; 得分点:未设置 解析: 无 12. (填空题) 交换二次积分顺序,___.(本题3.0分) 答案: (1) ;
最新山东大学网络教育期末英语模拟题三及答案
模拟题三 第一部分:交际用语 此部分共有5个未完成的对话,针对每个对话有4个选项,请从A、B、C、D四个选项中选出可以填入空白处的最佳选项,并用铅笔将答题卡上的相应字母涂黑。 1. –Hello! I want to make a person-to-person call to Toronto, Canada. The number is 932-0806. --___B_____. A. But I don’t know whom do you want to call. B. What’s the name of the party you’re calling? C. What’s the address of the person you’re calling? D. What’s the extension number you’re calling? 2. ---Have you ever been to the Temple of Heaven in Beijing? -- ___B__. A. No, but I have no time. B. No, but I’d like to. C. Yes. I was too busy then. D. Yes. I couldn’t do it right now. 3. –Is everyone always so helpful to you in your office? --- __D___. A. Yes. What can I do for you now? B. Yes, there is a hotel nearby. C. Yes. Can I help you? D. Yes. It’s a great place to work. 4. ---It’s a beautiful day today! How about a little trip out into the country? --- ___A______. A. That sounds great. What should I do for the preparation? B. I don’t know. I really haven’t thought about what we’d do. C. Well, would you like me to pack picnic or to buy something? D. It’s all right. Thank you. 5. –Excuse me. Could you show me the way to the nearest subway station? --- ___C____. A. Any time. It’s next to the post office. B. All right. Do you want me to go with you? C. No problem. With pleasure. D. Of course not. Go down this street and turn right. 第二部分:阅读理解 此部分共有2篇短文,每篇短文后有5个问题。请从每个问题后的A、B、C、D四个选项中,选出可以填入空白处的最佳选项,并用铅笔将答题卡上的相应字母涂黑。 Passage 1 The greatest recent social changes have been in the lives of women. During the twentieth century there has been a remarkable shortening of the proportion of a woman’s life spent in caring for children. A woman marrying at the end of the nineteenth century world probably have been in her middle twenties, and would be likely to have seven or eight children, of whom four or five lived till they were five years old. By the time the youngest was fifteen, the mother would have been in her early fifties and would expect to live a further twenty years, during which custom, opportunity and health made it unusual for her to get paid work. Today women marry younger and have fewer children. Usually a woman’s youngest child will be fifteen when she is forty-five and can be expected to live another thirty-five years and is likely to take paid work until retirement at sixty. Even while she has the care of children, her work is lightened by household appliances and convenience foods. The important change in women’s life-pattern has only recently begun to have its full effect on women’s economic p osition. Even a few years ago most girls left school at the first opportunity, and most of them took a full-time job.
山东大学网络教育考试模拟题及答案(计算机信息管理)—网页设计与制作2
网页设计与制作模拟题2 一、单项选择题 1.在配置连接一个SQL Server数据库的ODBC,下列说法中,(C)是不准确的。 A. 配置时,可以直接测试数据源 B. 配置时,必须指定数据库的主机地址 C. 配置时无须输入用户和密码 D. 对Web应用而言,应该建立System DSN 2.因特网上的域名服务称为( B )。 A. WINS B. DNS C. ARP D. TELNET 3.构成DHTML的各种技术中不包括( B )。 A. 客户机端脚本 B. 服务器端脚本 C. CSS D. DOM 4.HTML是一种页面( D )型的语言。 A. 程序设计 B. 执行 C. 编译 D. 描述 5.在HTML中定义一个表单应该使用以下标记( A ) A.