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,萬世不竭.”如果把“一尺之錘”的長度看成單位“1”,那么從第1天開始,每天得到的“錘”的長度依次是1/2,1/4,1/8,1/16,1/32,… ④3.在營養(yǎng)和生存空間沒有限制的情況下,某種細(xì)菌每20 min 就通過分裂繁殖一代,那么一個(gè)這種細(xì)菌從第1次分裂開始,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
高斯(Gauss,1777-1855),德國數(shù)學(xué)家,近代數(shù)學(xué)的奠基者之一. 他在天文學(xué)、大地測量學(xué)、磁學(xué)、光學(xué)等領(lǐng)域都做出過杰出貢獻(xiàn). 問題1:為什么1+100=2+99=…=50+51呢?這是巧合嗎?試從數(shù)列角度給出解釋.高斯的算法:(1+100)+(2+99)+…+(50+51)= 101×50=5050高斯的算法實(shí)際上解決了求等差數(shù)列:1,2,3,…,n,"… " 前100項(xiàng)的和問題.等差數(shù)列中,下標(biāo)和相等的兩項(xiàng)和相等.設(shè) an=n,則 a1=1,a2=2,a3=3,…如果數(shù)列{an} 是等差數(shù)列,p,q,s,t∈N*,且 p+q=s+t,則 ap+aq=as+at 可得:a_1+a_100=a_2+a_99=?=a_50+a_51問題2: 你能用上述方法計(jì)算1+2+3+… +101嗎?問題3: 你能計(jì)算1+2+3+… +n嗎?需要對項(xiàng)數(shù)的奇偶進(jìn)行分類討論.當(dāng)n為偶數(shù)時(shí), S_n=(1+n)+[(2+(n-1)]+?+[(n/2+(n/2-1)]=(1+n)+(1+n)…+(1+n)=n/2 (1+n) =(n(1+n))/2當(dāng)n為奇數(shù)數(shù)時(shí), n-1為偶數(shù)
新知探究國際象棋起源于古代印度.相傳國王要獎(jiǎng)賞國際象棋的發(fā)明者,問他想要什么.發(fā)明者說:“請?jiān)谄灞P的第1個(gè)格子里放上1顆麥粒,第2個(gè)格子里放上2顆麥粒,第3個(gè)格子里放上4顆麥粒,依次類推,每個(gè)格子里放的麥粒都是前一個(gè)格子里放的麥粒數(shù)的2倍,直到第64個(gè)格子.請給我足夠的麥粒以實(shí)現(xiàn)上述要求.”國王覺得這個(gè)要求不高,就欣然同意了.假定千粒麥粒的質(zhì)量為40克,據(jù)查,2016--2017年度世界年度小麥產(chǎn)量約為7.5億噸,根據(jù)以上數(shù)據(jù),判斷國王是否能實(shí)現(xiàn)他的諾言.問題1:每個(gè)格子里放的麥粒數(shù)可以構(gòu)成一個(gè)數(shù)列,請判斷分析這個(gè)數(shù)列是否是等比數(shù)列?并寫出這個(gè)等比數(shù)列的通項(xiàng)公式.是等比數(shù)列,首項(xiàng)是1,公比是2,共64項(xiàng). 通項(xiàng)公式為〖a_n=2〗^(n-1)問題2:請將發(fā)明者的要求表述成數(shù)學(xué)問題.
我們知道數(shù)列是一種特殊的函數(shù),在函數(shù)的研究中,我們在理解了函數(shù)的一般概念,了解了函數(shù)變化規(guī)律的研究內(nèi)容(如單調(diào)性,奇偶性等)后,通過研究基本初等函數(shù)不僅加深了對函數(shù)的理解,而且掌握了冪函數(shù),指數(shù)函數(shù),對數(shù)函數(shù),三角函數(shù)等非常有用的函數(shù)模型。類似地,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)際問題和數(shù)學(xué)問題,從中感受數(shù)學(xué)模型的現(xiàn)實(shí)意義與應(yīng)用,下面,我們從一類取值規(guī)律比較簡單的數(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型號的女裝上對應(yīng)的尺碼分別是38,40,42,44,46,48 ②3.測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
情景導(dǎo)學(xué)古語云:“勤學(xué)如春起之苗,不見其增,日有所長”如果對“春起之苗”每日用精密儀器度量,則每日的高度值按日期排在一起,可組成一個(gè)數(shù)列. 那么什么叫數(shù)列呢?二、問題探究1. 王芳從一歲到17歲,每年生日那天測量身高,將這些身高數(shù)據(jù)(單位:厘米)依次排成一列數(shù):75,87,96,103,110,116,120,128,138,145,153,158,160,162,163,165,168 ①記王芳第i歲的身高為 h_i ,那么h_1=75 , h_2=87, 〖"…" ,h〗_17=168.我們發(fā)現(xiàn)h_i中的i反映了身高按歲數(shù)從1到17的順序排列時(shí)的確定位置,即h_1=75 是排在第1位的數(shù),h_2=87是排在第2位的數(shù)〖"…" ,h〗_17 =168是排在第17位的數(shù),它們之間不能交換位置,所以①具有確定順序的一列數(shù)。2. 在兩河流域發(fā)掘的一塊泥板(編號K90,約生產(chǎn)于公元前7世紀(jì))上,有一列依次表示一個(gè)月中從第1天到第15天,每天月亮可見部分的數(shù):5,10,20,40,80,96,112,128,144,160,176,192,208,224,240. ②
天上有明月,年年照相思。她夜夜沉醉在夢中。夢把空間縮短了,夢把時(shí)間凝固了,夢把世界凈化了。夢中沒有污穢,沒有嘈雜,沒有邪惡;夢中沒有分離,沒有創(chuàng)傷,沒有痛苦;夢中只有柔和的月色,只有溫馨的愛;夢使她永遠(yuǎn)年輕,使她不原醒來?!?,那個(gè)世界,是為天下最真最善最美的心靈準(zhǔn)備的,藝術(shù)家懷著虔誠的情感,用充滿魔力的琴弦,在人們的心中筑起了一座不朽的天堂,它像天地一樣長久,日月一樣永恒!新月微微地閉著眼睛,她清清楚楚地看到了那座天堂,真真切切地觸到了那座天堂,冰凌砌成墻壁,白云鋪成房頂,霧靄織成紗幔,星星串成明燈;在那里,她的頭發(fā)像沐浴之后那樣清爽柔軟,隨風(fēng)飄拂,她的肌膚像披著月光那樣清涼潤滑,她的那顆心啊,像浸潤著蒙蒙細(xì)雨的花蕾,掛著晶瑩的露珠,自由地呼吸……她沉醉在那個(gè)一塵不染的美好的境界,如歌如詩,如夢如幻,如云如月,如水如煙……
3.作者為什么不直接描寫人們看見東西呢?請同學(xué)們找出其中的細(xì)節(jié)描寫,并說明有什么表達(dá)效果。答:側(cè)面烘托,正是作者高明之處,這也是許多佳作常用之法。細(xì)節(jié)描寫往往會(huì)成為事情的切入點(diǎn)和突破口,一篇佳作往往離不開一些細(xì)節(jié)描寫,本文也不例外,有些細(xì)節(jié)描寫耐人尋味,如:“德國人撤退時(shí)炸毀的布熱金卡毒氣室和焚尸爐廢墟上,雛菊花在怒放。”“這是一個(gè)二十多歲的姑娘,長得豐滿,可愛,皮膚細(xì)白,金發(fā)碧眼。她在溫和地微笑著,似乎是為著一個(gè)美好而又隱秘的夢想而微笑?!?.句子賞析:“對另外一些人來說,這樣一個(gè)事實(shí)使他們終生難忘:在德國人撤退時(shí)炸毀的布熱金卡毒氣室和焚尸爐廢墟上,雛菊花在怒放?!泵鞔_:一邊是戕害生命的毒氣室和焚尸爐,一邊是生機(jī)勃勃的生命,兩種反差極大的事物擺在一起。表達(dá)了作者對納粹的諷刺:納粹的殘暴終歸阻止不了生命的進(jìn)程。同時(shí)也表達(dá)了作者的控訴:生命的綻放是人世間最美好的事情,對生命的戕害是最惡劣的罪行。
對于教材最后一段內(nèi)容,設(shè)計(jì)如下一個(gè)課堂研討題。讓學(xué)生課前查找有關(guān)資料,在主動(dòng)獲取知識的過程中,對比17、18世紀(jì)中國和歐洲的歷史,了解為什么會(huì)出現(xiàn)不同的發(fā)展趨勢?【課堂研討】17、18世紀(jì)中國和歐洲的封建國家都進(jìn)行了加強(qiáng)君主專制的改革措施。如東方有康熙大帝,西方有路易“太陽王”,他們都使中、法兩國進(jìn)入到封建的鼎盛時(shí)代。但改革卻在中國和歐洲產(chǎn)生了不同影響。這是為什么?通過網(wǎng)絡(luò)或有關(guān)論著,查找有關(guān)資料讓學(xué)生發(fā)表自己的觀點(diǎn)和看法。啟示:17、18世紀(jì)的中國在政治上空前強(qiáng)化君主專制,在經(jīng)濟(jì)上重農(nóng)抑商,在外交上閉關(guān)鎖國,影響了中國資本主義萌芽的正常發(fā)展;文化上文字獄,禁錮了文化。17、18世紀(jì)的歐洲在政治上加強(qiáng)君主專制來反對羅馬教廷的控制,卻實(shí)行君主開明專制;在經(jīng)濟(jì)上實(shí)行重商主義;在外交上鼓勵(lì)對外擴(kuò)張,促進(jìn)了資本主義在歐洲的發(fā)展;文化上,啟蒙思想蓬勃發(fā)展。
一、 教學(xué)目標(biāo) (一)知識與能力通過了解多極化趨勢和對世界的影響、歐盟的形成和擴(kuò)展、日本成為經(jīng)濟(jì)大國的過程和原因、中國和第三世界的崛起等基本史實(shí),培養(yǎng)學(xué)生綜合探究和歸納知識的能力(二)過程與方法以合作學(xué)習(xí)的“創(chuàng)設(shè)情境—目標(biāo)顯示—自學(xué)嘗試—合作學(xué)習(xí)—成果匯報(bào)—總結(jié)評價(jià)”模式為主線,以學(xué)生自主探究活動(dòng)為主體,以教師點(diǎn)撥為主導(dǎo),以培養(yǎng)學(xué)生學(xué)習(xí)的興趣和能力為中心,來優(yōu)化課堂教學(xué)。教師創(chuàng)設(shè)重大國際事件的情境,讓學(xué)生親自探索各個(gè)主要國家對朝鮮戰(zhàn)爭和伊拉克戰(zhàn)爭立場和態(tài)度的決策,培養(yǎng)學(xué)生解讀歷史信息能力,并能夠根據(jù)自身的實(shí)際情況和外部環(huán)境,正確應(yīng)對重大事件。 (三)情感態(tài)度與價(jià)值觀提高學(xué)生對二戰(zhàn)后美蘇兩極以外的各種政治經(jīng)濟(jì)力量增長的認(rèn)識,初步理解世界多極化趨勢的形成及影響,樹立世界走向多極化是不可阻擋的歷史潮流的價(jià)值判斷標(biāo)準(zhǔn)。
【教材分析】This teaching period mainly deals with the grammar: tag questions.This period carries a considerable significance to the cultivation of students’ spoken English. The teacher is expected to enable students to master this period thoroughly and consolidate the knowledge by doing some exercise of good quality.【教學(xué)目標(biāo)與核心素養(yǎng)】1. Get students to have a good understanding of the basic usages of tag questions.2. Enable students to use the basic phrases structures flexibly.3. Develop students’ speaking and cooperating abilities.4. Strengthen students’ great interest in grammar learning.【教學(xué)重難點(diǎn)】1. How to enable students to have a good understanding of the basic usages of tag questions.2. How to enable students to use the basic usages of tag questions flexibly.【教學(xué)過程】Step1: 語法自主探究一、基本組成方法1.肯定式陳述部分+否定附加疑問部分(前肯后否) You often play badminton, don’t you? 你經(jīng)常打羽毛球,是嗎?You are going to the gym with me, aren’t you?你要和我一起去健身房,是嗎?She’s been to shanghai before, hasn’t she? 她以前去過上海,是嗎?2.否定式陳述部分+肯定附加疑問部分(前否后肯) It isn't a beautiful flower, is it? 那不是美麗的花,是嗎?You didn't go skating yesterday, did you? 你昨天沒去滑冰,是嗎?They can’t finish it by Friday, can they?他們不能在星期五之前完成,是嗎?
The theme of this section is “Talk about festival activities and festival experiences”.Festival and holiday is a relaxing and interesting topic for students. This part talks about the topic from the daily life of students’. In the part A ---Listening and Speaking, there are three conversations among different speakers from three countries(Japan, Rio and China), where the speakers are participating in or going to participate in the festivals and celebrations. So listening for the relationship among them is a fundamental task. Actually, with the globalization and more international communication, it is normal for Chinese or foreigners to witness different festivals and celebrations in or out of China. In the Conversation 1, a foreign reporter is interviewing a Japanese young girl who just had participated in the ceremony of the Coming-of-Age Day on the street and asking her feeling about the ceremony and the afterwards activities. Conversation 2, Chinese girl Li Mei is witnessing the Rio Carnival for the first time, and her friend Carla gives her some advice on the costumes which enables her to match with the carnival to have a good time. Conversation 3, a Chinese guide is showing a group of foreign visitors around the Lantern Festival and introducing the customs of the festival to them. The three conversations have a strong vitality and insert the festival and cultural elements from different countries. So perceiving the festivals and cultures from different countries is the second task. At the same time, the scripts also insert the targeted grammar --- v-ing as attributive and predicative, which students can perceive and experience in a real context and make a road for the further study. That is the third task. In the Part B--- Listening and Talking, the theme is “Talk about festival experience”, which is the common topic in our daily conversations. During the conversation, Song Lin, a Chinese student, asked Canadian friend Max about how to spend Christmas. In the conversation, Song Lin talked about experience and the feelings during the Chinese Spring Festival, during which there are not only some enjoyable things but some unpleasant things. After the listening, perhaps students find there are some similarities between Christmas and the Chinese Spring Festival as there are some differences in the origins and celebrations. For example, people always visit friends and relatives, decorate their houses, have a big dinner together, chat and give presents to each other.
Step 3 Analyzing article structureActivity 31. Teachers raise questions to guide students to analyze the chapter structure of this diary and think about how to describe the festival experience. (1)What should be included in the opening/body/closing paragraph(s)?(2)How did the writer arrange his/her ideas?(3)What kind of interesting details did the writer describe?(4)How did the writer describe his/her feelings/emotions during the event?2. Students read and compare the three sentence patterns in activity 2. Try to rewrite the first paragraph of the diary with these three sentence patterns. After that, students exchange corrections with their partners. Such as:●This was my first time spending three days experiencing the Naadam Festival in China’s Inner Mongolia Autonomous Region and it was an enjoyable and exciting experience. ●I'll never forget my experience at the Naadam Festival because it was my first time to watch the exciting Mongolian games of horse racing, wrestling, and archery so closely. ●I'll always remember my first experience at the Naadam Festival in China’s Inner Mongolia Autonomous Region because it was so amazing to spend three days witnessing a grand Mongolian ceremony. Step 4 Accumulation of statementsActivity 41. Ask the students to read the diary again. Look for sentences that express feelings and emotions, especially those with the -ing form and the past participle. Such as:● …h(huán)orse racing, wrestling, and archery, which are all so exciting to watch. ● some amazing performances● I was surprised to see…● I was a little worried about. . . ● feeling really tiredOther emotional statements:●I absolutely enjoyed the archery, too, but the horse races were my favourite part. ●I'm finally back home now, feeling really tired, but celebrating Naadam with my friend was totally worth it. ●He invited me back for the winter to stay in a traditional Mongolian tent and cat hot pot. I can’t wait!2. In addition to the use of the -ing form and the past participle, the teacher should guide the students in the appreciation of these statements, ask them to memorize them, and encourage them to use them reasonably in writing practice.
The topic of this part is “Write about your festival experience”.During the Listening and Speaking and Talking, students are just asked to say out their festival experiences such as the Spring Festival, Mid-autumn Day, but this part students will be asked to write down their own festival experiences. During the reading part, it introduces the Naadam Festival in Inner Mongolia Autonomous Region, which can give students a good example to imitate. Students not only learn the festival, but touch and feel the Inner Mongolian’s character, the spirit and cultural atmosphere, which can help students form the cultural awareness and learn to enjoy and value the diversity of Chinese culture.Concretely, the dairy tells the experience that the author spent the Naadam Festival in Inner Mongolia Autonomous Region with his/her friend. The structure is clear. In the opening paragraph, it introduces the topic of the Naadam Festival and the whole feeling. Then it introduces the items of the festival like the ceremony, wrestling and horse racing. Finally, it summarizes this experience. Because this part is a travel journal, we must guide students pay more attention to these details: 1. use the first person. 2. use the past tense to tell the past thing and use the present or future tense to describe the scenery. 3. use the timeline to tell the development. 4. be careful for the author’s psychology, emotion and feeling, etc.1. Read quickly to get main idea; read carefully to get the detailed information about Naadam Festival.2. Learn the structure of the reading article and language.3. Write an article about a festival experience4. Learn to use the psychology, emotions and feeling in the writing.1. Write an article about a festival experience.2. Use the structure of the reading article and language.
淺層地下水是貯存于地表松散堆積物中的潛水。主要受降水、氣溫、蒸發(fā)等氣象因素影響,有明顯的季節(jié)變化與日變化,并與河水有相應(yīng)補(bǔ)給關(guān)系,即河水高于潛水面時(shí),河水補(bǔ)給地下水,反之地下水補(bǔ)給河流;深層地下水是長時(shí)間內(nèi)滲入地下深入儲存起來的,它緩慢地流出補(bǔ)給河流,受氣象因素影響很小,通常只有年變化,季節(jié)變化已不明顯。當(dāng)然,一條河流的河水補(bǔ)給來源往往不是單一的,而是以某一種形式為主的混合補(bǔ)給形式,對流域自然條件復(fù)雜的大的河流來說尤其如此。我國長江上游地區(qū)除雨水、地下水外,高原高山上冰川、積雪在夏季融化也補(bǔ)給河流;東北地區(qū)的河流,由春季融化積雪補(bǔ)給,夏季則由雨水和地下水補(bǔ)給;西北內(nèi)陸盆地除雨水外,夏季高山冰川、積雪融化成為河流的主要補(bǔ)給形式。我國季風(fēng)地區(qū),大部分河流以雨水補(bǔ)給為主,而冬季則由地下水補(bǔ)給。
1.流水堆積地貌由于河床坡度降低,導(dǎo)致流速減小 ,或者其他原因,引起河流搬運(yùn)能力降低,促使沉積發(fā)生,形成堆積地貌。常見的河流堆積地貌主要有以下幾種:(1)沖積扇平原沖積扇是河流出山口處的扇形堆積體。河流出 山口后,比降顯著減小,水流又分成許多交漢,成扇狀向外流動(dòng),河流能量顯著降低,大量物質(zhì)堆積下來,又有利于河流改道。隨著各支汊的不斷堆積和變遷,就形成沖積扇。沖積扇的物質(zhì)結(jié)構(gòu),一般是頂部物質(zhì)較粗,主要為沙、礫 ,隨著水流搬運(yùn)能力向邊緣減弱,堆積的物質(zhì)逐漸變細(xì),邊緣一般多為沙、粉沙及亞粘土,分選性較好,所以沖積扇是較好的含水層,邊緣常有泉水出 露,可發(fā)展自流灌 溉。若山地河谷隨山地間歇抬升,也可形成疊置沖積扇。(2)河漫灘平原河漫灘平原發(fā)源于河流中下游。在河流中下游地區(qū),河流下蝕作用減弱,側(cè)蝕作用加強(qiáng),河流往往凹岸侵蝕,在凸岸堆積形成水下堆積體。堆積體 的面積逐漸擴(kuò)大,在枯水季節(jié)露出水面,形成河漫灘(見下圖)。
一、知識和技能1.使學(xué)生能夠正確認(rèn)識太陽的基本特征及其外部結(jié)構(gòu);2.了解太陽能量的來源,理解太陽是地球的主要能量源;3.了解太陽活動(dòng)(主要是黑子和耀斑)對地球的影響。二、過程和方法1.能通過展示的圖片理解太陽活動(dòng)增強(qiáng)時(shí)會(huì)使地球無線電短波通訊受干擾及產(chǎn)生磁暴現(xiàn)象的原因。2.通過對各種資料的觀察以及課前室外的觀測,培養(yǎng)學(xué)生獲取地理信息的能力和分析、判斷、推理等邏輯思維能力三、情感、態(tài)度、價(jià)值觀培養(yǎng)學(xué)生樹立正確的人地觀、科學(xué)的宇宙觀,和熱愛科學(xué)勇于探索的精神【教學(xué)重點(diǎn)】1.知道太陽輻射對地球的影響; 2.知道太陽活動(dòng)對地球的影響;3.太陽的外部結(jié)構(gòu)和能量來源【教學(xué)難點(diǎn)】太陽活動(dòng)(黑子和耀斑)對地球的影響
一、知識和技能1.使學(xué)生了解地球的圈層構(gòu)造,初步掌握地球內(nèi)部圈層的組成和劃分依據(jù)2.使學(xué)生了解各內(nèi)部圈層的界限、厚度、物理性狀等。二、過程和方法1.使學(xué)生了解研究地球內(nèi)部構(gòu)造的方法,從而認(rèn)識人類對未知事物所進(jìn)行的探索實(shí)踐,激發(fā)同學(xué)們學(xué)科學(xué)、愛科學(xué)的興趣及責(zé)任感。2.了解地球內(nèi)部圈層劃分實(shí)況及各層主要特點(diǎn),從宏觀上認(rèn)識全球的整體面貌,形成地球系統(tǒng)觀念。3.通過歸納、總結(jié)、對比地球內(nèi)部各層的特點(diǎn),對學(xué)生進(jìn)行綜合歸納等思維能力的培養(yǎng)和訓(xùn)練。三、情感、態(tài)度、價(jià)值觀通過學(xué)習(xí)對學(xué)生進(jìn)行熱愛自然、熱愛科學(xué)的教育,鼓勵(lì)學(xué)生獻(xiàn)身于科學(xué)教育事業(yè)?!窘虒W(xué)重點(diǎn)】1.地震波的波速及傳播特點(diǎn),區(qū)別橫波與縱波。2.地球內(nèi)部圈層劃分實(shí)況及各層主要特點(diǎn),特別是地殼的特點(diǎn)。3.巖石圈概念,軟流層知識。
討論:二氧化碳在大氣的受熱過程中起到了什么作用?(吸收太陽輻射中的紅外線輻射和地面輻射,保溫作用)大氣中的二氧化碳濃度增大對氣溫有什么影響?(全球氣候變暖)閱讀:我們知道了太陽輻射中的可見光和紅外 光能量的吸收和轉(zhuǎn)化,那么紫外區(qū)的能量到哪兒去了?請同學(xué)們查閱資料,自主探討。小結(jié):大氣的受熱過 程就是太陽曬熱了地面,地面烘熱了大氣。太陽輻射是大氣的根本熱源,地面輻射是大氣的直接熱源。這就是為什么海拔越高,氣溫越低的原因,難怪高處不勝寒!轉(zhuǎn)承:大氣的直接熱源是地面,不同性質(zhì)的地面溫度是不同的,同緯度,海洋和陸地就有溫差。提問:請學(xué)生說說白天和晚上在海邊的不同感受。由白天和晚上的風(fēng)向不同切入實(shí)驗(yàn)P32活動(dòng)。討論:通過煙霧的飄動(dòng),我們得出了什么規(guī)律?冷熱不均引起了熱力環(huán)流板書: 二、熱力環(huán)流板圖與分析:結(jié)合試驗(yàn),學(xué)生分析熱力環(huán)流 的產(chǎn)生
晶晶和亮亮是兩滴巖漿,他們生活在地球內(nèi)部的:巖漿之家。一天,他們得到批準(zhǔn),與其他同伴一起到地球表面進(jìn)行旅行。他們飛快地奔向地表,半路上,晶晶覺得累了,于是就與亮亮約好,在地表匯合。亮亮沒有停步,與其他伙伴一起跳出地表,并沿著山坡往低處流動(dòng)。忽然,亮亮發(fā)現(xiàn)自己不能再動(dòng)了,不禁問旁邊的同伴這是怎么一回事。同伴笑著說:“別擔(dān)心,只不過你已經(jīng)不再是巖漿罷了?!眴栴}1、為什么同伴說亮亮已經(jīng)不再是一滴巖漿了?2、你認(rèn)為亮亮還可以繼續(xù)他的地表旅行嗎?請說明原因。(由學(xué)生討論回答。)過了好長的一段時(shí)間,亮亮發(fā)現(xiàn)自己的個(gè)頭變小了,并隨著風(fēng)和流水往前運(yùn)動(dòng)了。亮亮邊走邊欣賞著地表美麗的風(fēng)光。忽然,亮亮發(fā)現(xiàn)一個(gè)熟悉的身影,認(rèn)真一看,原來是晶晶。亮亮驚訝地問:“你是怎么來到地表的?”3、請你簡要推測晶晶到達(dá)地表的過程。(由學(xué)生討論回答。)亮亮和晶晶又一起踏上旅程。
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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