
(1觀察圖解,色盲基因在性別間是如何傳遞的呢?(女--女、女--男、男--女)(2)為什么不能由男性傳給男性?(色盲基因是在X染色體上,因此色盲基因是隨X染色體的傳遞而傳遞。)(3)男性的色盲基因怎樣才能傳給男性呢?(通過(guò)女兒,傳給外孫即交叉遺傳)(4)從圖解看色盲在男女中的發(fā)病情況怎樣?(男性多于女性)(5)從社會(huì)調(diào)查也是這樣,你是否能從基因和染色體的角度加以解釋?zhuān)浚ㄌ崾荆号匀旧w的構(gòu)成,結(jié)合基因位置及顯隱性進(jìn)行分析)歸納特點(diǎn):歸納出色盲基因遺傳的特點(diǎn)并擴(kuò)展到X染色體隱性遺傳的特點(diǎn)上。色盲基因遺傳(X隱性遺傳)的特點(diǎn):(1)男患者多于女患者(2)交叉遺傳(3)女病兒子必病,男正女兒必正等。問(wèn)題探討:利用“遺傳圖解”結(jié)合“問(wèn)題鏈”繼續(xù)探討,拓展到抗維生素D即X 染色體顯性遺傳的特點(diǎn)。(6)色盲基因在X染色體上屬隱性基因,子代表現(xiàn)男多于女,對(duì)應(yīng)的正常色覺(jué)基因則屬于X顯性基因,子代表現(xiàn)應(yīng)如何?(女多于男)

三、孟德?tīng)栠z傳規(guī)律的現(xiàn)代解釋①分離定律:在雜合體的細(xì)胞中,位于一對(duì)同源染色體上的等位基因,具有一定的獨(dú)立性;在減數(shù)分裂形成配子的過(guò)程中,等位基因隨同源染色體的分開(kāi)而分離,獨(dú)立地隨配子遺傳給后代。②自由組合定律:位于非同源染色體上的非等位基因的分離或組合是互不干擾的;在減數(shù)分裂過(guò)程中,同源染色體的等位基因彼此分離的同時(shí),非同源染色體上的非等位基因自由組合??偨Y(jié):再次強(qiáng)調(diào)孟德?tīng)栠z傳定律的現(xiàn)代解釋課堂練習(xí):書(shū)本31頁(yè)6、教學(xué)反思:本節(jié)課設(shè)置了一系列問(wèn)題情境,層層設(shè)問(wèn),在學(xué)生答問(wèn)、質(zhì)疑、討論過(guò)程中讓學(xué)生建構(gòu)新概念和新的知識(shí)體系,并通過(guò)教師及時(shí)掌握反饋信息,適時(shí)點(diǎn)撥、調(diào)節(jié),讓學(xué)生在推理判斷中培養(yǎng)良好的思維習(xí)慣和對(duì)知識(shí)的遷移能力,而且通過(guò)留出一定的時(shí)間讓學(xué)生提問(wèn),體現(xiàn)了以學(xué)生為主體的思想。

2. let the Ss complete the forms paragraph by paragraph. Purpose here is to help Ss to get the habit of reading a passage as a whole, and pay attention to the organization of the text, as a result the Ss will fully understand the whole passage.3. ask Ss to retell the passage with the help of the key words in the form.Since the Ss in the class are in different levels, so I let them to fill in the blank to understand the meaning of the words and phrases better. ( That’s all for the while-reading. Now let’s move to the fifth step.)Step V: Post-reading (10mins) ---DiscussionIn this part students are asked to discuss in groups and list Wang Kun’s and Wang Wei’s attitudes about the trip. After that, Ss are encouraged to express their attitudes with the whole class. Collect their answers and don’t forget to praise them even if their answers may not be perfect.In this activity, discussion provides a vivid and active learning environment for Ss to communicate in English with newly learned language items. (Finally it comes to the homework.)StepⅥ: Homework (1min)1. Ss are required to read the text again after class and figure out the meaning of some complex sentences.2. Do the exercises on P19; This can help Ss to consolidate what they’ve learnt and make preparation for the next lessonPart4. Blackboard design.(說(shuō)板書(shū)設(shè)計(jì))On the top, there is the title of this lesson. On the left, there are main ideas for each paragraph. On the right, there are some new words and expressions.Unit 3 Travel journalJourney down the MekongMain idea of each para.:Para1: deciding to take a great bike trip along the Mekong river.Para2: Different attitudes between Wang kun and Wang wei.

Textbook: Senior English for China (Book 4), by Liu Daoyi Time Allotment: 1 period (40 minutes)Date: March 20, 2014Teaching aids: blackboard, Multi-media, Power Point, chalk I. Text Analysis (教材分析)This unit is about body language, and the text selected in the reading part demonstrates the difference and similarity of body language in many parts of the world. Through learning this passage, students are required to raise their awareness of using body language in different parts of the world. As body language is closely related to our daily life, it is easy to arouse students’ interest in learning this text. Reading skills and speaking training are designed around the text.II. Teaching Objectives (教學(xué)目標(biāo))By the end of the lesson, students will be able to:1. Language Skill Objective(語(yǔ)言技能目標(biāo)): develop reading ability (skimming and scanning)as well as speaking ability.2. Cultural Knowledge Objective(文化知識(shí)目標(biāo)): know about the cultural differences of using body language.3. Affective Objective(情感目標(biāo)): increase students’ awareness of using body language correctly in different cultures. III.Teaching Focuses and Difficulties(教學(xué)重點(diǎn)和難點(diǎn))1. Teaching Focuses(教學(xué)重點(diǎn)): the difference and similarity of body language in many parts of the world.2. Teaching Difficulties(教學(xué)難點(diǎn)): develop students’ reading abilities of skimming and scanning and ask the students to show their opinions with fluent English.

(3)v. 給:提出;展現(xiàn),顯現(xiàn)present sb. with sth. ; present sth. to sb. 把. . 交給;頒發(fā);授予present sth. (for sth. )/present sth. to sb. e. g. Om his birthday, his friends presented him a collection of stamps. 在他生日時(shí),他的朋友們送給他一套郵票作為禮物。The sword was presented by the family to the museum. 這家人把寶劍捐贈(zèng)給了博物館。The committee will present the final report to Parliament in June. 委員會(huì)將在六月向議會(huì)提交最后的報(bào)告。You need to present yourself better. 你需要更善于展現(xiàn)自己。It is essential that we present a united front. 至關(guān)重要的是我們要表現(xiàn)得更加團(tuán)結(jié)。Step 4 ConsolidationT:Now that we have got a general idea of these words and phrases. Lets make up some sentences using them to master them. Suggested sentences:1. Your duties include typing letters and answering the telephone. 2. It is one of the greatest roles that she has played. 3. A large number of people have applied for the job. 4. The number of the panda is declining. 5. I'11 go there, even if I have to walk. 6. He came up to me to ask for a light. 7. The novel is about a family who can't communicate with each other. 8. He based his plan on interests of most people. 9. Why doesn't he make use of his singing talent?Step 5 Summary and homeworkT:Today we dealt with several new words and phrases. After class I hope that youcan read them again and again to keep them in mind. That's all for today. You aredismissed.

Ⅲ. Analysis of the teaching material:The topic of this unit is cultural relics. Students are quite interested in topics about different cultures around the world. This is the second period of the whole unit. As a reading class, the passage mainly talks about the history of the amber room (how it was made, sent as a gift, lost and rebuilt).According to the new national curriculum, when teaching reading, much emphasis should be put on training the students’ reading skills.Ⅳ. Teaching objectives1. Language objectives:1) Students are required to master the key words and phrases occurred in the passage (e.g. amazing, decorate, belong, in return, less than etc.)2) Students are required to learn the attributive clause and acquire the sentence pattern.2. 1) Students are required to describe a certain thing by using the new sentence patterns.2) Students are required to master two kinds of reading skills—skimming and scanning, and learn to use them in their daily reading.3. 1) Students are required to know the history of the amber room.2) Students are required to appreciate cultural relics and understand the importance of protecting them.Ⅴ. Teaching important and difficult points1) the new words, phrases, and sentence pattern in the course of reading.2) Teaching difficult point: Help the students master two kinds of reading skills—skimmingand scanning and learn to apply them in daily use.Ⅵ. Teaching methods:Task-based method & Top-down model Ⅶ. Teaching aids: PPT, pictures, blackboard Ⅷ. Teaching procedure:

Good afternoon, everyone. It’s my great pleasure to be here sharing my lesson with you. The content of my lesson is Senior English for China Book5 Unit 3 Life in the Future. I’ll be ready to begin this lesson from six parts: Analysis of the teaching material, Analysis of the students, Teaching aims and important and difficult points, Teaching methods and aids, Teaching procedures, and Blackboard design. First, let me talk about the teaching material.Part 1 Analysis of the Teaching Material:This unit is about what human beings’ life will be like in about one thousand years. By studying of this unit, we’ll Enable the students to know the changes in humans’ life and some new inventions bringing about the change and develop the interest in science. This lesson plays an important part in the English teaching in this unit. This is an important lesson in Book Five. From this lesson, it starts asking the Ss to grasp contents of each passage. Therefore, this lesson is in the important position of the teaching material. If the Ss can learn it well, it will be helpful to make the Ss learn the rest of this unit.Part 2 Analysis of the SsAs Senior2 Ss, they are at different levels of English fluency, some of them have lost interest in English. So during the lesson, I arrange a variety of activities to let all of them join in to attract their interest and let them be confident and taste the joy of success.

Teaching Aims:Knowledge 1. Get the students to learn the useful new words and expressions in this section. Aims:2. Let the students learn about how the UK was formed and the four groups of invaders.1. Develop students’ reading ability and let them learn different Ability reading skills. Aims:2. Enable students to learn to talk about the United Kingdom and the Union Jack Emotional 1. Let students know more about the UK2. Develop students’ sense of cooperative learning Aims:Teaching Important Points:1. Let the students learn about the countries of the United Kingdom and the Union Jack2. Get the students to read the passage and know about how the UK was formed and the four groups of invaders.3. Have the students learn different reading skills.Teaching Difficult Ponts:1. Develop students’ reading ability.2. Enable students to talk about the United Kingdom and the Union Jack.3. Let students learn how the UK was formed geographically and historically.Teaching Methods:Showing pictures, asking, exercising, listening, reading etc.Teaching Aids:A computer,a projector and a blackboard.Teaching Procedures: 1) Show a map of the world, ask students the following questions:Where is the UK?What’s the full name of the UK?2) Ask the students work in pairs to do the quiz on Page 9.Do you want to test how many things you know about the United Kingdom? Let’s have a small test.Using the map on P9, students answer the following questions:?How many countries does the UK consist of? What are they??England is divided into three main areas. Do you know what they are? 1) Scanning (10Minutes )Let the students hold the questions asked in pre-reading and read the passagequickly and then let them do the following exercise.Join lines to the right answer.

各小組派代表匯報(bào)。4、教師提出問(wèn)題組織學(xué)生討論:⑴要想了解更多的綠色食品,了解綠色食品的銷(xiāo)售情況,我們應(yīng)該怎么做?⑵要想了解廣大消費(fèi)者對(duì)綠色食品的態(tài)度,食用綠色食品的意義,是否懂得辨認(rèn)綠色食品,以及什么樣的人群對(duì)此知識(shí)最缺乏等,我們應(yīng)該怎么做?組織學(xué)生匯報(bào)交流。5、做個(gè)“綠色食品”廣告設(shè)計(jì)師。為你喜歡的綠色食品設(shè)計(jì)廣告語(yǔ),每組推薦一個(gè)。6、讓學(xué)生了解綠色食品認(rèn)證程序。7、綠色食品打“假”隊(duì)員在行動(dòng)。8、向?qū)W生介紹生態(tài)綠色食品基地。三、活動(dòng)總結(jié):通過(guò)研究、探討,了解學(xué)生對(duì)綠色食品的態(tài)度。提問(wèn):民以食為天,吃,是一個(gè)大問(wèn)題,如果你的爸爸媽媽讓你到超市買(mǎi)牛奶、方便面等,你會(huì)選擇什么樣的食品?為什么?希望通過(guò)今天的學(xué)習(xí),同學(xué)們能夠做到綠色消費(fèi),也希望你們向自己的家人、向周?chē)牧私鈱W(xué)生對(duì)“無(wú)公害食品”、“有機(jī)食品”與“綠色食品”的認(rèn)識(shí)。

Good morning, distinguished judges:It’s my honor to talk about my teaching ideas with you. Today my topic is Women of Achievement. My presentation consists of six parts: the analysis of teaching material and student, teaching aims, key and difficult points, teaching and studying method, teaching procedures and blackboard design.First, let’s focus on the analysis of teaching material. This lesson is from New Senior English for China Student’s Book 4 Unit 1, the reading part. The main topic of the passage is the introduction of a student of Africanwildlife. After this lesson, the students will learn more information about her studying chimps in Africa, and their reading and speaking abilities can be developed as well.The next part is the analysis of students. My students are in senior high students. They have learnt English for many years, they’ve known many words and sentences, but their speaking and reading abilities are still not very good. So I will practice their speaking and reading abilities through different exercises.According to the New Standard Curriculum and the present situation, I set the teaching aims as follows: firstly, knowledge aims. Students can grasp some new words, such as worthwhile, move off. Moreover, students can understand the content of the passage and get familiar with the topic of studying chimps in wildlife. Secondly, ability aims. Students can use reading strategies such as skimming and scanning in reading process. Thirdly, emotional aims. Students can have the awareness of protecting animals and care about animals.Based on the above analysis, the key point of this lesson is to get the main idea and the detailed information from the passage; the difficult point is to talk about the wildlife protection and use reading strategies.

In this class, I have 3 teaching aims, that is, knowledge aims, ability aims and emotion aims.1) Knowledge-Teach students new words and expressions, such as temporary, bleed,sprain choke, first aid, fall ill and so on.-Enable students to have a better understanding for some basic knowledge of first aid.2) Ability-Train students’ speaking, reading and writing abilities by different teaching activities, such as skimming, comprehending, team work, role play, retelling and writing.-Develop students’ reading strategy on how to move general idea to specific information.3) Emotion-Promote students’ awareness of giving first aid.- Cultivate students’ creativities.Then let’s come to my teaching methods and activities.III. Teaching methods and activities:To achieve different teaching aims, various kinds of teaching methods and activities will be adopted throughout this period, such as TBL (task-based learning), skimming, team work, brainstorm and others, which can offer students opportunities to fulfill tasks in which they can use language to achieve a specific outcome.IV. Teaching aids:Computer and blackboardV. Teaching important points:1) Make students have a clear mind for the structure of the text.2) Help students understand the theme of the text.VI. Teaching difficulties:1) So many new words may affect students’ understanding.2) How to get students to know about the functions of the skin and thecauses, characteristics and treatments for different degree burns,and the knowledge about giving first aid. VII. Blackboard design:

一、說(shuō)教材本節(jié)課選自于人教版語(yǔ)文必修二第二單元詩(shī)三首中的一首詩(shī)歌,它是陶淵明歸隱后的作品。寫(xiě)的是田園之樂(lè),實(shí)際表明的是作者不愿與世俗同流合污的心聲,甘愿守著自己的拙志回歸田園。學(xué)習(xí)該詩(shī),有助于學(xué)生了解山水田園詩(shī)的特點(diǎn),感受者作者不同流俗的高尚情操,同時(shí)可以培養(yǎng)學(xué)生初步的鑒賞古典詩(shī)歌的能力。

科學(xué)是人類(lèi)認(rèn)識(shí)世界的重要工具,閱讀科普說(shuō)明文不僅可以啟迪心智,了解更多知識(shí)。而且更夠激發(fā)學(xué)生對(duì)科學(xué)的興趣。學(xué)習(xí)這些文章要注重學(xué)生科學(xué)精神的培養(yǎng),關(guān)注科學(xué)探索的過(guò)程,感受科學(xué)家在科學(xué)探索中表現(xiàn)的人格魅力。我們知道一些科學(xué)家就是因?yàn)殚喿x了相關(guān)的科普文章才對(duì)某一學(xué)科產(chǎn)生興趣,從而走上成功之路的。我們?cè)谥v解的時(shí)候可以跟學(xué)生列舉一些例子,讓學(xué)生認(rèn)識(shí)到一篇好的科普文章的重大意義。

新知探究我們知道,等差數(shù)列的特征是“從第2項(xiàng)起,每一項(xiàng)與它的前一項(xiàng)的差都等于同一個(gè)常數(shù)” 。類(lèi)比等差數(shù)列的研究思路和方法,從運(yùn)算的角度出發(fā),你覺(jué)得還有怎樣的數(shù)列是值得研究的?1.兩河流域發(fā)掘的古巴比倫時(shí)期的泥版上記錄了下面的數(shù)列:9,9^2,9^3,…,9^10; ①100,100^2,100^3,…,100^10; ②5,5^2,5^3,…,5^10. ③2.《莊子·天下》中提到:“一尺之錘,日取其半,萬(wàn)世不竭.”如果把“一尺之錘”的長(zhǎng)度看成單位“1”,那么從第1天開(kāi)始,每天得到的“錘”的長(zhǎng)度依次是1/2,1/4,1/8,1/16,1/32,… ④3.在營(yíng)養(yǎng)和生存空間沒(méi)有限制的情況下,某種細(xì)菌每20 min 就通過(guò)分裂繁殖一代,那么一個(gè)這種細(xì)菌從第1次分裂開(kāi)始,各次分裂產(chǎn)生的后代個(gè)數(shù)依次是2,4,8,16,32,64,… ⑤4.某人存入銀行a元,存期為5年,年利率為 r ,那么按照復(fù)利,他5年內(nèi)每年末得到的本利和分別是a(1+r),a〖(1+r)〗^2,a〖(1+r)〗^3,a〖(1+r)〗^4,a〖(1+r)〗^5 ⑥

求函數(shù)的導(dǎo)數(shù)的策略(1)先區(qū)分函數(shù)的運(yùn)算特點(diǎn),即函數(shù)的和、差、積、商,再根據(jù)導(dǎo)數(shù)的運(yùn)算法則求導(dǎo)數(shù);(2)對(duì)于三個(gè)以上函數(shù)的積、商的導(dǎo)數(shù),依次轉(zhuǎn)化為“兩個(gè)”函數(shù)的積、商的導(dǎo)數(shù)計(jì)算.跟蹤訓(xùn)練1 求下列函數(shù)的導(dǎo)數(shù):(1)y=x2+log3x; (2)y=x3·ex; (3)y=cos xx.[解] (1)y′=(x2+log3x)′=(x2)′+(log3x)′=2x+1xln 3.(2)y′=(x3·ex)′=(x3)′·ex+x3·(ex)′=3x2·ex+x3·ex=ex(x3+3x2).(3)y′=cos xx′=?cos x?′·x-cos x·?x?′x2=-x·sin x-cos xx2=-xsin x+cos xx2.跟蹤訓(xùn)練2 求下列函數(shù)的導(dǎo)數(shù)(1)y=tan x; (2)y=2sin x2cos x2解析:(1)y=tan x=sin xcos x,故y′=?sin x?′cos x-?cos x?′sin x?cos x?2=cos2x+sin2xcos2x=1cos2x.(2)y=2sin x2cos x2=sin x,故y′=cos x.例5 日常生活中的飲用水通常是經(jīng)過(guò)凈化的,隨著水的純凈度的提高,所需進(jìn)化費(fèi)用不斷增加,已知將1t水進(jìn)化到純凈度為x%所需費(fèi)用(單位:元),為c(x)=5284/(100-x) (80<x<100)求進(jìn)化到下列純凈度時(shí),所需進(jìn)化費(fèi)用的瞬時(shí)變化率:(1) 90% ;(2) 98%解:凈化費(fèi)用的瞬時(shí)變化率就是凈化費(fèi)用函數(shù)的導(dǎo)數(shù);c^' (x)=〖(5284/(100-x))〗^'=(5284^’×(100-x)-"5284 " 〖(100-x)〗^’)/〖(100-x)〗^2 =(0×(100-x)-"5284 " ×(-1))/〖(100-x)〗^2 ="5284 " /〖(100-x)〗^2

新知探究前面我們研究了兩類(lèi)變化率問(wèn)題:一類(lèi)是物理學(xué)中的問(wèn)題,涉及平均速度和瞬時(shí)速度;另一類(lèi)是幾何學(xué)中的問(wèn)題,涉及割線斜率和切線斜率。這兩類(lèi)問(wèn)題來(lái)自不同的學(xué)科領(lǐng)域,但在解決問(wèn)題時(shí),都采用了由“平均變化率”逼近“瞬時(shí)變化率”的思想方法;問(wèn)題的答案也是一樣的表示形式。下面我們用上述思想方法研究更一般的問(wèn)題。探究1: 對(duì)于函數(shù)y=f(x) ,設(shè)自變量x從x_0變化到x_0+ ?x ,相應(yīng)地,函數(shù)值y就從f(x_0)變化到f(〖x+x〗_0) 。這時(shí), x的變化量為?x,y的變化量為?y=f(x_0+?x)-f(x_0)我們把比值?y/?x,即?y/?x=(f(x_0+?x)-f(x_0)" " )/?x叫做函數(shù)從x_0到x_0+?x的平均變化率。1.導(dǎo)數(shù)的概念如果當(dāng)Δx→0時(shí),平均變化率ΔyΔx無(wú)限趨近于一個(gè)確定的值,即ΔyΔx有極限,則稱(chēng)y=f (x)在x=x0處____,并把這個(gè)________叫做y=f (x)在x=x0處的導(dǎo)數(shù)(也稱(chēng)為_(kāi)_________),記作f ′(x0)或________,即

二、典例解析例4. 用 10 000元購(gòu)買(mǎi)某個(gè)理財(cái)產(chǎn)品一年.(1)若以月利率0.400%的復(fù)利計(jì)息,12個(gè)月能獲得多少利息(精確到1元)?(2)若以季度復(fù)利計(jì)息,存4個(gè)季度,則當(dāng)每季度利率為多少時(shí),按季結(jié)算的利息不少于按月結(jié)算的利息(精確到10^(-5))?分析:復(fù)利是指把前一期的利息與本金之和算作本金,再計(jì)算下一期的利息.所以若原始本金為a元,每期的利率為r ,則從第一期開(kāi)始,各期的本利和a , a(1+r),a(1+r)^2…構(gòu)成等比數(shù)列.解:(1)設(shè)這筆錢(qián)存 n 個(gè)月以后的本利和組成一個(gè)數(shù)列{a_n },則{a_n }是等比數(shù)列,首項(xiàng)a_1=10^4 (1+0.400%),公比 q=1+0.400%,所以a_12=a_1 q^11 〖=10〗^4 (1+0.400%)^12≈10 490.7.所以,12個(gè)月后的利息為10 490.7-10^4≈491(元).解:(2)設(shè)季度利率為 r ,這筆錢(qián)存 n 個(gè)季度以后的本利和組成一個(gè)數(shù)列{b_n },則{b_n }也是一個(gè)等比數(shù)列,首項(xiàng) b_1=10^4 (1+r),公比為1+r,于是 b_4=10^4 (1+r)^4.

我們知道數(shù)列是一種特殊的函數(shù),在函數(shù)的研究中,我們?cè)诶斫饬撕瘮?shù)的一般概念,了解了函數(shù)變化規(guī)律的研究?jī)?nèi)容(如單調(diào)性,奇偶性等)后,通過(guò)研究基本初等函數(shù)不僅加深了對(duì)函數(shù)的理解,而且掌握了冪函數(shù),指數(shù)函數(shù),對(duì)數(shù)函數(shù),三角函數(shù)等非常有用的函數(shù)模型。類(lèi)似地,在了解了數(shù)列的一般概念后,我們要研究一些具有特殊變化規(guī)律的數(shù)列,建立它們的通項(xiàng)公式和前n項(xiàng)和公式,并應(yīng)用它們解決實(shí)際問(wèn)題和數(shù)學(xué)問(wèn)題,從中感受數(shù)學(xué)模型的現(xiàn)實(shí)意義與應(yīng)用,下面,我們從一類(lèi)取值規(guī)律比較簡(jiǎn)單的數(shù)列入手。新知探究1.北京天壇圜丘壇,的地面有十板布置,最中間是圓形的天心石,圍繞天心石的是9圈扇環(huán)形的石板,從內(nèi)到外各圈的示板數(shù)依次為9,18,27,36,45,54,63,72,81 ①2.S,M,L,XL,XXL,XXXL型號(hào)的女裝上對(duì)應(yīng)的尺碼分別是38,40,42,44,46,48 ②3.測(cè)量某地垂直地面方向上海拔500米以下的大氣溫度,得到從距離地面20米起每升高100米處的大氣溫度(單位℃)依次為25,24,23,22,21 ③

二、典例解析例3.某公司購(gòu)置了一臺(tái)價(jià)值為220萬(wàn)元的設(shè)備,隨著設(shè)備在使用過(guò)程中老化,其價(jià)值會(huì)逐年減少.經(jīng)驗(yàn)表明,每經(jīng)過(guò)一年其價(jià)值會(huì)減少d(d為正常數(shù))萬(wàn)元.已知這臺(tái)設(shè)備的使用年限為10年,超過(guò)10年 ,它的價(jià)值將低于購(gòu)進(jìn)價(jià)值的5%,設(shè)備將報(bào)廢.請(qǐng)確定d的范圍.分析:該設(shè)備使用n年后的價(jià)值構(gòu)成數(shù)列{an},由題意可知,an=an-1-d (n≥2). 即:an-an-1=-d.所以{an}為公差為-d的等差數(shù)列.10年之內(nèi)(含10年),該設(shè)備的價(jià)值不小于(220×5%=)11萬(wàn)元;10年后,該設(shè)備的價(jià)值需小于11萬(wàn)元.利用{an}的通項(xiàng)公式列不等式求解.解:設(shè)使用n年后,這臺(tái)設(shè)備的價(jià)值為an萬(wàn)元,則可得數(shù)列{an}.由已知條件,得an=an-1-d(n≥2).所以數(shù)列{an}是一個(gè)公差為-d的等差數(shù)列.因?yàn)閍1=220-d,所以an=220-d+(n-1)(-d)=220-nd. 由題意,得a10≥11,a11<11. 即:{█("220-10d≥11" @"220-11d<11" )┤解得19<d≤20.9所以,d的求值范圍為19<d≤20.9

1.判斷正誤(正確的打“√”,錯(cuò)誤的打“×”)(1)函數(shù)f (x)在區(qū)間(a,b)上都有f ′(x)<0,則函數(shù)f (x)在這個(gè)區(qū)間上單調(diào)遞減. ( )(2)函數(shù)在某一點(diǎn)的導(dǎo)數(shù)越大,函數(shù)在該點(diǎn)處的切線越“陡峭”. ( )(3)函數(shù)在某個(gè)區(qū)間上變化越快,函數(shù)在這個(gè)區(qū)間上導(dǎo)數(shù)的絕對(duì)值越大.( )(4)判斷函數(shù)單調(diào)性時(shí),在區(qū)間內(nèi)的個(gè)別點(diǎn)f ′(x)=0,不影響函數(shù)在此區(qū)間的單調(diào)性.( )[解析] (1)√ 函數(shù)f (x)在區(qū)間(a,b)上都有f ′(x)<0,所以函數(shù)f (x)在這個(gè)區(qū)間上單調(diào)遞減,故正確.(2)× 切線的“陡峭”程度與|f ′(x)|的大小有關(guān),故錯(cuò)誤.(3)√ 函數(shù)在某個(gè)區(qū)間上變化的快慢,和函數(shù)導(dǎo)數(shù)的絕對(duì)值大小一致.(4)√ 若f ′(x)≥0(≤0),則函數(shù)f (x)在區(qū)間內(nèi)單調(diào)遞增(減),故f ′(x)=0不影響函數(shù)單調(diào)性.[答案] (1)√ (2)× (3)√ (4)√例1. 利用導(dǎo)數(shù)判斷下列函數(shù)的單調(diào)性:(1)f(x)=x^3+3x; (2) f(x)=sinx-x,x∈(0,π); (3)f(x)=(x-1)/x解: (1) 因?yàn)閒(x)=x^3+3x, 所以f^' (x)=〖3x〗^2+3=3(x^2+1)>0所以f(x)=x^3+3x ,函數(shù)在R上單調(diào)遞增,如圖(1)所示
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