9.函数的最小值是 查看更多

 

题目列表(包括答案和解析)

给出下列四个结论:①函数在其定义域内是增函数;②函数的最小正周期是2π;③函数的图象关于直线对称;④函数是偶函数.其中正确结论的序号是       .

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(本题14分)设

(1)当时,求处的切线方程;

(2)当时,求的极值;

(3)当时,求的最小值。

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(本题12分)定义在R上的函数,已知上有最小值3。

(1)求的单调区间;

(2)求上的最大值。

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第二节:以下是五个应聘者的信息请阅读A至F职位招聘的信息,选出符合他们要求的最佳选项。选项中有一项是多余选项。(答案写在答题卷上)

Elizabeth Nagata.

 Elizabeth once studied in a secretarial program when she was at university. She has worked in Sumitomo Corporation as an executive assistant for eight years.

James Florian.

James once worked as a salesperson and served as the director of new home sales in both Forest Lakes and Glenmore for three years. He can speak excellent German and English, and he is very good at dealing with people.

Arthur Smith.

Arthur, a 22-year-old boy, has just graduated from college. He’s got a diploma in Library Technician Program. Wishing to have some free time, he doesn’t want to work full time.

Gillian Anderson.

Gillian graduated from the University of Manchester and got a Master’s Degree in Library Science five years ago. As soon as she left school, she worked in St. Bride Printing Library as a librarian. Now she is skilled in dealing with almost everything in the library system.

.Jerome Fingelhamm.

Jerome, aged 32, majored in computer science when he was at university. He has worked in a software company for six years and is an expert at both software and hardware. He got a driver’s license when he was eighteen years old.

Sales Executive

We are looking for intelligent sales staff for our ever-growing team. Applicants must have at least one year sales experience, knowledge of English language publications and media, good English and social skills.

B. Executive Assistant Vancouver

Island Regional Library (VIRL) has an opportunity for an executive assistant. A diploma in Business Administration or a secretarial program is needed. A minimum (最小值) of five years’ experience as an executive assistant to an executive director is required.

C. Reference Specialist

You’re responsible for providing support for reference services in the library system. The successful applicant must have a Master’s Degree in Library Science and a minimum of three years’ experience as a professional librarian.

D. Library Technician

We need a part-time library technician. Your position is responsible for library cataloging (编目录), binding, ordering publications, assisting in legal research. Both technical and reference services are required. The successful applicant should have a Library Technician diploma (文凭).

E. Circulation Director(发行总监)

We are looking for a circulation director. The successful applicant must have good managing skills, including the ability to assign tasks to ensure the work of the circulation department is done to the highest standard. A sales experience of at least ten years is needed.

F. Computer & Network Assistant

This position is responsible for the activities related to the use of automated (自动化的) systems. Duties include installing (安装), repairing and updating software and hardware. A driver’s license is necessary.

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以下是五个应聘者的信息请阅读A至F职位招聘的信息,选出符合他们要求的最佳选项。选项中有一项是多余选项。(答案写在答题卷上)

1.Elizabeth Nagata.

 Elizabeth once studied in a secretarial program when she was at university. She has worked in Sumitomo Corporation as an executive assistant for eight years.

2.James Florian.

James once worked as a salesperson and served as the director of new home sales in both Forest Lakes and Glenmore for three years. He can speak excellent German and English, and he is very good at dealing with people.

3.Arthur Smith.

Arthur, a 22-year-old boy, has just graduated from college. He’s got a diploma in Library Technician Program. Wishing to have some free time, he doesn’t want to work full time.

4.Gillian Anderson.

Gillian graduated from the University of Manchester and got a Master’s Degree in Library Science five years ago. As soon as she left school, she worked in St. Bride Printing Library as a librarian. Now she is skilled in dealing with almost everything in the library system.

5..Jerome Fingelhamm.

Jerome, aged 32, majored in computer science when he was at university. He has worked in a software company for six years and is an expert at both software and hardware. He got a driver’s license when he was eighteen years old.

A.Sales Executive

We are looking for intelligent sales staff for our ever-growing team. Applicants must have at least one year sales experience, knowledge of English language publications and media, good English and social skills.

B.Executive Assistant Vancouver

Island Regional Library (VIRL) has an opportunity for an executive assistant. A diploma in Business Administration or a secretarial program is needed. A minimum (最小值) of five years’ experience as an executive assistant to an executive director is required.

C.Reference Specialist

You’re responsible for providing support for reference services in the library system. The successful applicant must have a Master’s Degree in Library Science and a minimum of three years’ experience as a professional librarian.

D.Library Technician

We need a part-time library technician. Your position is responsible for library cataloging (编目录), binding, ordering publications, assisting in legal research. Both technical and reference services are required. The successful applicant should have a Library Technician diploma (文凭).

E. Circulation Director(发行总监)

We are looking for a circulation director. The successful applicant must have good managing skills, including the ability to assign tasks to ensure the work of the circulation department is done to the highest standard. A sales experience of at least ten years is needed.

F. Computer & Network Assistant

This position is responsible for the activities related to the use of automated (自动化的) systems. Duties include installing (安装), repairing and updating software and hardware. A driver’s license is necessary.

 

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1.解析:,故选A。

2.解析:∵

故选B。

3.解析:由,得,此时,所以,,故选C。

4.解析:显然,若共线,则共线;若共线,则,即,得,∴共线,∴共线是共线的充要条件,故选C。

5.解析:设公差为,由题意得,,解得,故选C。

6.解析:∵双曲线的右焦点到一条渐近线的距离等于焦距的,∴,又∵,∴,∴,∴双曲线的离心率是。故选B.

7.解析:∵为正实数,∴,∴;由均值不等式得恒成立,,故②不恒成立,又因为函数是增函数,∴,故恒成立的不等式是①③④。故选C.

8.解析:∵,∴在区间上恒成立,即在区间上恒成立,∴,故选D。

9.解析:∵

,此函数的最小值为,故选C。

10.解析:如图,∵正三角形的边长为,∴,∴,又∵,∴,故选D。

11.解析:∵在区间上是增函数且,∴其反函数在区间上是增函数,∴,故选A

12.解析:如图,①当时,圆面被分成2块,涂色方法有20种;②当时,圆面被分成3块,涂色方法有60种;

③当时,圆面被分成4块,涂色方法有120种,所以m的取值范围是,故选A。

13.解析:做出表示的平面区域如图,当直线经过点时,取得最大值5。

学科网(Zxxk.Com)14.解析:∵,∴时,,又时,满足上式,因此,

学科网(Zxxk.Com)15.解析:设正四面体的棱长为,连,取的中点,连,∵的中点,∴,∴或其补角为所成角,∵,∴,∴,又∵,∴,∴所成角的余弦值为

学科网(Zxxk.Com)16.解析:∵,∴,∵点的准线与轴的交点,由向量的加法法则及抛物线的对称性可知,点为抛物线上关于轴对称的两点且做出图形如右图,其中为点到准线的距离,四边形为菱形,∴,∴,∴,∴,∴,∴向量的夹角为

17.(10分)解析:(Ⅰ)由正弦定理得,,…2分

,………4分

(Ⅱ)∵,∴,∴,………………………6分

又∵,∴,∴,………………………8分

。………………………10分

18.解析:(Ⅰ)∵,∴;……………………理3文4分

(Ⅱ)∵三科会考不合格的概率均为,∴学生甲不能拿到高中毕业证的概率;……………………理6文8分

(Ⅲ)∵每科得A,B的概率分别为,∴学生甲被评为三好学生的概率为。……………………12分

(理)∵。……………………9分

的分布列如下表:

0

1

2

3

的数学期望。……………………12分

19.(12分)解析:(Ⅰ)时,

    

得,   ………3分

 

 

+

0

0

+

递增

极大值

递减

极小值

递增

      ………………………6分

(Ⅱ)在定义域上是增函数,

恒成立,即 

   ………………………9分

(当且仅当时,

               

 ………………………4分

学科网(Zxxk.Com)              

20.解析:(Ⅰ)∵,∴,∵底面,∴,∴平面,∴,又∵平面,∴,∴平面,∴。………………………4分

(Ⅱ)∵平面,∴,∴为二面角的平面角,………………………6分

,∴,又∵平面,∴,∴二面角的正切值的大小为。………………………8分

(Ⅲ)过点,交于点,∵平面,∴在平面内的射影,∴与平面所成的角,………………………10分

学科网(Zxxk.Com),∴,又∵,∴与平面所成的角相等,∴与平面所成角的正切值为。………………………12分

解法2:如图建立空间直角坐标系,(Ⅰ)∵,,∴点的坐标分别是,∴,设,∵平面,∴,∴,取,∴,∴。………………………4分

(Ⅱ)设二面角的大小为,∵平面的法向量是,平面的法向量是,∴,∴,∴二面角的正切值的大小为。………………………8分

(Ⅲ)设与平面所成角的大小为,∵平面的法向量是,∴,∴,∴与平面所成角的正切值为。………………………12分

21.(Ⅰ) 解析:如图,设右准线轴的交点为,过点


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