COURSE SYLLABUS Qualitative Research for Education: Theory and Methods
Fall 2008
Instructor:
Professor Ling Li
College of Education
Southwest University
Office hours in TJB Building #219 by appointment lingli2@https://www.doczj.com/doc/0810553777.html,
I. Course Description
II. Course Objectives
III. Course Textbook and Readings IV. Course Requirements
V. Evaluation
VI. Course Outline and Schedules
Education research is a complex endeavor involving several different methodological approaches. This course focuses on one kind of approach: qualitative methods. Qualitative research has a different tradition and founding theories from quantitative research, and the two modes of methodology are mutually complementary. This course includes two modules. The first module focuses on an introduction and inquiry into the theories and methodologies of qualitative research. And the second module will present a series of qualitative research projects to show how qualitative research is done in specific cases.
The first module is divided into seven sections. (1) Origins, development and theoretical underpinnings, which will cover Chicago Sociology, the Sociology of Education, European connections and the Social Movement, and many other political, ideological and social events that promoted the development of qualitative research, and cover theories such as phenomenology, symbolic interaction, feminism and postmodernism. (2) Research design, which will introduce the designing of different types of qualitative research such as case studies and multi-site studies. (3) Field work, including issues and challenges for access, cultural, political and emotional issues in the field and approaches of doing fieldwork like interview and tape recording. (4) Collection of qualitative data, introducing approaches of data collection such as field notes, transcripts, photography, documents and others. (5) Data analysis and interpretation, focusing on data category, the coding system, and interpretation. (6) Writing process, which touches the decisions to be made in the process, and what a good qualitative research writing is like. (7) Application in education, covering evaluation and policy research, action research and others. In this module, the major forms of instruction will be lectures based on the course text. Also, students are required to read lists of reading materials, relevant to the section topics. Based on their personal understanding of the lecture and readings, and on the real issues that they come across in doing qualitative research projects, student groups are requested to give 30-minute presentations on the following weeks after each lecture, and they are responsible for leading the class discussion about the topics and their presentations. In this way, the course aims to enhance and ensure students’ real acquisition of the knowledge and theories of the qualitative research methodology.
The second module will focus on the real practice and application of qualitative research methods. It includes a series of qualitative research projects presentations given by two students, the course instructor, and several professional scholars from Canada and the US, who are specialized in qualitative research methods, via long-distant internet videos. Apart from the theories of qualitative research, this course is intended as a practice for conducting fieldwork and applying techniques to researching and analyzing educational phenomena on a practical setting. Therefore, the second module, on the basis of the first, attempts to make students really involved in the real context of qualitative research and to make them learn by doing it themselves and learn by viewing how others are doing it. The long-distant lectures by the international professors aim to contribute international perspectives for students to view and understand qualitative research in different cultures.
1.Develop a basic understanding of the theoretical orientations that underlie
qualitative methods in education.
2.Understand the kinds of questions which have been and can be addressed with
qualitative research.
3.Understand the features and procedures in qualitative research methods and
approaches.
4.Know how to formulate a viable research question independently.
5.Learn about and practice qualitative data collection methods.
6.Learn and practice qualitative data analysis and interpretation.
7.Know how to prepare and conduct a research project
8.Begin work on a small research project in the field, requiring the use of
qualitative data collection and analysis methods.
9.Prepare and write a qualitative research proposal/paper/report/thesis
III. Course Textbook and Readings
Required Text
Bogdan, R.C. & Biklen, S.K. (2006). Qualitative research for education: An introduction to theory and methods. (5th edition.). Boston: Pearson.
Other Required Readings
Creswell, J.W. (2004). Educational research: Planning, conducting, and evaluating quantitative and qualitative research. (2nd edition.). Upper Saddle River, NJ:
Merrill Prentice Hall.
Li, L. (2008). Constructing teacher’s professional identity in China and Canada：Life stories in context. Saarbrucken, Germany: VDM Verlag Dr. Müller
Aktiengesellschaft & Co. KG.
Li, L. & Niyozov, S. (2008). Negotiating teacher's professional identity in a changing Chinese society. Education and Society, 26 (2), 69-84.
Li, L. (2006). Constructing professional identity through narrative inquiry into educational experiences of four generations of women in my family. Paper
presented at The 2006 Annual Meeting of the Canadian Society for the Study of Education, in Toronto, Canada.
Maxwell, J.A. (1996). Qualitative research design: An interactive approach.
Thousand Oaks, CA: Sage Publications.
Maxwell, J.A. (2004). Qualitative research design. (2nd edition.). Sage publications. Miles, M. & Huberman, A.M. (1994). Qualitative data analysis. (2nd edition.). Sage publications.
Strauss, A. & Corbin, J. (2008). Basics of qualitative research: Techniques and procedures for developing grounded theory. (3rd edition.). Sage publications. (see more in VI. Course outline and schedules)
Classes will be a combination of instructor lectures, student-led discussions on lectures and readings, student collaborative presentations, and finally practice project presentations. In addition to class participation, students are required to complete assignments and a final course paper using what will be learned through the course and in the practice. Students who are going to use qualitative research as methods in the graduation thesis will be required to submit thesis proposal and draft accordingly.
(1) Class Participation (10%). Students will be expected to attend all the lectures
and contribute to class discussion. Students are encouraged to propose
questions and opinions related to the instructor’s lectures, preparation of the
class and required reading materials. Students should participate and interact
actively with the lecturer’s and other classmates’ presentations
(2) Weekly Presentation (30%). Students will be divided into seven groups, with
four or five in each group. The groups will be expected to give a 30 minute
collaborative presentations of their work concerning a topic related to the
previous lecture theme. Presentations will pertain to the additional readings
for the previous week lecture and should come to class prepared to lead
discussion and critique about the readings of that topic.
(3) Research Paper (60%). This is the main requirement for the course. The paper
will serve as an important exercise in how to design an educational research
project using qualitative research methods and based on fieldwork. For those
who plan to conduct empirical research in their graduation thesis, this paper
can be replaced by a thesis proposal or even the thesis draft. Students should
consult with instructor about the research question at some point during the
semester and begin the development of a conceptual framework for a
qualitative research study as soon during the process of the course.
V. Evaluation
Grading Policy:
Students will receive a grade for their class participation (10% of the final grade), group presentation (30%) and the final paper (60%).
VI. Course outline and schedule
Week 1: Course orientation
1. What the course is about?
2. What you will learn?
3. What you will do?
4. What we will read?
5. How I will grade?
6. What is “Qualitative Research”?
7. The difference between qualitative and quantitative research
8. What you will be able to do after the course?
9. Discussion
Week 2: Foundations of Qualitative Research for Education
1. Characteristics of Qualitative Research
2. Traditions of Qualitative Research
2.1 Disciplinary Traditions
2.2 Chicago Sociology
2.3 The Sociology of Education
2.4 European Connections and the Social Movement
2.5 Ideological and Political Practices
2.6 Ideologies and Social Change
2.7 Politics and Theory in the Academy
3. Theoretical Underpinnings
3.1 Phenomenological Approach
3.2 Symbolic Interaction
3.3 A Story
3.4 Culture
3.5 Ethno-methodology
3.6 The Current Theoretical Scene: Cultural Studies, Feminism,
Postmodernism,
3.7 Critical theory and Institutional Ethnography
3.8 On Methods and Methodology
Week 3: Student-led Presentation and Discussion
Additional readings:
Bruner, J. (1990). Acts of meaning. Cambridge, MA: Harvard University Press. Denzin, N. K., & Lincoln, Y. S. (1994). Handbook of qualitative research. Thousand Oaks, CA: Sage.
Denzin, N. K., & Lincoln, Y. S. (2000). Handbook of qualitative research (2nd edition). Thousand Oaks, CA: Sage.
Denzin, N. K., & Lincoln, Y. S. (2004). Handbook of qualitative research (3rd edition). Thousand Oaks, CA: Sage.
Gadamer, H. (1975). Truth and method. New York: The Seabury Press.
Husserl, E. (1965). Phenomenology and the crisis of Philosophy. New York: Harper Torchbooks.
Mills, C. W. (1970). The sociological imagination. Harmondsworth: Penguin.
Ryle, G. (1949). The concept of mind. Harmondsworth: Penguin Books Ltd.
Week 4: Research Design
1. Choosing a Study
2. Case Studies
2.1 Historical Organizational Case Studies
2.2 Observational Case Studies
2.3 Life History
2.4 Documents
2.5 Other Forms of Case Studies
2.6 Case-study Design Issues
2.7 Multi-case Studies
3. Multisite Studies
3.1 Modified Analytic Induction
3.2 The Constant Comparative Method
3.3 Multi-Site Ethnography
4. Additional Issues Related to Design
4.1 Proposal Writing
4.2 Interview Schedules and Observer Guides
4.3 Team Research and the Lone Ranger
4.4 Qualitative Research and Historical Research
Week 5: Student-led Presentation and Discussion
Additional readings:
Cole, A. L., & Knowles, J. G. (2001). Lives in context: The art of life history research.
Walnut Creek, CA: AltaMira Press.
Gubrium, J. F., & Holstein, J. A. (Eds.) (2001). Handbook of interview research: Context and methods. Thousand Oaks, CA: Sage.
Heshusius, L. (1994). Freeing ourselves from objectivity: Managing subjectivity or turning toward a participatory mode of consciousness. Education Researcher,
23(3). 15-22
King, T. (2003). The truth about stories: A native narrative. Toronto, ON: House of Anansi Press.
Lawrence-Lightfoot, S., &Davis, J. H. (1997). The art and science of portraiture. San Francisco, CA: Jossey-Bass Publishers, Ch. 3.
Merriam, S. B. (1988). Case study research in education: A qualitative approach. San Francisco, CA: Jossey-Bass, Ch. 5.
Sparkes, A. (1994).Life histories and the issue of voice: Reflections on an emerging relationship. Qualitative Studies in Education, 7(2), 165-183.
Week 6: Fieldwork
1. Gaining Access
2. First Days in the Fields
3. The Participant/Observer Continuum
4. Doing Fieldwork in Another Culture
5. Research Characteristics and Special Problem with Rapport
6. Be Discreet
7. Researching in Politically Charged and Conflict-Ridden Settings
8. Feelings
9. Interviewing
9.1 Focus Groups
9.2 Audio Recording
10.Visual Recording and Fieldwork
11.Triangulation
12.Leaving the Field
Week 7: Student-led Presentation and Discussion
Additional readings:
Morgan, D. L. (2001). Focus group interviewing. In J. F. Gubrium & J. A. Holstein (Eds.) Handbook of interview research: Context and methods. Thousand Oaks, CA: Sage.
Schram, T. H. (2003). Conceptualizing qualitative inquiry: Mindwork for fieldwork in education and the social sciences. Upper Saddle River, NJ/Columbus, OH:
Merrill Prentice Hall.
Burgess, R. G. (1989). Grey areas: Ethical dilemmas in educational ethnography. In R.
G. Burgess (Ed.). The ethics of educational research. Barcombe, Lewes, East
Sussex: Falmer Press.
Kvale, S. (1996). Ethical issues in interview inquires. InterViews. Thousand Oaks, CA: Sage, Ch. 6.
Phtiaka, H. (1994). What’s in it for us? Qualitative Studies in Education, 7(2), 155-164.
Riddell, S. (1989). Exploiting the exploited: The ethics of feminist educational research. In R. G. Burgess (Ed.). The ethics of educational research. Barcombe, Lewes, East Sussex: Falmer Press.
Week 8: Qualitative Data
1. Some Friendly Advice
2. Fieldnotes
2.1 The content of fieldnotes
2.2 The Form of Fieldnotes
3. The Process of Writing Fieldnotes
4. Transcripts from Taped Interviews
4.1 The Form of Transcripts
4.2 Recording Equipment
5. Documents
5.1 Personal Documents
5.2 Official Documents
5.3 Popular culture documents
6. Photography
6.1 Found photographs
6.2 Research-Produced Photographs
6.3 Photographs as Analysis
6.4 Technique and Equipment
7. Official Statistics and Other Quantitative Data
8. Concluding Remarks
Week 9: Student-led Presentation and Discussion
Additional readings:
Hill, M.R. (1993). Archival Strategies and Techniques. Newbury Park: Sage Publications.
Jupp, V. (1996). Documents and Critical Research. In Roger Sapsford and Victor Jupp (eds.) Data Collection and Analysis. (pp. 298-316). Thousand Oaks, CA: Sage Publications.
Plummer, K. (2001). Documents of life: An invitation to a critical humanism.
Thousand Oaks, CA: Sage, Ch 8.
Wengraf,Tom.(2001). Qualitative Research Interviewing. London: Sage Publications. Week 10: Data Analysis and Interpretation
1. Analysis and Interpretation in the Field
1.1 More Tips
2. Analysis and Interpretation after Data Collection
2.1 Developing Coding Categories
2.2 Preassigned Coding Systems
2.3 Influences on Coding and Analysis
3. The Mechanics of Working with Data
4. Computers and Data Analysis
5. Interpretation
6. Concluding Remarks
Week 11: Student-led Presentation and Discussion
Additional readings:
Cole, A. L., & Mclntyre, M. (2004). Research as aesthetic contemplation: The role of the audience in research interpretation. Educational Insights, 9(1),
https://www.doczj.com/doc/0810553777.html,c.ubc.ca/publication/insights/v0901/articles/cole.html.
Wolcott, H. F. (1994). Transforming qualitative data: Description, analysis, and interpretation. Thousand Oaks, CA: Sage.
Denzin, N. K. (1997). Interpretive ethnography: Ethnographic practices for the 21st Century. Thousand Oaks, CA: Sage, Ch. 8.
Week 12: Writing It Up
1. Writing Choices
1.1 Decision about Your Argument
1.2 Decision about Your Presence in the Text
1.3 Decision about Your Audience
1.4 Decision about Disciplines
1.5 Decision about the Introduction
1.6 Decision about the Core of the Paper and Strategies for Communicating
Evidence
1.7 Decision about the conclusion
2. More Writing Tips
2.1 Call It a Draft
2.2 Styles of Presentation
2.3 Overwriting
2.4 “Yes. But…?”
2.5 Keep It Simple Up Front
2.6 Whose Perspective Are You Writing From?
2.7 Jargon and Code
2.8 On Giving V oices
2.9 General Advice
3. Criteria for Evaluating Writing
3.1 Is It Convincing?
3.2 Is the Author in Control of the Writing?
3.3 Does It Make a Contribution?
4. Texts
5. A Final Point about Getting Started
Week 13: Student-led Presentation and Discussion
Additional readings:
Hewett, H. (2004). In search of an “I”: Embodied voice and the personal essay.
Women’s Studies, 33, 719-741.
Richardson, L. (2000). Writing: A method of inquiry. In N. K Denzin, & Y. S.
Lincoln (Eds.) (2000). Handbook of qualitative research (2nd edition). Thousand Oaks, CA: Sage.
Week 14: Applied Qualitative Research for Education
1. Writing a Qualitative Research Proposal and Report
1.1 Writing a Qualitative Research Proposal
1.2 Writing a Qualitative Research Report
1.3 Qualitative Research: New Directions
2. Action Research
2.1 The Case of It Not Adding Up: Description
2.2 The Case of It Not Adding Up: Discussion
2.3 Political Action Research
2.4 What Action Research Can Do?
2.5 The Action Research Approach to Data
2.6 Action Research and the Qualitative Tradition
3. Practitioner Uses of Qualitative Research
3.1 Employing Qualitative Research to Improve Your Teaching
3.2 The Qualitative Approach and Teacher Education
Week 15: Student-led Presentation and Discussion
Additional readings:
Eisner, E. (1991). Do qualitative case studies have lessons to teach? In The enlightened eye. New York: Macmillan, ChIX (pp. 197-212).
Kvale,S. (1995). The social construction of validity. Qualitative Inquiry, 1 (1). 19-40. Neilsen, L. (2002). Learning from the liminal: Fiction as knowledge. Alberta Journal of Educational Research, 48(3). 206-214.
Peshkin, A. (1993). The goodness of qualitative research. Educational Researcher, 22(2), 24-30.
Week 16: Doing Qualitative Research —A Series of Presentations
1. 教育专业免费师范生职业认同研究
Presenter: Wu Yang-Ping
2. 免费师范生专业承诺与就业情况调查—以某大学为例
Presenter: Jia Ju-Ping
Week 17: Doing Qualitative Research —A Series of Presentations
1. Carving Beautiful Lives: Shaping Folk Arts in the Yangtze Three Gorges
Instructor: Professor Li Ling
2. Ethnic Minority Education of Southwestern China
Instructor: Professor Yao Jia-Li
Week 18: Doing Qualitative Research —A Series of Presentations
1. Ethnographical Approach to Teaching and Learning
Instructor: Professor Grace Feuerverger（OISE/University of Toronto）
2. Narrative Inquiry: Narrative in Educational Studies
Instructors: Professor Micheal Connelly（OISE/University of Toronto）
Associate Professor Xu Shi-Jing (University of Windsor）and
Associate Professor Fang Yan-Ping（Nanyang Technological
University, Singapore）
3. Qualitative Research and Ethical Review in Canada
Instructor: Dr. Terry Sefton (University of Windsor)
大一高等数学期末考试卷（精编试题）及答案详解 一、单项选择题 (本大题有4小题, 每小题4分, 共16分) 1. )( 0),sin (cos )( 处有则在设=+=x x x x x f . （A ）(0)2f '= （B ）(0)1f '=（C ）(0)0f '= （D ）()f x 不可导. 2. ）时（ ，则当，设133)(11)(3→-=+-= x x x x x x βα. （A ）()()x x αβ与是同阶无穷小，但不是等价无穷小； （B ）()()x x αβ与是 等价无穷小； （C ）()x α是比()x β高阶的无穷小； （D ）()x β是比()x α高阶的无穷小. 3. 若 ()()()0 2x F x t x f t dt =-?，其中()f x 在区间上(1,1)-二阶可导且 '>()0f x ，则（ ）. （A ）函数()F x 必在0x =处取得极大值； （B ）函数()F x 必在0x =处取得极小值； （C ）函数()F x 在0x =处没有极值，但点(0,(0))F 为曲线()y F x =的拐点； （D ）函数()F x 在0x =处没有极值，点(0,(0))F 也不是曲线()y F x =的拐点。 4. ) ( )( , )(2)( )(1 =+=?x f dt t f x x f x f 则是连续函数，且设 （A ）2 2x （B ）2 2 2x +（C ）1x - （D ）2x +. 二、填空题（本大题有4小题，每小题4分，共16分） 5. = +→x x x sin 20 ) 31(lim . 6. ,)(cos 的一个原函数是已知 x f x x =? ?x x x x f d cos )(则 . 7. lim (cos cos cos )→∞ -+++=2 2 2 21 n n n n n n π π ππ . 8. = -+? 2 12 12 211 arcsin － dx x x x . 三、解答题（本大题有5小题，每小题8分，共40分） 9. 设函数=()y y x 由方程 sin()1x y e xy ++=确定，求'()y x 以及'(0)y . 10. .d )1(17 7 x x x x ?+-求
大一高等数学期末考试试卷 一、选择题（共12分） 1. （3分）若2,0,(),0 x e x f x a x x ?<=?+>?为连续函数,则a 的值为( ). (A)1 (B)2 (C)3 (D)-1 2. （3分）已知(3)2,f '=则0(3)(3)lim 2h f h f h →--的值为（ ）. (A)1 (B)3 (C)-1 (D) 12 3. （3 分）定积分22 ππ-?的值为（ ）. (A)0 (B)-2 (C)1 (D)2 4. （3分）若()f x 在0x x =处不连续,则()f x 在该点处( ). (A)必不可导 (B)一定可导(C)可能可导 (D)必无极限 二、填空题（共12分） 1．（3分） 平面上过点(0,1)，且在任意一点(,)x y 处的切线斜率为23x 的曲线方程为 . 2. （3分） 1 241(sin )x x x dx -+=? . 3. （3分） 201lim sin x x x →= . 4. （3分） 3223y x x =-的极大值为 . 三、计算题（共42分） 1. （6分）求2 0ln(15)lim .sin 3x x x x →+ 2. （6 分）设2,1 y x =+求.y ' 3. （6分）求不定积分2ln(1).x x dx +? 4. （6分）求3 0(1),f x dx -?其中,1,()1cos 1, 1.x x x f x x e x ?≤?=+??+>?
5. （6分）设函数()y f x =由方程00cos 0y x t e dt tdt +=??所确定,求.dy 6. （6分）设2()sin ,f x dx x C =+?求(23).f x dx +? 7. （6分）求极限3lim 1.2n n n →∞??+ ??? 四、解答题（共28分） 1. （7分）设(ln )1,f x x '=+且(0)1,f =求().f x 2. （7分）求由曲线cos 2 2y x x ππ??=-≤≤ ???与x 轴所围成图形绕着x 轴旋转一周所得旋转体的体积. 3. （7分）求曲线3232419y x x x =-+-在拐点处的切线方程. 4. （7 分）求函数y x =+[5,1]-上的最小值和最大值. 五、证明题(6分) 设()f x ''在区间[,]a b 上连续,证明 1()[()()]()()().22b b a a b a f x dx f a f b x a x b f x dx -''=++--?? 标准答案 一、 1 B; 2 C; 3 D; 4 A. 二、 1 31;y x =+ 2 2;3 3 0; 4 0. 三、 1 解 原式2 05lim 3x x x x →?= 5分 53 = 1分 2 解 22ln ln ln(1),12 x y x x ==-++Q 2分 2212[]121 x y x x '∴=-++ 4分
大一高等数学期末考试试卷 （一） 一、选择题（共12分） 1. （3分）若2,0, (),0x e x f x a x x ?<=?+>? 为连续函数,则a 的值为( ). (A)1 (B)2 (C)3 (D)-1 2. （3分）已知(3)2,f '=则0 (3)(3) lim 2h f h f h →--的值为（ ）. (A)1 (B)3 (C)-1 (D) 12 3. （3分）定积分 22 π π - ?的值为（ ）. (A)0 (B)-2 (C)1 (D)2 4. （3分）若()f x 在0x x =处不连续,则()f x 在该点处( ). (A)必不可导 (B)一定可导(C)可能可导 (D)必无极限 二、填空题（共12分） 1．（3分） 平面上过点(0,1)，且在任意一点(,)x y 处的切线斜率为2 3x 的曲线方程为 . 2. （3分） 1 241 (sin )x x x dx -+=? . 3. （3分） 2 1 lim sin x x x →= . 4. （3分） 3 2 23y x x =-的极大值为 . 三、计算题（共42分） 1. （6分）求2 ln(15) lim .sin 3x x x x →+ 2. （6分）设y =求.y ' 3. （6分）求不定积分2 ln(1).x x dx +?
4. （6分）求 3 (1),f x dx -? 其中,1,()1cos 1, 1.x x x f x x e x ?≤? =+??+>? 5. （6分）设函数()y f x =由方程0 cos 0y x t e dt tdt +=? ?所确定,求.dy 6. （6分）设 2 ()sin ,f x dx x C =+?求(23).f x dx +? 7. （6分）求极限3lim 1.2n n n →∞? ?+ ??? 四、解答题（共28分） 1. （7分）设(ln )1,f x x '=+且(0)1,f =求().f x 2. （7分）求由曲线cos 2 2y x x π π??=- ≤≤ ???与x 轴所围成图形绕着x 轴旋转一周所得旋 转体的体积. 3. （7分）求曲线32 32419y x x x =-+-在拐点处的切线方程. 4. （7 分）求函数y x =+[5,1]-上的最小值和最大值. 五、证明题(6分) 设()f x ''在区间[,]a b 上连续,证明 1()[()()]()()().22b b a a b a f x dx f a f b x a x b f x dx -''=++--? ? （二） 一、 填空题（每小题3分，共18分） 1．设函数()2 31 22+--=x x x x f ，则1=x 是()x f 的第 类间断点. 2．函数( )2 1ln x y +=，则='y . 3． =? ? ? ??+∞→x x x x 21lim . 4．曲线x y 1=在点?? ? ??2,21处的切线方程为 .
( 大一上学期高数期末考试 一、单项选择题 (本大题有4小题, 每小题4分, 共16分) 1. )( 0),sin (cos )( 处有则在设=+=x x x x x f . （A ）(0)2f '= （B ）(0)1f '=（C ）(0)0f '= （D ）()f x 不可导. 2. ） 时（ ，则当，设133)(11)(3→-=+-=x x x x x x βα. （A ）()()x x αβ与是同阶无穷小，但不是等价无穷小； （B ）()()x x αβ与是 等价无穷小； （C ）()x α是比()x β高阶的无穷小； （D ）()x β是比()x α高阶的无穷小. 3. … 4. 若 ()()()0 2x F x t x f t dt =-?，其中()f x 在区间上(1,1)-二阶可导且 '>()0f x ，则（ ）. （A ）函数()F x 必在0x =处取得极大值； （B ）函数()F x 必在0x =处取得极小值； （C ）函数()F x 在0x =处没有极值，但点(0,(0))F 为曲线()y F x =的拐点； （D ）函数()F x 在0x =处没有极值，点(0,(0))F 也不是曲线()y F x =的拐点。 5. ) ( )( , )(2)( )(1 =+=?x f dt t f x x f x f 则是连续函数，且设 （A ）22x （B ）2 2 2x +（C ）1x - （D ）2x +. 二、填空题（本大题有4小题，每小题4分，共16分） 6. , 7. = +→x x x sin 20 ) 31(lim . 8. ,)(cos 的一个原函数是已知 x f x x =? ?x x x x f d cos )(则 . 9. lim (cos cos cos )→∞ -+++=2 2 2 21 n n n n n n π π ππ . 10. = -+? 2 12 1 2 211 arcsin － dx x x x . 三、解答题（本大题有5小题，每小题8分，共40分） 11. 设函数=()y y x 由方程 sin()1x y e xy ++=确定，求'()y x 以及'(0)y .
大一上学期高数期末考试 一、单项选择题 (本大题有4小题, 每小题4分, 共16分) 1. )( 0),sin (cos )( 处有则在设=+=x x x x x f . （A ）(0)2f '= （B ）(0)1f '=（C ）(0)0f '= （D ）()f x 不可导. 2. ） 时（ ，则当，设133)(11)(3→-=+-=x x x x x x βα. （A ）()()x x αβ与是同阶无穷小，但不是等价无穷小； （B ）()() x x αβ与是等价无穷小； （C ）()x α是比()x β高阶的无穷小； （D ）()x β是比()x α高阶的无穷小. 3. 若 ()()()0 2x F x t x f t dt =-?，其中()f x 在区间上(1,1)-二阶可导且 '>()0f x ，则（ ）. （A ）函数()F x 必在0x =处取得极大值； （B ）函数()F x 必在0x =处取得极小值； （C ）函数()F x 在0x =处没有极值，但点(0,(0))F 为曲线()y F x =的拐点； （D ）函数()F x 在0x =处没有极值，点(0,(0))F 也不是曲线()y F x =的拐点。 4. ) ( )( , )(2)( )(1 =+=?x f dt t f x x f x f 则是连续函数，且设 （A ）22x （B ）2 2 2x +（C ）1x - （D ）2x +. 二、填空题（本大题有4小题，每小题4分，共16分） 5. = +→x x x sin 2 ) 31(lim . 6. ,)(cos 的一个原函数是已知 x f x x =? ?x x x x f d cos )(则 . 7. lim (cos cos cos )→∞-+++= 2 2 221 n n n n n n ππ ππ . 8. = -+? 2 12 12 211 arcsin － dx x x x . 三、解答题（本大题有5小题，每小题8分，共40分） 9. 设函数=()y y x 由方程 sin()1x y e xy ++=确定，求'()y x 以及'(0)y . 10. .d )1(17 7 x x x x ?+-求
高等数学II 填空题 1、()1 3 1sin x x dx -+=? _______________________. 2、设()1 1 x x f x e dx e C =+?, 则()f x =_________________. 3、微分方程2220d y dy y dx dx -+=的通解为_______________________. 4、函数 (,)ln 1f x y x y =--_______________. 5、椭圆22 1169 x y += 绕x 轴旋转一周所得旋转体的体积为______________________. 计算题 1、计算不定积分 2211sec dx x x ?. 2 、计算不定积分 dx , ()0a >. 3、计算定积分 320sin cos x x dx π? 4、计算定积分 1 0arcsin x dx ? 解答题 1、设函数()f x 的原函数()F x 恒正, (0)1F =且()()f x F x x =, 且()f x 的表达式. 2、解微分方程()52211dy y x dx x =+++，并求出其满足初始条件01|3 x y ==-的特解. 3、设2ln z u v =，且x u y =， 32v x y =-, 求z x ??和z y ??, 并写出dz . 4、设02 (), 0() , 0 x tf t dt x F x x A x ??≠=??=??, 其中()f x 具有连续导数且(0)0f =. (1) 如果()F x 在点0x =处连续, 求A 的值; (2) 在(1)的前提下, 证明()F x 在点0x =处可导, 并求(0)F '的值.
（2010至2011学年第一学期） 课程名称： 高等数学(上)(A 卷) 考试(考查)： 考试 2008年 1 月 10日 共 6 页 1、 满分100分。要求卷面整洁、字迹工整、无错别字。 2、 考生必须将姓名、班级、学号完整、准确、清楚地填写在试卷规定的地方，否 则视为废卷。 3、 考生必须在签到单上签到，若出现遗漏，后果自负。 4、 如有答题纸，答案请全部写在答题纸上，否则不给分；考完请将试卷和答题卷 分别一同交回，否则不给分。 试 题 一、单选题（请将正确的答案填在对应括号内，每题3分，共15分） 1. =--→1 ) 1sin(lim 21x x x ( ) (A) 1； (B) 0； (C) 2； (D) 2 1 2.若)(x f 的一个原函数为)(x F ，则dx e f e x x )(? --为( ) (A) c e F x +)(； (B) c e F x +--)(； (C) c e F x +-)(； (D ) c x e F x +-) ( 3.下列广义积分中 ( )是收敛的. (A) ? +∞ ∞ -xdx sin ； (B)dx x ? -1 11； (C) dx x x ?+∞∞-+2 1； (D)?∞-0dx e x 。 4. )(x f 为定义在[]b a ,上的函数，则下列结论错误的是( ) (A) )(x f 可导，则)(x f 一定连续； (B) )(x f 可微，则)(x f 不一定
可导； (C) )(x f 可积（常义），则)(x f 一定有界； (D) 函数)(x f 连续，则? x a dt t f )(在[]b a ,上一定可导。 5. 设函数=)(x f n n x x 211lim ++∞→ ，则下列结论正确的为( ) (A) 不存在间断点； (B) 存在间断点1=x ； (C) 存在间断点0=x ； (D) 存在间断点1-=x 二、填空题（请将正确的结果填在横线上.每题3分，共18分） 1. 极限=-+→x x x 1 1lim 20 _____. 2. 曲线???=+=3 2 1t y t x 在2=t 处的切线方程为______. 3. 已知方程x xe y y y 265=+'-''的一个特解为x e x x 22 )2(2 1+- ，则该方程的通解为 . 4. 设)(x f 在2=x 处连续，且22 ) (lim 2=-→x x f x ，则_____)2(='f 5．由实验知道，弹簧在拉伸过程中需要的力F （牛顿）与伸长量s 成正比，即ks F =（k 为比例系数），当把弹簧由原长拉伸6cm 时，所作的功为_________焦耳。 6．曲线23 3 2 x y =上相应于x 从3到8的一段弧长为 . 三、设0→x 时，)(22 c bx ax e x ++-是比2 x 高阶的无穷小，求常数c b a ,,的值（6分）
2019-2020 学年第二学期试卷（A 卷） 课程：《高等数学》 一、填空题：（每空 3分，共 30分） （说明：将运算结果．．．． 填写在每小题相应的横线） 1．设函数22 ()30 x x f x x b x ?+<=? +≥? 在0x =处连续，则常数b = ． 2．如果0sin 3lim 1x x kx →=，则k = ． 3．如果()f x 在0x 处可导，则00(2)() lim x h f x h f x h →+-= ． 4．设函数1 y x = ，当x 时此函数为无穷小量，当x 时此函数为无穷大量． 5．曲线2 2 4x xy y ++= 在点(2,2)-处的切线方程为 ． 6．函数1 ()lg(5) f x x = -定义域为 ． 7．曲线3 352y x x =-++的拐点是 ． 8．曲线1 2 x y x += -的水平渐近线为 ，铅直渐近线为 ． 9．设x e -是()f x 的一个原函数，则()f x dx =? ． 10． 1 31 5sin xdx -=? ． 二、选择题：（每题5分，共 15 分） （说明：将认为正确答案的字母填写在每小题相应的括号内） 1．下列函数在1x =-处连续，但不可导的是【 】． A.1y x =+ B.2ln(1)y x =+ C. 1 1 y x = + D. 2(1)y x =+ 2．设2 11x y x -=+，则1x =-是函数的【 】． A.连续点 B. 可去间断点 C.跳跃间断点 D. 无穷间断点 3．下列等式不正确是【 】． A. 1 2 lim(12)x x x e →+= B. 110 lim(1) x x x e --→-= C. sin lim 0x x x →∞= D. 0tan lim 1x x x →=
1、(本小题5分) 求极限 lim x x x x x x →-+-+-233 21216 29124 2、(本小题5分) .d )1(2 2x x x ? +求 3、(本小题5分) 求极限limarctan arcsin x x x →∞ ?1 4、(本小题5分) ? -.d 1x x x 求 5、(本小题5分) ． 求dt t dx d x ? +2 21 6、(本小题5分) ??. d csc cot 46x x x 求
（第七题删掉了） 8、(本小题5分) 设确定了函数求．x e t y e t y y x dy dx t t ==?????=cos sin (),2 2 9、(本小题5分) ． 求dx x x ?+3 1 10、(本小题5分) 求函数 的单调区间 y x x =+-422 11、(本小题5分) ． 求? π +20 2sin 8sin dx x x 12、(本小题5分) ．，求设 dx t t e t x kt )sin 4cos 3()(ωω+=- 13、(本小题5分) 设函数由方程所确定求 ．y y x y y x dy dx =+=()ln ,226 14、(本小题5分) 求函数的极值y e e x x =+-2
15、(本小题5分) 求极限lim ()()()()()()x x x x x x x →∞++++++++--121311011011112222 Λ 16、(本小题5分) . d cos sin 12cos x x x x ? +求 二、解答下列各题 (本大题共2小题，总计14分) 1、(本小题7分) ,,512沿一边可用原来的石条围平方米的矩形的晒谷场某农场需建一个面积为.,,才能使材料最省多少时问晒谷场的长和宽各为另三边需砌新石条围沿 2、(本小题7分) . 823 2体积轴旋转所得的旋转体的所围成的平面图形绕和求由曲线ox x y x y == 三、解答下列各题 ( 本 大 题6分 ) 设证明有且仅有三个实根f x x x x x f x ()()()(),().=---'=1230 (答案) 一、解答下列各题 (本大题共16小题，总计77分) 1、(本小题3分)
解 大一高等数学期末考试试卷 (一)一、选择题(共12分) x,2,0,ex,fx(),1. (3分)若为连续函数,则的值为( ). a,axx，,,0,(A)1 (B)2 (C)3 (D)-1fhf(3)(3),,,2. (3分)已知则的值为( ). limf(3)2,,h,02h 1(A)1 (B)3 (C)-1 (D) 2 ,223. (3分)定积分的值为( ). 1cos,xdx,,,2 (A)0 (B)-2 (C)1 (D)2 4. (3分)若在处不连续,则在该点处( ).xx,fx()fx()0(A)必不可导(B)一定可导(C)可能可导(D)必无极限二、填空题(共12分)23x1((3分)平面上过点，且在任意一点处的切线斜率为的曲线方程(0,1)(,)xy为. 124(sin)xxxdx，,2. (3分) . ,,1 12xlimsin3. (3分) = . x,0x 324. (3分)的极大值为. yxx,,23 三、计算题(共42分) xxln(15)，lim.1. (6分)求2x,0sin3x xe,y,,2. (6分)设求y. 2x，1 2xxdxln(1).，3. (6分)求不定积分, x,3,1,x,,fxdx(1),,4. (6分)求其中()fx,1cos，x,,0x,1,1.ex，,,1 yxt5. (6分)设函数由方程所确定,求edttdt，,cos0yfx,()dy.,,0026. (6分)设求fxdxxC()sin,,，fxdx(23).，,, n3,,7. (6分)求极限lim1.，,,,,nn2,, 四、解答题(共28分)
,1. (7分)设且求fxx(ln)1,,，f(0)1,,fx(). ,,,,2. (7分)求由曲线与轴所围成图形绕着轴旋转一周所得旋 xxyxxcos,,,,,,22,, 转体的体积. 323. (7分)求曲线在拐点处的切线方程. yxxx,,，,32419 4. (7分)求函数在上的最小值和最大值. [5,1],yxx,，,1 五、证明题(6分) ,,设在区间上连续,证明fx()[,]ab bbba,1,, fxdxfafbxaxbfxdx()[()()]()()().,，，,,,,aa22 (二) 一、填空题(每小题3分，共18分) 2x,1x,1，，fx,，，1(设函数，则是的第类间断点. fx2x,3x， 则. y,y,ln1，x x2 x，1,,( 3 . ,lim,,x,, x,, 11,,y,4(曲线在点处的切线方程为. ,2,,x2,, 32,,,1,45(函数在上的最大值，最小值. y,2x,3x xarctandx,6(. ,21，x 222,，，2(函数，二、单项选择题(每小题4分，共20分) 1(数列有界是它收敛的( ) . ,,xn必要但非充分条件;充分但非必要条件;，，，，A B 充分必要条件;无关条件.，，，，C D 2(下列各式正确的是( ) .1,x,xxdx,，C; ;ln，，edx,e，C，，A B ,,x
高等数学（上）模拟试卷一 一、 填空题（每空3分，共42分） 1 、函数lg(1)y x = -的定义域是 ； 2、设函数 20() 0x x f x a x x ?<=? +≥?在点0x =连续，则a = ； 3、曲线 4 5y x =-在（-1，-4）处的切线方程是 ； 4、已知 3()f x dx x C =+? ，则()f x = ； 5、2 1lim(1) x x x →∞ -= ； 6、函数32 ()1f x x x =-+的极大点是 ； 7、设()(1)(2)2006)f x x x x x =---……(，则(1)f '= ； 8、曲线x y xe =的拐点是 ； 9、 2 1x dx -? = ； 10、设32,a i j k b i j k λ=+-=-+r r r r r r r r ，且a b ⊥r r ，则λ= ； 11、2lim()01x x ax b x →∞--=+，则a = ，b = ； 12、 3 11 lim x x x -→= ； 13、设()f x 可微，则 ()()f x d e = 。 二、 计算下列各题（每题5分，共20分） 1、 011 lim()ln(1)x x x →-+ 2 、y =y '； 3、设函数()y y x =由方程 xy e x y =+所确定，求0x dy =； 4、已知cos sin cos x t y t t t =?? =-?，求dy dx 。 三、 求解下列各题（每题5分，共20分） 1、4 21x dx x +? 2、2 sec x xdx ?
3 、 40? 4 、2201 dx a x + 四、 求解下列各题（共18分）： 1、求证：当0x >时， 2 ln(1)2x x x +>- （本题8分） 2、求由,,0x y e y e x ===所围成的图形的面积，并求该图形绕x 轴旋转一周所形成的旋转 体的体积。（本题10分） 高等数学（上）模拟试卷二 一、填空题（每空3分，共42分） 1 、函数 lg(1)y x =-的定义域是 ； 2、设函数 sin 0()20 x x f x x a x x ?
一、单选题（共15分，每小题3分） 1．设函数(,)f x y 在00(,)P x y 的两个偏导00(,)x f x y ，00(,)y f x y 都存在，则 ( ) A ．(,)f x y 在P 连续 B ．(,)f x y 在P 可微 C ． 0 0lim (,)x x f x y →及 0 0lim (,)y y f x y →都存在 D ． 00(,)(,) lim (,)x y x y f x y →存在 2．若x y z ln =，则dz 等于（ ）． ln ln ln ln .x x y y y y A x y + ln ln .x y y B x ln ln ln .ln x x y y C y ydx dy x + ln ln ln ln . x x y y y x D dx dy x y + 3．设Ω是圆柱面2 2 2x y x +=及平面01,z z ==所围成的区域，则 (),,(=???Ωdxdydz z y x f ） ． 21 2 0cos .(cos ,sin ,)A d dr f r r z dz π θ θθθ? ? ? 212 00 cos .(cos ,sin ,)B d rdr f r r z dz π θ θθθ? ? ? 212 2 cos .(cos ,sin ,)C d rdr f r r z dz π θ πθθθ-?? ? 21 0cos .(cos ,sin ,)x D d rdr f r r z dz π θθθ?? ? 4． 4．若 1 (1) n n n a x ∞ =-∑在1x =-处收敛，则此级数在2x =处（ ）． A ． 条件收敛 B ． 绝对收敛 C ． 发散 D ． 敛散性不能确定 5．曲线22 2 x y z z x y -+=?? =+?在点（1，1，2）处的一个切线方向向量为（ ）. A. （-1，3，4） B.（3，-1，4） C. （-1，0，3） D. （3，0，-1） 二、填空题（共15分，每小题3分） 1．设220x y xyz +-=，则' (1,1)x z = . 2．交 换ln 1 (,)e x I dx f x y dy = ? ? 的积分次序后，I =_____________________． 3．设2 2z xy u -=，则u 在点)1,1,2(-M 处的梯度为 . 4. 已知0!n x n x e n ∞ ==∑，则x xe -= . 5. 函数3322 33z x y x y =+--的极小值点是 . 三、解答题（共54分，每小题6--7分） 1.（本小题满分6分）设arctan y z y x =, 求z x ??,z y ??. 2.（本小题满分6分）求椭球面222 239x y z ++=的平行于平面23210x y z -++=的切平面方程，并求切点处的 法线方程. 3. （本小题满分7分）求函数2 2 z x y =+在点(1,2) 处沿向量122 l i j =+ r r r 方向的方向导数。 4. （本小题满分7分）将x x f 1 )(=展开成3-x 的幂级数，并求收敛域。 5．（本小题满分7分）求由方程088222 22=+-+++z yz z y x 所确定的隐函数),(y x z z =的极值。 6．（本小题满分7分）计算二重积分 1,1,1,)(222 =-=--=+??y y y x D d y x D 由曲线σ及2-=x 围成.
中国传媒大学 2009-2010学年第 一 学期期末考试试卷（B 卷） 及参考解答与评分标准 考试科目： 高等数学A （上） 考试班级： 2009级工科各班 考试方式： 闭卷 命题教师： 本大题共3小题，每小题3分，总计9分 ） 1、0)(0='x f 是可导函数)(x f 在0x 点处取得极值的 必要 条件。 2、设 )20() 1tan(cos ln π <
)(B 每个不定积分都可以表示为初等函数； )(C 初等函数的原函数必定是初等函数； )(D C B A ,,都不对。 答( D ) 3、若?-=x e x e dt t f dx d 0)(，则=)(x f x x e D e C x B x A 2222)( )()( )(----- 答( A ) 2小题，每小题5分，总计10分 ） 1、求极限0lim →x x x x 3sin arcsin -。 解：0lim →x =-x x x 3sin arcsin 0lim →x 3 arcsin x x x - （3分） lim →=x 31112 2=-- x x 0lim →x () ()x x x 621212 3 2---61-=。 （5分） 2、2tan ln x y =,求dx dy 。 解: 2sec 212 tan 12x x y ??= ' （3分） x x x x csc sin 1 2 cos 2sin 21==?=。 （5 分）
总复习(上) 一、求极限的方法： 1、利用运算法则与基本初等函数的极限； ①、定理 若lim (),lim ()f x A g x B ==, 则 (加减运算) lim[()()]f x g x A B +=+ (乘法运算) lim ()()f x g x AB = (除法运算) ()0,lim () f x A B g x B ≠=若 推论1: lim (),lim[()][lim ()]n n n f x A f x f x A === (n 为正整数) 推论2: lim ()[lim ()]cf x c f x = ②结论 结论2: ()f x 是基本初等函数，其定义区间为D ，若0x D ∈，则 0lim ()()x x f x f x →= 2、利用等价无穷小代换及无穷小的性质； ①定义1: 若0 lim ()0x x f x →=或（lim ()0x f x →∞=） 则称()f x 是当0x x → (或x →∞)时的无穷小. 定义2: ,αβ是自变量在同一变化过程中的无穷小: 若lim 1βα =, 则称α 与β是等价无穷小, 记为αβ . ②性质1：有限个无穷小的和也是无穷小. 性质2: 有界函数与无穷小的乘积是无穷小.
推论1: 常数与无穷小的乘积是无穷小. 推论2: 有限个无穷小的乘积也是无穷小. 定理2(等价无穷小替换定理) 设~,~ααββ'', 且lim βα'' 存在, 则 (因式替换原则) 常用等价无穷小: sin ~,tan ~,arcsin ~,arctan ~,x x x x x x x x ()()2 12 1cos ~ ,1~,11~,ln 1~,x x x e x x x x x μ μ--+-+ 1~ln ,x a x a -()0→x 3、利用夹逼准则和单调有界收敛准则； ①准则I(夹逼准则)若数列,,n n n x y z (n=1,2,…)满足下列条件: (1)(,,,)n n n y x z n ≤≤=123 ; (2)lim lim n n n n y z a →∞ →∞ ==, 则数列n x 的极限存在, 且lim n n x a →∞ =. ②准则II: 单调有界数列必有极限. 4、利用两个重要极限。 sin lim 1x x x →= 1 lim (1)x x x e →+= 1lim (1)x x e x →∞+ = 5、利用洛必达法则。 未定式为0,,,0,00∞ ∞∞-∞?∞∞ 类型.
2017-1-9 1. 设11ln(1)10()0x x x f x e x -+-<≤??=??>?，求()f x 的间断点，并指出间断点的类型。 0x =为跳跃间断点； 1x =为第二类间断点。 2.求,a b 的值，使点（1, 3）为曲线32y ax bx =+的拐点。 39,22 a b =-=。 3.已知两曲线()y f x =与2arctan 0 x t y e dt -=?在点(0, 0)处的切线相同，写出此切线方程，并求极限2lim ()n nf n →∞ 解 2()(0)2l i m ()l i m 2(0)2 1n n f f n nf f n n →∞→∞ -'=== 4. 求定积分 1 换元1x u = 5.求不定积分2x xe dx -? 221124 x x e x e C --=--+。 6.计算反常积分 21(1)dx x x +∞+? 11lim ln 2ln 222x →+∞== 7. 已知arctan x y t t ??=?=-??，求22d y dx 解 221111dy t t t dx t - +==+ 2222111d y t t dx t t +==+ 8. 判断级数1(1)(0)n n a n n a n ∞ +=+>∑的敛散性。
(1) 1l i m l i m (1)1n n a n n n a n n e n n +→∞→∞+=+= ， 所以，当1a >时，级数1 ()n n a n n a n ∞+=+ ∑收敛； 当01a <≤时，级数1 ()n n a n n a n ∞+=+∑发散。 9.设函数()y f x =在0x =的某邻域内具有一阶连续导数，且(0)0,(0)0f f '≠≠， 若()(2)(0)af h bf h f +-在0h →时是比h 高阶的无穷小，试确定,a b 的值 2,1a b ==-。 二、（9分）求极限111393lim 24(2)n n n →∞??? 11133934 lim 24(2)2n n n →∞???=。 三、（9分）设0A >，D 是由曲线段sin (0)2y A x x π=≤≤及直线0,2 y x π==所围成的平面区域，12,V V 分别表示D 绕x 轴与y 轴旋转所成旋转体的体积，若12V V =，求A 的值。 8A π= 四、（9分）设1 30()lim 1x x f x x e x →??++=???? ，其中f (x )在x = 0处二阶可导，求f (0)，f '(0)，f ''(0)。 (0)0f = 0()(0)lim (0)0x f x f f x →-'== f ''(0) = 4 五、(9分) 越野赛在湖滨举行，场地如图，出发点在陆地A 处，终点在湖心B 处，A ，B 南北相距5km ，东西相距7km ，湖岸位于A 点南侧2km, 是一条东西走向的笔直长堤。比赛中运动员可自行选择路线，但必须先从A 出发跑步到达长堤，再从长堤处下水游泳到达终点B 。已知某运动员跑步速度为118/v km h =，游泳速度为26/v km h =，问他应该在长堤的何处下水才能使比赛用时最少？ 6x = 此驻点是唯一的，则在点(6,0)R 下水，用时最少。
第一学期期末高等数学试卷 一、解答下列各题 (本大题共16小题，总计80分) 1、(本小题5分) 求极限 lim x x x x x x →-+-+-233 21216 29124 2、(本小题5分) .d )1(2 2x x x ? +求 3、(本小题5分) 求极限lim arctan arcsin x x x →∞ ?1 4、(本小题5分) ? -.d 1x x x 求 5、(本小题5分) ． 求dt t dx d x ? +2 21 6、(本小题5分) ??. d csc cot 46x x x 求 7、(本小题5分) ． 求? ππ 212 1cos 1dx x x 8、(本小题5分) 设确定了函数求．x e t y e t y y x dy dx t t ==?????=cos sin (),2 2 9、(本小题5分) ． 求dx x x ?+30 1 10、(本小题5分) 求函数 的单调区间y x x =+-422 11、(本小题5分) ．求? π +20 2 sin 8sin dx x x 12、(本小题5分) ．，求设 dx t t e t x kt )sin 4cos 3()(ωω+=- 13、(本小题5分) 设函数由方程所确定求 ．y y x y y x dy dx =+=()ln ,226 14、(本小题5分) 求函数的极值y e e x x =+-2 15、(本小题5分) 求极限lim ()()()()()()x x x x x x x →∞++++++++--121311011011112222 16、(本小题5分) . d cos sin 12cos x x x x ? +求
高等数学I 1. 当0x x →时，()(),x x αβ都是无穷小，则当0x x →时（ D ）不一定是 无穷小. (A) ()()x x βα+ (B) ()()x x 2 2βα+ (C) [])()(1ln x x βα?+ (D) )() (2x x βα 2. 极限a x a x a x -→??? ??1sin sin lim 的值是（ C ）. （A ） 1 （B ） e （C ） a e cot （D ） a e tan 3. ??? ??=≠-+=001 sin )(2x a x x e x x f ax 在0x =处连续，则a =（ D ）. （A ） 1 （B ） 0 （C ） e （D ） 1- 4. 设)(x f 在点x a =处可导，那么=--+→h h a f h a f h )2()(lim 0（ A ）. （A ） )(3a f ' （B ） )(2a f ' (C) )(a f ' （D ） ) (31 a f ' 二、填空题（本大题有4小题，每小题4分，共16分） 5. 极限) 0(ln )ln(lim 0>-+→a x a a x x 的值是 a 1. 6. 由x x y e y x 2cos ln =+确定函数y (x )，则导函数='y x xe ye x y x xy xy ln 2sin 2+++ - . 7. 直线l 过点M (,,)123且与两平面x y z x y z +-=-+=202356,都平行，则直 线l 的方程为 13 1211--=--=-z y x . 8. 求函数2 )4ln(2x x y -=的单调递增区间为 （－∞，0）和（1，+∞ ） . 三、解答题（本大题有4小题，每小题8分，共32分） 9. 计算极限10(1)lim x x x e x →+-.