有用资料

非常有用的150个生活小常识（国外英文资料）Very useful150life tips.Believe that everyone can be usefulIn autumn and winter,the hands and feet are prone to crack, but you can wash your hands and feet with hot water for about10minutes,for a week,the skin will be smooth and smooth.Use plastic bag to keep fresh chives:put the Chinese leek in a plastic bag in a cool place,but it can be kept for about three or four days,and it can be kept fresh inwinter for a week.In winter,the weather is dry and cold,the hands and feet are prone to crack,and if you put some toothpaste on the cleft,you can stop the pain and make the tear heal quickly.It is difficult to clean the oil box on the lampblack machine,but in a clean oil case,you can put water in it, let the oil drip on the water,and then pour it all out.5,chemical fiber material is the quilt of bedding,quiltis not suitable to be exposed in the sun,can cover a layer of cloth in the quilt,prevent the direct sunlight.The white sweater is worn over long time gradually black, the sweater is cleaned and put in the freezer for one hour, take out air dry,can be white as new.The grease of the milk of milk in winter will coagulate onthe wall of the bag,not easy to scrape,but it can be preheated by the stove before cooking,and the oil is melted.8,the sweater is worn long,some part will grind bright, use vinegar,water each half of mixed liquid to spray a bit, wash again,can restore the original.In the autumn and winter season,the daily boiled andedible white radish,even the soup and vegetable dishes in the morning and evening clothes a small bowl,the long-term persistence can effectively cure chronic bronchitis.In the cold season,you will be able to prevent chilblains by rubbing your ear and losing weight every day,and then using a hair dryer to warm them for a while.When decorating in winter,the wood should be careful to protect the moisture from deformation.The woodworking products should be sealed in time to prevent shrinkage.The wooden floor wants to set apart2millimeter to be in the expansion seam.Experts advise eating more red peppers,carrots,hawthorn and other foods in the winter,or a cup of yoghurt a day,a bowl of chicken soup,to prevent colds.Place a cloth with glycerin and egg yolk on the surface of the stain and place it for a moment.Rinse it with water.It can be cured by the nose of the nose,and it will berubbed into the nostrils.The potassium and essential oils in the grass will keep the nose open.When the silk is ironed yellow,use a little baking soda to add water to make a paste,besmear in the mark place,wait for the water to evaporate,again the wet cloth iron,the yellow can be removed.Freshly bought ceramic cutlery,boiled in4percent vinegar water,can remove most of the toxic substances.The cotton clothes appear the mildew spot,use a few green bean sprouts in the place of the mould spot repeatedly knead,then use clear water to rinse clean,can clear.The skin of grapefruit is boiled water can cure frostbite, boil water in the skin of a grapefruit to scrub the disease, 1~2times a day,a few times can be effective.The water mist wet towel that is in the bathroom mirror is very difficult to clean,but now the mirror is coated with soap,use dry dishcloth again,the mirror is easy torestore clear.When the lime flies into the eye,it can relieve the painby dripping a little sugar water.The drawer,the closet,the clothes box contain the musty smell,put a bar of soap in inside,can remove.When buying a gift box,the price tag is hard to tear off.The dryer can be blown hot and torn,and it will be easily ripped and left without any trace.Raw peanut can cure presbyopia,eat about25grams of peanuts a day,once a day,long-term persistence is helpful for the restoration of presbyopia.Ginger juice is a medicine for carsickness,and tea and water to rinse mouth and mouth.In winter,licking your lips will make you more and more dry.Don't burn your hands after freezing,you can easily get chilblains.Avoid washing your hair before bed to avoid catching a cold.Avoid wearing face mask,can make mucosa mucosa become delicate,easy catch cold.The banana peel can cure frostbite effectively,rub the inside face of banana skin gently to rub frostbite area,until fever,several times can effect.27,the green bean has the trick of cure the cold:can boil mung beans first,boil bad hind add ginger and cola,while hot drink to be able to return to the fever to cure the flu.The flower chilli leaf water bubble foot cure heel pain,the fresh flower pepper leaves water boil,while hot bubble foot,even bubble a few days,half an hour,quick cure.Remove egg white from the clothes,but first use cold water bubble,then wash with the tea water,then rinse with water, then remove the egg white.The banana ice sugar is steamed cough,the banana3,the sugar5grams,put in the bowl,the wen fire steamed a quarter of the food,the cough effect is very good.Wash your face with orange peel,soak a few slices of orange peel in boiling water,and wash your face with orange peel water when the temperature is right.32,the date cure the arms and legs crack,take several dates to remove the skin core,add water to make a paste, daub in the crack,two days a day,can heal a few days.The pork oil honey cream can cure the chilblains,take20 grams of lard,honey80grams,and put it together into a paste.Apply to the affected area three times a day and can be cured in a few days.Starch juice for the nose.Take starch one or two,open water a bowl with cold water,stir well,empty stomach, every morning and evening,three days of treatment.If the clothes are stained by oil stains,the oil can be removed by gently rubbing the fresh white bread.The hot pepper should be applied to the gout.Cut thechilli into strips and stick them in the affected area for 24hours.The white radish is the nasal plug.Remove3to4radishes, add water to the pot,boil and steam after boiling.After a few minutes,the nose will be free.The lyssus can cure e two to three drops of warm water foam feet every night.After a few times,the frostbite is good.Coke can cure colds.When colds start,you can boil a coke with a few slices of ginger and a lemon,and then drink it with a significant effect.Use hot rice soup to make a wooden ear,half an hour later fish out,the wooden ear that USES this method bubble not only the appearance is very loose and loose,and the tasteis fresh and tender after stir-fry.1,licorice green bean soup to solve drug poisoning.In the case of drug intoxication,15grams of licorice,50gramsof mung bean,one dose a day,three times.Vinegar can eliminate the smell of refrigerators.Put some vinegar into your open glass bottle and put it in the fridge.43,qiao wash woolen sweater:wash in warm water whenadding suitable amount of laundry detergent and ammonia,add a few drops of vinegar rinse,can help to restore the luster and softness of original wool fabric.In the area of the affected area,the area of the diseasecan be cured by the tinea.4to5times a day in the areaof the disease,the skin gradually dries out and the tinea is cured.Drinking white wine can prevent canker sores.After theoral mucous membrane is bitten,the small amount of white wine in the mouth is gargle,and after5~10minutes,the oral ulcer is no longer happening.To brush the leather shoes:use alcohol and yellow rice noodles to make a paste on the face of the shoes,dry and then brush off the yellow rice noodles,and the dirt wi11 be removed.47,baijiu is the treatment of sweat and feet.After washing the feet every night,use the white wine a littleto rub the foot,and natural air dried,hold for a month, can cure the foot stink.The beer mouthwash can go to dust disinfection.Rinsing your mouth with a beer can wash down the dust in yourthroat and make your throat more comfortable.49,apply a bit of gesso powder and chalk and ash water on the glass first,wash with dry cloth again,can brush glass easily.Break the egg,separate the egg yolks and the egg whites, pour the egg yolks into the milk and cook it,and drink it to the effect of the town brain.After51,soap in water softening,quite inconvenient to use,half an hour to put it in the refrigerator freezer, refrigerator can absorb excess water,to restore the soap hardness.When the eye is dry,use boiling water to make tea,close the eyes to the cup,both hands protect the cup,each time ten minutes can soothe the eyes,moisten the eyeball, protect the vision.The folk divide the people with acne:fresh cucumber juice, white vinegar the same amount of evenly,first use hot water wash a face,then rub face,a day three times,after the powder of the day to wash away with warm water in10 minutes.54,eat leek and cure the throat.Stir-fry a handful of unchopped leek and swallow it to the throat.The jujube bark ointment can cure the burn.Take the proper amount of jujube,wash it with boiled water,bake,grind it up,add sesame oil and paste it to the spot.The chewing ginger can divide the oral cavity.When ablister is in the mouth,a few slices of ginger can be sliced and chewed,and the blisters will slowly disappear.Make your teeth quickly white:use the same amount of salt, baking soda,water,and brush your teeth once a day for four days to whiten your teeth.A quick marinade:rinse the eggs with clean water,then wash them with vinegar,then put them in salt water and serve in a week.A dish of water,which is filled with a plate of water,will fall into the water in the dust and blink severaltimes in a row to remove the foreign object.Food hypnosis method:(1)eat a small amount of bread half an hour before going to bed.(2)drink the right amount of milk to sleep.Treatment of anaemic soil:the blood flow to a white sheet of white paper,dried and dried up to powder,red wine,a day and a half of powder,twice a day.Foot pillow pillow to cure cramp.Sleep with a pillow under your feet every night to prevent cramps from occurring during sleep.When you eat hot pot,you can put a proper amount of beerin the soup to make a decrease internal heat effect,eathot pot and drink beer,and the carbon dioxide in the wine helps to heat the heat and prevent food from burning the mouth.Peppermint liquorice tea is effective in protecting the voice.Make tea with5grams of mint,3grams of licorice, and drink this tea to prevent throat itching and coughing.65,licorice zinc can be treated with repeated canker sores.Oral ulceration can be treated with oral licorice and zinc.The salt water except the chicken eyes.Boil the water with a teaspoon of table salt,then heat the feet after a cool, and then dry the feet for half an hour.67,the seaweed is mixed with honey to cure the mouth sores. Burn the kelp(or eggplant skin)and mash it with honey and apply it to the affected area.It works well.Apply soap to reduce the pain.If you are burned by hot water or fire,rub some soap in the area immediately to relieve the pain.Strawberries and sugar stew can stop coughing.Take strawberry to the sugar(2:1)and make it three times a day for several days to stop coughing.70,white sugar is the best use:make fish and white sugar, fish fillet is easy to form;White sugar can shorten the fermentation time;The dish is sour and white sugar can be removed.Milk can make fish soup beautiful.A few drops of milk can be dripped in the pan while stewed fish soup at home,which will not only make the fish tender,but also the fish soup.Eating peanuts is a good way to treat your teeth.Munch on a few peanuts or a piece of raw onion,and the teeth are immediately restored,and you can continue to chew.Massage eye socket for rhinitis.The index finger is placed in two pairs of eyes,two hundred times a day for a periodof time.To remove mold from the refrigerator,use a dry cloth torub the soap and water.If you can*t rub it,use a drycloth to dip in a small amount of alcohol.If the sweater cuff or hem has lost its elasticity,soak it in hot water for20minutes,and when the dryness is dried, the elasticity will be restored.Salt and almonds add white to the face.Take a tablespoonof salt,150grams of almond powder,and paste it withwater and apply it to your face.The onion drives the cockroaches.Put a plate of sliced onion in the room,the smell of cockroach will be intoxicated,and it can also slow the deterioration of indoor food.78,vinegar and soybean milk shampoo are good.Wash the shampoo with the water with soybean milk,wash with the water of adding rice vinegar,and two days,the effect is good.It is easy to fish scales with vinegar.In the case of microscale fish,you can add a few tablespoons of vinegarto the fish in the water for the first two hours before you kill.Wash the fresh and tender garlic seedlings in the cut section,add sugar,vinegar,salt,soy sauce,soak for a week,and then when the salty dish is eaten,caneffectively remove the worm.The boiled beans can be distended.Pour the beans into a proper amount of sugar,and take a few tablespoons a dayfor a week to effectively treat abdominal distension.The water is frozen in the bottle,the beer is poured from the drink bottle,the fridge is put in the refrigerator,40 minutes is fine,and the water is two hours without water.The freshly butchered chicken has a foul smell,such as a mixture of salt,pepper and beer in a mixture of salt, pepper and beer.84,wipe the toothpaste to stop the pain to prevent the infection,small area skin injury or burn burn,apply alittle bit of toothpaste,but immediately stop the blood pain to prevent the infection.When you have a blisters on your lips,wash the area with warm water,then blisters the oily liquid,and at least three times a day,you can accelerate the blisters.It is easier to put the soap on the head before the screwis screwed,and then the head is turned into the wood.When the symptoms of cold symptoms such as sore throat,nasal congestion,fever and other cold symptoms can befound in the thick tea,the symptoms can be effectively approached.Salt water can prevent heatstroke.People who sweat too much in the summer,drink water in moderation,not only quench thirst,but also prevent heatstroke.89,the clothes are accidentally stained with milk,blood stain,new trace should be washed in cold water immediately, the trace should be washed with detergent first,then use light ammonia water to wash.Fried kiwi fruit for hepatitis.Take kiwi fruit100grams, red jujube12,the water is Fried as tea drinking,the effective treatment acute hepatitis has the promotion effect.Eating apples can alleviate the acid.Often anti-acid,eating an apple during a bad acid condition relieves such symptoms.When it is difficult to sleep in a hot climate,you can chop up a few Onions,wrap them in gauze,and sniff before bed.Take150grams of salt,100grams of chrysanthemum,soak in boiling water,wash the armpit after temperature,and twice a day,except the body odor.Take a watermelon skin250grams,add500grams of water,boil water to half,add some ice sugar and take it forthroat throat.Take60ml of fresh silk melon juice,add honey to theright amount,stir well,twice a day,have certaintreatment for pertussis.Treatment of myopia:often squatting is effective in reducing the flow of blood to the venous vein,relievingthe blood stasis in the abdomen,alleviating the fatigue of the eyes,and preventing shortsightedness and the loss of vision.The method of arranging flowers:cut the end of the branch of the flower branch with the scissors every day to make sure that it is fresh,and keep the branch of the flower branch in good condition.98,plantain grass can cure urine frequency.Wash the roots of the front grass and boil the water for3to4times a day.The tip of the dandruff:combine the salt with a little bit of borax to clear the water,make it completely dissolveand then wash the head,can effectively stop the tickling.After you wake up in the morning,rinse with water anddrink a cup of honey water.After an hour,you will eat breakfast,and you will be able to treat gastritis for a long time.The heat of the summer heat,the heat rash,the area that can use warm water to have heat rash is washed,besmear a layer of toothpaste,heat rash soon can disappear.The oxalic acid in bitter melon can interfere with the absorption of calcium in food.Before frying the bitter melon,it should be blanched in boiling water,remove oxalic acid and stir-fry.103,can use beer to wipe the ornamental leaf plant,after the beer is wiped out not only the dust not,the dirt of the long years can also be removed,the leaf noodles also leave the natural luster.At the beginning of the case of diarrhea,eat fresh peach (eat fresh peach before the meal and eat large garlic cloves in rice),and the average diarrhea can be relieved after12hours.Make a small cut of a fresh pear,add water and sugar to the boil,and then use it for a cough tone and dry throat.Remove from vegetable oil.Boil a moderate amount of vegetable oil,then apply it to the scab,and it will soon be removed.107,the chewing sesame can stop the anti-acid,the anti­acid,the advisable amount of the sesame to chew after chewing,after a moment,can stop the anti-acid,the curative effect is remarkable.108,air oil cure burn.For minor scalding,the oil can be applied directly to the burn area and applied every four hours.The hot pepper most people love to eat,the chilli is hot and hot,can be scrubbed with white wine,wash with clean water,the hand is not hot in a moment.110,when toothache,use vinegar to boil Chinese woIfberry, bletilla of bleaching mouth,have the pain effect,when brushing teeth the vinegar that drops a bit of vinegar on the toothpaste can clear the soot from the teeth.When the cold seat is bought or used,apply the brush tothe hot water to wash and dry for20minutes,which will clear the sweat and mite.112,wooden furniture apply dry cloth to wipe and the waxto maintain,if the dirt that is touched,can use cloth to dip in toothpaste to wipe first,after,use wet cloth to wipe.113,tooth whitening and partial:use papaya slice,wipe tooth twice every day,every time2minutes,insist January, must be effective.Boil the right amount of green beans,add sugar,and drink water every day.Cure mouth ulcer small side:take a walnut shell10to be around every day,use water to fry soup orally,3times aday,3days can be cured.Mix the baking soda with salt in proportion to1to1,add water to make the paste,use it to brush your teeth sooner or later,and keep using your teeth.117,cod liver oil treatment tinea.Break the fish liveroil pills,take a few external compresses,and after a few hours,if there is no adverse reaction,you can apply it three times a day.118,armor tips.After you finish your manicure,soak your nails in olive oil with a little lemon juice for10minutes each time.When bleeding,pinch a handful of jasmine tea in your mouth to make a paste,stick to the wound and don,t let go,and then stop the bleeding.The honey can be used to treat canker sores,wash the mouth and coat the surface of the ulcer,hold for a few minutes, then swallow,three times a day.。

结晶果糖结晶果糖具有高甜度的特点，它的甜度是蔗糖的1.3～1.8倍。

同时，具有风味强化、甜味强化、高保湿性、低水活性、可强化Maill ard反应、高渗透压、降低凝冻温度、快速／强化成胶等功能特性。

由于研究的不断深入，使其应用领域愈加宽广。

果糖在水果罐头、果冻、果酱、调味品和糖果等产品中对提高质量、降低热量和成本以及新产品开发都有很大帮助。

结晶果糖为单糖，是糖类中化学活性最高的糖，天然存在于蜂蜜及菊芋、菊苣等菊科植物中。

果糖甜度高，有水果香味，热值低，在体内代谢比葡萄糖快，易被机体吸收利用，且不依赖胰岛素，对血糖影响小，适用于葡萄糖代谢及肝功能不全的患者补充能量。

在人体内能促进有益细菌如双歧杆菌类生长繁殖，抑制有害菌生长，改善人肠胃功能和代谢，降低血脂，不致龋齿，是糖尿病人、肥胖病人、儿童食品的理想甜味剂。

果糖甜度高、热能低，健康饮品常使用果糖来降低甜味剂的固形物的含量。

果糖与其他甜味剂如葡萄糖、蔗糖以及阿斯巴甜混合使用具有甜味强化的效果，从而能够降低甜味的材料成本。

试验表明，将果糖与蔗糖以1∶1比例混合添加在饮料中，可比单纯用蔗糖减少20％的甜味剂用量结晶果糖是一种高档食品糖料，是一种天然健康糖，结晶果糖是一种单糖、吸收快、不会引起血糖升高、不至龋齿、是一种新的健康食糖，代蔗糖放面效果好摘要:纯果糖虽是一种天然营养甜味剂，但过去难以应用于各种食品配方中，原因是价格昂贵。

但随着工业化生产，纯结晶果糖在欧美、日本等发达国家已用于功能食品、营养保健食品、冷饮食品以及低热值食品和运动型饮料配方中。

随着纯结晶果糖逐渐在我国进入工业化规模生产，可以预计这种天然营养甜味剂在食品中的应用也将会越来越多。

山东西王生化科技有限公司是国内最早研发结晶果糖的上市公司、也是亚洲最大的结晶果糖生产企业。

结晶果糖英文名：Fructose分子式：C6H12O6分子量：180.16性状：吸湿性极强的白色无臭结晶或结晶性粉末。

味甜，舔度约为蔗糖的1.6倍，为糖类中最甜者。

专升本最有用的复习资料专升本是大专升本的简称。

许多在职人士、成人考生和待业人士都希望通过专升本考试来提升自己的学历和能力。

然而，专升本考试的难度相比于高考等级要高一些。

因此，为了能够顺利通过考试，需要认真备考，选择一些有针对性的复习资料。

本文将介绍一些最有用的复习资料，以便广大考生进行备考。

工具书工具书是指专业性比较强、内容比较繁多的书籍。

通过工具书的学习，可以有效地提高考生对专业知识的认识和理解。

例如，有些专业需要掌握比较复杂的计算方法和公式，这时工具书可以帮助考生更好地掌握这些知识点。

历年真题历年真题是指以往的专升本考试的真实试卷。

通过做历年真题，可以了解考试的难度级别和题型类型，并可以逐渐培养抽象思维和推理能力。

同时，做历年真题还能让考生更好地了解自己的实际水平，从而调整自己的备考策略，达到事半功倍的效果。

教材和课本教材和课本是指专业教师编写的教学资料。

通常都会包含专业知识的基本内容，因此是备考的重要参考资料之一。

在学习中，考生可以结合教材和课本，更好地掌握专业知识。

尤其是对于基础知识和原理的理解，教材和课本具体优势。

网络资源网络资源是指通过互联网获取的资料、信息和知识。

在备考过程中，如果能够走进网络系统，将可以发现很多针对性和有价值的学习资料。

它们可以来自公共知识平台，也可以来自具有一定行业实践经验的人士和专业机构。

通过优秀的网络资源，考生可以获取更加深入、翔实和实战经验的资讯。

复习辅导书复习辅导书是指专门针对专升本考试编写的复习资料。

它们可以包含历年考题、重点知识、考试技巧、答题技巧、练习题和模拟试卷等多种内容，可以让考生更好地进行全面、系统和高效的备考。

在选择复习辅导书时，考生应该结合自己的实际情况选择书籍，包括题型、内容、形式和价格等多个方面。

在选择具体的复习资料时，考生需要根据自己的实际情况和需求进行选择。

不同的考生可能对于不同的资料有不同的需求和喜好。

无论选择哪种资料，重要的是勤奋备考和精心组织时间。

GRE]俞敏洪GRE词汇串讲GRE蓝宝书Word版GRE作文必备资源——美国科学文摘精选GRE 710+800+5.0经验谈GRE 数学800分战略申请学校代码和专业代码GRE作文练习软件—AWP173GRE作文电子书2.0艾宾浩斯遗忘曲线（背单词前先看看）美国八所名校的GRE 和托福分数要求[TOEFL]新托福听力王托福历年真题汇总王玉梅托福词汇Excel版胡敏读故事记单词托福TOEFL词汇mp3 TOEFL报名事项+全国考场点评任治远老师toefl词汇讲义 word版许杨TOEFL听力胜经（pdf版）TOEFL单词测试软件（像机考阅读词汇题）托福经典句子结构100句阅读听力经典加试PDF版[IELTS]雅思G类书信各个击破名师总结大作文常见烤鸭小心！雅思听力七大陷阱浅析文化背景知识在提高雅思听力中的重要雅思阅读实战16篇2009雅思口语机经下载雅思作文---高分作文三大要素雅思官方评分标准（listening）雅思笔记精华汇总（不得不知的技巧）新东方雅思经典句式(实用)[GMAT]俞敏洪老师《GMAT词汇串讲》7天背完GMAT单词之纯洁版《GMAT语法大全》新GMAT作文黄金80题范文石林GMAT语法总结(WORD版)王鹏阅读课堂笔记韦氏新世界基本词汇GMATPREP数学DS完整版GMATPREP（破解版）《新编英语语法》电子版[SAT]2009年5月SAT真题下载SAT写作笔记整理版SAT考试报分新政策的利与弊！SAT online course答案和解析sat必备手册——你想问的都知道！SAT国内备考方案SAT官方作文题库SAT满分作文真迹SAT词汇常用的词根前后缀一、政治类：1. 日益昌盛 become increasingly prosperous2. 快速发展 develop rapidly3. 隆重集会 gather ceremoniously4. 热爱和平 love peace5. 追求进步 pursue progress6. 履行权利和义务 perform the responsibilities and obligations7. 回顾奋斗历程 review the course of struggle8. 展望伟大征程 look into the great journey9. 充满信心和力量 be filled with confidence and strength10. 必胜 be bound to win11. 主张各国政府采取行动 urge governments of all countries to take action12. 和平共处 coexist peacefully13. 对内开放和对外开放 open up both externally and internally14. 经历两个不同时期 experience two different periods15. 战胜无数的困难 overcome numerous difficulties16. 赢得一个又一个胜利 win one victory after another17. 完全意识到 be fully aware that18. 迈出重要的一步 make an important step19. 采取各种措施 adopt various measures20. 得出结论 ,告一段落 draw ( arrive at, come to reach ) a conclusion21. 实现民族独立 realize national independence22. 追求真理 seek the truth23. 建立社会主义制度 establish a socialist system24. 根除 (防止,消除)腐败 root out (prevent, eliminate) corruption25响应号召 respond to the call26. 进入新时期 enter a new period27. 实行新政策 practice new policies28. 展现生机和活力 display one’s vigor and vitality29. 增强综合国力 enhance comprehensive(overall) national strength and和国际竟争力 international competitiveness30. 进入世界先进行列 edge into the advanced ranks in the world31. 解决温饱问题 solve the problem of food and clothing32. 吸收各国文明的先进成果 absorb what is advanced in other civilizat ions33. 与日俱增 increase every day34. 实现夙愿 fulfill the long-cherished wishes35. 必将实现 be bound to come true36. 锻造一支人民军队 forge a people’s army37. 建立巩固的国防 build a strong national defense38. 进行和谈 hold peace talks39. 修改法律 amend the laws40. 在．．．中起（至关） play a major的(crucial, an important ) role in重要作用41. 对．．．做出重要(巨大)贡献make important (great, major )contribut ions to42. 遵循规则 follow the principles43. 把理论和实际结合起来 integrate theory with practice …44. 把．．．作为指导 take… as the guide45. 缓和紧张状况 ease the tension46. 高举伟大旗帜 hold high the great banner47. 解决新问题 resolve new problems48. 观察当今世界 observe the present-day world49. 开拓前进 open up new ways forward50. 增强凝聚力 enhance the rally power51. 结束暴力，开始和平谈判 end the violence and resume peace talks52. 进行战略性调整 make strategic readjustment53. 开始生效 go into effect / enter into force54. 就．．．接受妥协 accept a compromise on55. 接受．．．的采访 be interviewed by56. 把……看成社会公敌 look upon … as a threat to society57. 把……捐给慈善机构 donate …to charities58. 维护世界和平 maintain world peace59. 摆脱贫穷落后 get rid of poverty and backwardness60. 实现发展繁荣 bring about development and prosperity61. 反对各种形式的恐怖主义 be opposed to all forms of terrorism62. 宣布。

建筑参数(很有用的小资料)一、普通住宅建筑混凝土用量和用钢量：1、多层砌体住宅：钢筋：30KG/m2砼：0.3～0.33m3/m22、多层框架：钢筋：38～42KG/m2砼：0.33～0.35m3/m23、小高层11～12层：钢筋：50～52KG/m2砼：0.35m3/m24、高层17～18层：钢筋：54～60KG/m2砼：0.36m3/m25、高层30层H=94米：钢筋：65～75KG/m2砼：0.42～0.47m3/m26、高层酒店式公寓28层H=90米：钢筋：65～70KG/m2砼：0.38～0.42m3/m27、别墅：混凝土用量和用钢量介于多层砌体住宅和高层11～12层之间；以上数据按抗震7度区规则结构设计二、普通多层住宅楼施工预算经济指标1、室外门窗（不包括单元门、防盗门）面积占建筑面积0.20～0.242、模版面积占建筑面积2.2左右3、室外抹灰面积占建筑面积0.4左右4、室内抹灰面积占建筑面积3.8三、施工功效1、一个抹灰工一天抹灰在35平米2、一个砖工一天砌红砖1000～1800块3、一个砖工一天砌空心砖800～1000块4、瓷砖15平米5、刮大白第一遍300平米/天，第二遍180平米/天，第三遍压光90平米/天四、基础数据1、混凝土重量2500KG/m32、钢筋每延米重量0.00617×d×d3、干砂子重量1500KG/m3，湿砂重量1700KG/m34、石子重量2200KG/m35、一立方米红砖525块左右（分墙厚）6、一立方米空心砖175块左右7、筛一方干净砂需1.3方普通砂建筑程序歌要想建设效果好，选择队伍要招标。

中标以后订合同，免得约束无依照。

协议内容应详尽，权利义务与违约。

甲方按时交图纸，会审图纸别忘掉。

施工单位做“两算”，人工机械和材料。

施工现场先平整，线外两米要接牢。

找好方位来放线，按着规定挖地槽。

先做垫层后基础，地梁一般三百高。

基础部位有洞口，具体位置图示标。

高等数学（通用复习）师兄的忠告：记住我们只复习重点，不需要学得太多，这些是每年必须的重点，希望注意第一章 函数与极限函数○函数基础（高中函数部分相关知识）（★★★） ○邻域（去心邻域）（★）第一节 数列的极限○数列极限的证明（★）【题型示例】已知数列{}n x ，证明{}lim n x x a →∞=【证明示例】N -ε语言1．由n x a ε-<化简得()εg n >，∴()N g ε=⎡⎤⎣⎦2．即对0>∀ε，()N g ε∃=⎡⎤⎣⎦，当N n >时，始终有不等式n x a ε-<成立，∴{}a x n x =∞→lim第二节 函数的极限 ○0x x →时函数极限的证明（★）【题型示例】已知函数()x f ，证明()A x f x x =→0lim【证明示例】δε-语言1．由()f x A ε-<化简得()00x x g ε<-<，∴()εδg =2．即对0>∀ε，()εδg =∃，当00x x δ<-<时，始终有不等式()f x A ε-<成立，∴()A x f x x =→0lim○∞→x 时函数极限的证明（★）【题型示例】已知函数()x f ，证明()A x f x =∞→lim【证明示例】X -ε语言1．由()f x A ε-<化简得()x g ε>，∴()εg X =2．即对0>∀ε，()εg X =∃，当X x >时，始终有不等式()f x A ε-<成立，∴()A x f x =∞→lim第三节 无穷小与无穷大○无穷小与无穷大的本质（★） 函数()x f 无穷小⇔()0lim =x f 函数()x f 无穷大⇔()∞=x f lim○无穷小与无穷大的相关定理与推论（★★）（定理三）假设()x f 为有界函数，()x g 为无穷小，则()()lim 0f x g x ⋅=⎡⎤⎣⎦（定理四）在自变量的某个变化过程中，若()x f 为无穷大，则()1f x -为无穷小；反之，若()x f 为无穷小，且()0f x ≠，则()x f 1-为无穷大【题型示例】计算：()()0lim x x f x g x →⋅⎡⎤⎣⎦（或∞→x ）1．∵()f x ≤M ∴函数()f x 在0x x =的任一去心邻域()δ,0x U内是有界的； （∵()f x ≤M ，∴函数()f x 在D x ∈上有界；） 2．()0lim 0=→x g x x 即函数()x g 是0x x →时的无穷小；（()0lim =∞→x g x 即函数()x g 是∞→x 时的无穷小；）3．由定理可知()()0lim 0x x f x g x →⋅=⎡⎤⎣⎦（()()lim 0x f x g x →∞⋅=⎡⎤⎣⎦）第四节 极限运算法则○极限的四则运算法则（★★） （定理一）加减法则 （定理二）乘除法则关于多项式()p x 、()x q 商式的极限运算设：()()⎪⎩⎪⎨⎧+⋯++=+⋯++=--nn n mm m b x b x b x q a x a x a x p 110110 则有()()⎪⎪⎩⎪⎪⎨⎧∞=∞→0lim 0b a x q x p x m n m n m n >=<（特别地，当()()00lim 0x x f x g x →=（不定型）时，通常分子分母约去公因式即约去可去间断点便可求解出极限值，也可以用罗比达法则求解）【题型示例】求值233lim9x x x →--【求解示例】解：因为3→x ，从而可得3≠x ，所以原式()()23333311lim lim lim 93336x x x x x x x x x →→→--====-+-+ 其中3x =为函数()239x f x x -=-的可去间断点 倘若运用罗比达法则求解（详见第三章第二节）：解：()()0233323311lim lim lim 9269x L x x x x x x x '→→→'--===-'- ○连续函数穿越定理（复合函数的极限求解）（★★）（定理五）若函数()x f 是定义域上的连续函数，那么，()()00lim lim x xx x f x f x ϕϕ→→⎡⎤=⎡⎤⎣⎦⎢⎥⎣⎦【题型示例】求值：93lim 23--→x x x【求解示例】3x →=== 第五节 极限存在准则及两个重要极限○夹迫准则（P53）（★★★） 第一个重要极限：1sin lim0=→xxx∵⎪⎭⎫⎝⎛∈∀2,0πx ，x x x tan sin <<∴1sin lim 0=→xx x（特别地，000sin()lim1x x x x x x →-=-）○单调有界收敛准则（P57）（★★★）第二个重要极限：e x xx =⎪⎭⎫⎝⎛+∞→11lim （一般地，()()()()lim lim lim g x g x f x f x =⎡⎤⎡⎤⎣⎦⎣⎦，其中()0lim >x f ）【题型示例】求值：11232lim +∞→⎪⎭⎫ ⎝⎛++x x x x【求解示例】第六节 无穷小量的阶（无穷小的比较）○等价无穷小（★★） 1．()~sin ~tan ~arcsin ~arctan ~ln(1)~1UU U U U U U e +-2．U U cos 1~212- （乘除可替，加减不行）【题型示例】求值：()()xx x x x x 31ln 1ln lim 20++++→【求解示例】第七节 函数的连续性○函数连续的定义（★）○间断点的分类（P67）（★）⎩⎨⎧∞⋯⋯⎩⎨⎧）无穷间断点（极限为第二类间断点可去间断点（相等）跳越间断点（不等）限存在）第一类间断点（左右极（特别地，可去间断点能在分式中约去相应公因式）【题型示例】设函数()⎩⎨⎧+=xa e x f x 2 ，00≥<x x 应该怎样选择数a ，使得()x f 成为在R 上的连续函数【求解示例】1．∵()()()2010000f e e e f a a f a --⋅++⎧===⎪⎪=+=⎨⎪=⎪⎩2．由连续函数定义()()()e f x f x f x x ===+-→→0lim lim 00∴e a =第八节 闭区间上连续函数的性质○零点定理（★）【题型示例】证明：方程()()f x g x C =+至少有一个根介于a 与b 之间 【证明示例】 1．（建立辅助函数）函数()()()x f x g x C ϕ=--在闭区间[],a b 上连续； 2．∵()()0a b ϕϕ⋅<（端点异号）3．∴由零点定理，在开区间()b a ,内至少有一点ξ，使得()0=ξϕ，即()()0f g C ξξ--=（10<<ξ）4．这等式说明方程()()f x g x C =+在开区间()b a ,内至少有一个根ξ 第二章 导数与微分 第一节 导数概念○高等数学中导数的定义及几何意义（P83）（★★）【题型示例】已知函数()⎩⎨⎧++=bax e x f x 1 ，00>≤x x 在0=x 处可导，求a ，b【求解示例】1．∵()()0010f e f a -+'⎧==⎪⎨'=⎪⎩，()()()00001120012f e e f b f e --+⎧=+=+=⎪⎪=⎨⎪=+=⎪⎩2．由函数可导定义()()()()()0010002f f a f f f b -+-+''===⎧⎪⎨====⎪⎩∴1,2a b ==【题型示例】求()x f y =在a x =处的切线与法线方程 （或：过()x f y =图像上点(),a f a ⎡⎤⎣⎦处的切线与法线方程） 【求解示例】1．()x f y '='，()a f y a x '='=|2．切线方程：()()()y f a f a x a '-=-法线方程：()()()1y f a x a f a -=--' 第二节 函数的和（差）、积与商的求导法则○函数和（差）、积与商的求导法则（★★★） 1．线性组合（定理一）：()u v u v αβαβ'''±=+ 特别地，当1==βα时，有()u v u v '''±=± 2．函数积的求导法则（定理二）：()uv u v uv '''=+3．函数商的求导法则（定理三）：2u u v uv v v '''-⎛⎫= ⎪⎝⎭第三节 反函数和复合函数的求导法则○反函数的求导法则（★） 【题型示例】求函数()x f 1-的导数【求解示例】由题可得()x f 为直接函数，其在定于域D 上单调、可导，且()0≠'x f ；∴()()11f x f x -'⎡⎤=⎣⎦'○复合函数的求导法则（★★★）【题型示例】设(ln y e =，求y '【求解示例】第四节 高阶导数○()()()()1n n fx fx -'⎡⎤=⎣⎦（或()()11n n n n d y d y dx dx --'⎡⎤=⎢⎥⎣⎦）（★） 【题型示例】求函数()x y +=1ln 的n 阶导数 【求解示例】()1111y x x-'==++， ()()()12111y x x --'⎡⎤''=+=-⋅+⎣⎦， ……第五节 隐函数及参数方程型函数的导数 ○隐函数的求导（等式两边对x 求导）（★★★）【题型示例】试求：方程y e x y +=所给定的曲线C ：()x y y =在点()1,1e -的切线方程与法线方程【求解示例】由y e x y +=两边对x 求导即()y y x e '''=+化简得1y y e y ''=+⋅∴ee y -=-='11111 ∴切线方程：()e x ey +--=-1111 法线方程：()()e x e y +---=-111○参数方程型函数的求导【题型示例】设参数方程()()⎩⎨⎧==t y t x γϕ，求22dx yd【求解示例】()()t t dx dy ϕγ''=.()22dy d y dx dx t ϕ'⎛⎫⎪⎝⎭='第六节 变化率问题举例及相关变化率（不作要求）第七节 函数的微分○基本初等函数微分公式与微分运算法则（★★★）第三章 中值定理与导数的应用第一节 中值定理○引理（费马引理）（★） ○罗尔定理（★★★）【题型示例】现假设函数()f x 在[]0,π上连续，在()0,π 上可导，试证明：()0,ξπ∃∈， 使得()()cos sin 0f f ξξξξ'+=成立 【证明示例】 1．（建立辅助函数）令()()sin x f x x ϕ=显然函数()x ϕ在闭区间[]0,π上连续，在开区间()0,π上可导；2．又∵()()00sin00f ϕ==即()()00ϕϕπ==3．∴由罗尔定理知()0,ξπ∃∈，使得()()cos sin 0f f ξξξξ'+=成立○拉格朗日中值定理（★）【题型示例】证明不等式：当1x >时，x e e x >⋅ 【证明示例】 1．（建立辅助函数）令函数()x f x e =，则对1x ∀>，显然函数()f x 在闭区间[]1,x 上连续，在开区间()1,x 上可导，并且()x f x e '=；2．由拉格朗日中值定理可得，[]1,x ξ∃∈使得等式()11x e e x e ξ-=-成立， 又∵1e e ξ>，∴()111x e e x e e x e ->-=⋅-， 化简得x e e x >⋅，即证得：当1x >时，x e e x >⋅ 【题型示例】证明不等式：当0x >时，()ln 1x x +<【证明示例】 1．（建立辅助函数）令函数()()ln 1f x x =+，则对0x ∀>，函数()f x 在闭区间[]0,x 上连续，在开区间()0,π上可导，并且()11f x x'=+； 2．由拉格朗日中值定理可得，[]0,x ξ∃∈使得等式()()()1ln 1ln 1001x x ξ+-+=-+成立， 化简得()1ln 11x x ξ+=+，又∵[]0,x ξ∈， ∴()111f ξξ'=<+，∴()ln 11x x x +<⋅=， 即证得：当1x >时，x e e x >⋅第二节 罗比达法则○运用罗比达法则进行极限运算的基本步骤（★★） 1．☆等价无穷小的替换（以简化运算）2．判断极限不定型的所属类型及是否满足运用罗比达法则的三个前提条件A ．属于两大基本不定型（0,0∞∞）且满足条件， 则进行运算：()()()()lim limx a x a f x f x g x g x →→'=' （再进行1、2步骤，反复直到结果得出）B ．☆不属于两大基本不定型（转化为基本不定型） ⑴0⋅∞型（转乘为除，构造分式） 【题型示例】求值：0lim ln x x x α→⋅【求解示例】（一般地，()0lim ln 0x x x βα→⋅=，其中,R αβ∈）⑵∞-∞型（通分构造分式，观察分母） 【题型示例】求值：011lim sin x x x →⎛⎫- ⎪⎝⎭【求解示例】()()()()000002sin 1cos 1cos sin limlim lim lim 0222L x x L x x x x x x xx x x ''→→→→''---====='' ⑶00型（对数求极限法） 【题型示例】求值：0lim x x x →【求解示例】()()0000lim ln ln 000002ln ,ln ln ln 1ln ln 0lim ln lim lim111lim lim 0lim lim 11x x x x x L x yy x x x x x y x y x x x xx xx y xx x x y e e e x→∞∞'→→→→→→→===='→=='⎛⎫ ⎪⎝⎭==-=====-解：设两边取对数得：对对数取时的极限：，从而有 ⑷1∞型（对数求极限法）【题型示例】求值：()10lim cos sin xx x x →+【求解示例】⑸0∞型（对数求极限法）【题型示例】求值：tan 01lim xx x →⎛⎫⎪⎝⎭【求解示例】○运用罗比达法则进行极限运算的基本思路（★★） ⑴通分获得分式（通常伴有等价无穷小的替换） ⑵取倒数获得分式（将乘积形式转化为分式形式） ⑶取对数获得乘积式（通过对数运算将指数提前）第三节 泰勒中值定理（不作要求） 第四节 函数的单调性和曲线的凹凸性 ○连续函数单调性（单调区间）（★★★）【题型示例】试确定函数()3229123f x x x x =-+-的单调区间 【求解示例】1．∵函数()f x 在其定义域R 上连续，且可导∴()261812f x x x '=-+2．令()()()6120f x x x '=--=，解得：121,2x x ==f x ),1,2,-∞+∞； 单调递减区间为()1,2【题型示例】证明：当0x >时，1x e x >+【证明示例】 1．（构建辅助函数）设()1x x e x ϕ=--，（0x >） 2．()10x x e ϕ'=->，（0x >）∴()()00x ϕϕ>=3．既证：当0x >时，1x e x >+【题型示例】证明：当0x >时，()ln 1x x +<【证明示例】 1．（构建辅助函数）设()()ln 1x x x ϕ=+-，（0x >）2．()1101x xϕ'=-<+，（0x >） ∴()()00x ϕϕ<=3．既证：当0x >时，()ln 1x x +<○连续函数凹凸性（★★★）【题型示例】试讨论函数2313y x x =+-的单调性、极值、凹凸性及拐点 【证明示例】1．()()236326661y x x x x y x x '⎧=-+=--⎪⎨''=-+=--⎪⎩ 2．令()()320610y x x y x '=--=⎧⎪⎨''=--=⎪⎩解得：120,21x x x ==⎧⎨=⎩13y x x =+-(0,1),(1,2) 单调递增区间为(,0)-∞,(2,)+∞； ⑵函数2313y x x =+-的极小值在0x =时取到，为()01f =，极大值在2x =时取到，为()25f =；⑶函数2313y x x =+-在区间(,0)-∞,(0,1)上凹，在区间(1,2),(2,)+∞上凸； ⑷函数2313y x x =+-的拐点坐标为()1,3第五节 函数的极值和最大、最小值○函数的极值与最值的关系（★★★）⑴设函数()f x 的定义域为D ，如果M x ∃的某个邻域()M U x D ⊂，使得对()M x U x ∀∈，都适合不等式()()M f x f x <，我们则称函数()f x 在点(),M M x f x ⎡⎤⎣⎦处有极大值()M f x ；令{}123,,,...,M M M M Mn x x x x x ∈则函数()f x 在闭区间[],a b 上的最大值M 满足：()(){}123max ,,,,...,,M M M Mn M f a x x x x f b =；⑵设函数()f x 的定义域为D ，如果m x ∃的某个邻域()m U x D ⊂，使得对()m x U x ∀∈，都适合不等式()()m f x f x >，我们则称函数()f x 在点(),m m x f x ⎡⎤⎣⎦处有极小值()m f x ；令{}123,,,...,m m m m mn x x x x x ∈则函数()f x 在闭区间[],a b 上的最小值m 满足：()(){}123min ,,,,...,,m m m mn m f a x x x x f b =；【题型示例】求函数()33f x x x =-在[]1,3-上的最值 【求解示例】1．∵函数()f x 在其定义域[]1,3-上连续，且可导∴()233f x x '=-+2．令()()()3110f x x x '=--+=， 解得：121,1x x =-= 3．（三行表）4．又∵()(12,12,318f f f -=-==-∴()()()()max min 12,318f x f f x f ====-第六节 函数图形的描绘（不作要求） 第七节 曲率（不作要求） 第八节 方程的近似解（不作要求） 第四章 不定积分第一节 不定积分的概念与性质○原函数与不定积分的概念（★★） ⑴原函数的概念：假设在定义区间I 上，可导函数()F x 的导函数为()F x '，即当自变量x I ∈时，有()()F x f x '=或()()dF x f x dx =⋅成立，则称()F x 为()f x 的一个原函数⑵原函数存在定理：（★★）如果函数()f x 在定义区间I 上连续，则在I 上必存在可导函数()F x 使得()()F x f x '=，也就是说：连续函数一定存在原函数（可导必连续）⑶不定积分的概念（★★）在定义区间I 上，函数()f x 的带有任意常数项C 的原函数称为()f x 在定义区间I 上的不定积分，即表示为：()()f x dx F x C =+⎰（⎰称为积分号，()f x 称为被积函数，()f x dx 称为积分表达式，x 则称为积分变量） ○基本积分表（★★★）○不定积分的线性性质（分项积分公式）（★★★） 第二节 换元积分法○第一类换元法（凑微分）（★★★） （()dx x f dy ⋅'=的逆向应用） 【题型示例】求221dx a x+⎰ 【求解示例】222211111arctan 11x x dx dx d C a x a a a a x x a a ⎛⎫===+ ⎪+⎝⎭⎛⎫⎛⎫++ ⎪ ⎪⎝⎭⎝⎭⎰⎰⎰解：【题型示例】求 【求解示例】○第二类换元法（去根式）（★★）（()dx x f dy ⋅'=的正向应用） ⑴对于一次根式（0,a b R ≠∈）：：令t =，于是2t b x a-=，则原式可化为t⑵对于根号下平方和的形式（0a >）：tan x a t =（22t ππ-<<），于是arctan xt a=，则原式可化为sec a t ； ⑶对于根号下平方差的形式（0a >）： asin x a t =（22t ππ-<<），于是arcsin x t a=，则原式可化为cos a t ； bsec x a t =（02t π<<），于是arccos at x=，则原式可化为tan a t ；【题型示例】求（一次根式） 【求解示例】2221t x t dx tdttdt dt t C C t =-=⋅==+=⎰⎰【题型示例】求（三角换元）【求解示例】第三节 分部积分法 ○分部积分法（★★）⑴设函数()u f x =，()v g x =具有连续导数，则其分部积分公式可表示为：udv uv vdu =-⎰⎰⑵分部积分法函数排序次序：“反、对、幂、三、指” ○运用分部积分法计算不定积分的基本步骤：⑴遵照分部积分法函数排序次序对被积函数排序；⑵就近凑微分：（v dx dv '⋅=）⑶使用分部积分公式：udv uv vdu =-⎰⎰⑷展开尾项vdu v u dx '=⋅⎰⎰，判断a ．若v u dx '⋅⎰是容易求解的不定积分，则直接计算出答案（容易表示使用基本积分表、换元法与有理函数积分可以轻易求解出结果）；b ．若v u dx '⋅⎰依旧是相当复杂，无法通过a 中方法求解的不定积分，则重复⑵、⑶，直至出现容易求解的不定积分；若重复过程中出现循环，则联立方程求解，但是最后要注意添上常数C【题型示例】求2x e x dx ⋅⎰【求解示例】【题型示例】求sin x e xdx ⋅⎰【求解示例】 ∴()1sin sin cos 2x x e xdx e x x C ⋅=-+⎰第四节 有理函数的不定积分○有理函数（★）设：()()()()101101m m m n n n P x p x a x a x a Q x q x b x b x b --=++⋯+==++⋯+ 对于有理函数()()P x Q x ，当()P x 的次数小于()Q x 的次数时，有理函数()()P x Q x 是真分式；当()P x 的次数大于()Q x 的次数时，有理函数()()P x Q x 是假分式 ○有理函数（真分式）不定积分的求解思路（★）⑴将有理函数()()P x Q x 的分母()Q x 分拆成两个没有公因式的多项式的乘积：其中一个多项式可以表示为一次因式()k x a -；而另一个多项式可以表示为二次质因式()2lx px q ++，（240p q -<）； 即：()()()12Q x Q x Q x =⋅ 一般地：n mx n m x m ⎛⎫+=+⎪⎝⎭，则参数n a m=- 则参数,b c p q a a ==⑵则设有理函数()()P x Q x 的分拆和式为： 其中参数121212,,...,,,,...,l k lM M M A A A N N N ⎧⎧⎧⎨⎨⎨⎩⎩⎩由待定系数法（比较法）求出⑶得到分拆式后分项积分即可求解 【题型示例】求21x dx x +⎰（构造法）【求解示例】第五节 积分表的使用（不作要求）第五章 定积分极其应用第一节 定积分的概念与性质○定积分的定义（★）（()f x 称为被积函数，()f x dx 称为被积表达式，x 则称为积分变量，a 称为积分下限，b 称为积分上限，[],a b 称为积分区间）○定积分的性质（★★★）⑴()()b b a a f x dx f u du =⎰⎰⑵()0a a f x dx =⎰⑶()()b b a a kf x dx k f x dx =⎡⎤⎣⎦⎰⎰⑷（线性性质）⑸（积分区间的可加性）⑹若函数()f x 在积分区间[],a b 上满足()0f x >，则()0b a f x dx >⎰；（推论一）若函数()f x 、函数()g x 在积分区间[],a b 上满足()()f x g x ≤，则()()b b a a f x dx g x dx ≤⎰⎰；（推论二）()()bba a f x dx f x dx ≤⎰⎰ ○积分中值定理（不作要求）第二节 微积分基本公式○牛顿-莱布尼兹公式（★★★）（定理三）若果函数()F x 是连续函数()f x 在区间[],a b 上的一个原函数，则○变限积分的导数公式（★★★）（上上导―下下导） 【题型示例】求21cos 20lim t x x e dt x -→⎰【求解示例】第三节 定积分的换元法及分部积分法○定积分的换元法（★★★）⑴（第一换元法） 【题型示例】求20121dx x +⎰【求解示例】()[]222000111121ln 212122121ln 5ln 5ln122解：dx d x x x x =+=⎡+⎤⎣⎦++=-=⎰⎰ ⑵（第二换元法） 设函数()[],f x C a b ∈，函数()x t ϕ=满足： a ．,αβ∃，使得()(),a b ϕαϕβ==；b ．在区间[],αβ或[],βα上，()(),f t t ϕϕ'⎡⎤⎣⎦连续则：()()()b a f x dx f t t dt βαϕϕ'=⎡⎤⎣⎦⎰⎰ 【题型示例】求40dx ⎰ 【求解示例】⑶（分部积分法）○偶倍奇零（★★）设()[],f x C a a ∈-，则有以下结论成立：⑴若()()f x f x -=，则()()02a a a f x dx f x dx -=⎰⎰⑵若()()f x f x -=-，则()0a a f x dx -=⎰第四节 定积分在几何上的应用（暂时不作要求）第五节 定积分在物理上的应用（暂时不作要求）第六节 反常积分（不作要求） 如：不定积分公式21arctan 1dx x C x =++⎰的证明。

1填空题1.TD-SCDMA系统的中文说明：时分双工码分多址。

2.按QoS分类，3G业务可分为以下四种类型：会话类业务、流类业务、交互类业务、后台（背景）类业务。

3.双工技术，主要解决用户和网络之间同时收发信息（上下行区分）的问题；基本的双工技术有： FDD 、 TDD 。

4.TD-SCDMA系统中，资源是通过频率、_时隙_和_码字_来区分的。

5.无线接口协议结构中，物理层向MAC层提供_传输_信道，MAC层向RLC子层提供_逻辑_信道，_物理_信道由物理层定义。

6.TD-SCDMA子帧长度为 5MS 。

其帧结构中，常规时隙 TS0 总是固定为下行，常规时隙 TS1 总是固定为上行。

每个子帧总是从时隙 TS0 开始。

上行时隙和下行时隙间由时隙转换点分开，这在每个子帧中共有 2 个。

7.RNC与Node B之间通过 Iub 接口连接。

RNC与UE之间通过 Uu 空中接口进行数据交互。

8.TD-SCDMA系统是TDD模式，一条物理信道由频率、时隙、码道的组合来标志。

9.智能天线技术的核心是自适应天线波束赋形技术。

10.信道分配方案可分为以下三种，固定信道分配（FCA）、动态信道分配（DCA）、混合信道分配（HCA）方案。

TD-SCDMA采用的是动态信道分配（DCA）。

11.TD-SCDMA系统接力切换分为三个过程：测量过程、判决过程、执行过程。

12.定点CQT测试包括 CS域业务和 PS域业务。

13.TD-SCDMA码资源规划主要包括：下行同频码和复合码。

14.功率控制分为开环和闭环。

其中闭环功率控制又分为内环和外环。

15.对物理信道数据部分的扩频包括两步操作：一是扩频，增加信号的带宽；二是加扰。

16.QPSK数据调制就是把_2_个连续的二进制比特映射成一个复数值的数据符号，8PSK数据调制就是把_3_个连续的二进制比特映射成一个复数值的数据符号。

17.TD-SCDMA系统无线资源子系统RNS包括_RNC_和_NODE B_。

第1章1、通信：是指不在同一地点的双方或多方之间进行迅速有效的信息传递。

单工半双工全双工串行传输：传输慢、但传输距离远。

并行传输：传输快、但传输距离近。

两点间直通传输、分支传输和交换传输3、信号：是信息的一种电磁编码。

信号是信息的载体。

通信系统的基本模弄4、通信系统的主要性能指示有效性：是指信息传输的效率。

可靠性：是系统接收信息的准确度。

备注：衡量系统有效性最全面的指标是系统的频带利用率。

第二章一、调制的分类：1、根据调制信号分类：模拟调制和数字调制2、根据载波分类：连续载波调制和脉冲载波调制3、根据调制的功能分类：AM、FM、PM4、根据调制前后的频谱关系分类：线性调制和非线性调制5、线性调制分为：AM、DSB、SSB、VSB6、单边带调制方法有：滤波法、移相法、移相滤波法备注：常规双边带调制（AM）调制效率最低，而单边带调（SSB）制效率最高解调的方法：相干解调（同步检波）和非相干解调（包络检波）。

7、频率调制分为：划分依据是瞬时相位偏移是否小于0.5窄带调制（NBFM）宽带调制（WBFM）8、调频分为：直接调频和间接调频间接调频：是选积分，然后再调相 如下图：第3章1、PCM （脉冲编码调制）包括三个部分：抽样、量化、编码。

2、数字信息的电脉冲表过程称码型变换。

应该考虑的问题：低频和高频频率分量应尽量少，特别是不能含有直流分量； 不能有长连0和1码，以便提取同步定时信息；具有自检自纠能力。

3、二元码的极性图P534、抽样定理分为：自然抽样和平顶抽样（性能比自然抽样性能好）5、量化分为：均匀量化和非均匀量化备注：只要确定了量化器，则无论抽样值大小如何，其量化噪声的平均功率值都是固定不变的；因为，X （T ）较小时，输出信噪比就很低，弱信号的量化信噪比就可能无法达到额定要求而对还原解调产生较大的影响。

6、非均匀量化分为：A 率13折线（中国使用）和U 率15折线。

A=87.6 U=2557、编码：自然二进制码组、折叠二进制码组、格雷二进制码组。

It should be no surprise that extreme eating habits can be detrimental to one’s health. Supporting prior evidence of the harm of overdoing red and processed meats, a recent National Cancer Institute study of more than a half million older Americans found that a diet high in these foods causes a modest but statistically significant increase in the risk of death from heart disease and cancer.A well-balanced diet is essential to proper development, growth, and the maintenance of health, and studies indicate that balancing your diet helps decrease the risk of chronic disease. In 2002 the Institute of Medicine released "Dietary Reference Intakes for Energy, Carbohydrate, Fiber, Fat, Fatty Acids, Cholesterol, Protein, and Amino Acids", a report that recommends science-based amounts of proteins, fats, and carbohydrates that people need to maintain health. It states that adults should get 10 percent to 35 percent of their calories from protein each day. The report also recommended that people keep their intake of saturated fat , trans fat, and cholesterol as low as possible because they raise people's risk for coronary heart disease. Red meat contains significant amounts of both saturated fat and cholesterol.Because proteins, fats, and carbohydrates can substitute for one another as calorie sources, the report did not recommend a specific amount of meat or other protein sources that people should eat daily. The National Institutes of Health estimate that the average adult should consume approximately four ounces of meat per day and most Americans eat more than this.过度的饮食习惯会危害健康这点应该没有人会觉得奇怪。

对江西新高考有用的教辅资料
《蝶变笔记》
这本书不管是学习基础知识的阶段还是复习的阶段都是适用的，搭配课堂上老师讲课使用可以做到学习的持续灌输。

同比世面上的其他教辅书，色彩更加鲜艳生动。

在照顾内容全面的同时也注重外观的美丽大方，是宝藏教辅书没错了。

这本书真的是很好用了，里面都是干货知识点，基础类的。

很适合基础不好的同学使用，以及基础还行想要巩固基础的同学使用。

里面的知识点解析详细全面，特别厚实，书拿在手里的质感也是非常好的，可以180度平铺，大大加强了学习效率，而且里面的内容丰富，封面也美观大方。

《教材完全解读》
高中阶段都可以使用，每天预习新课的时候，可以用它来查看你不会的知识点；课后复习或者做题的时候，遇到不会的知识点，也可以在上面查找。

这本书把课本上的内容全部细细地讲了一遍，左边是讲解，右边是例题。

反正就是和课程同步，课上到哪，就跟到哪，很方便。

《金考卷》
优点是它题量特别大，题型也蛮多的，你用这一套就能把题练精练透。

适合对象是备考时间比较多的高三小伙伴。

这本高中含金量高的辅导书分了基础卷、能力卷、提升卷、强化卷、借鉴卷和原创卷4种类型。