第二章命题逻辑 §2.2 主要解题方法 2.2.1 证明命题公式恒真或恒假 主要有如下方法： 方法一.真值表方法。即列出公式的真值表，若表中对应公式所在列的每一取值全为1，这说明该公式在它的所有解释下都是真，因此是恒真的；若表中对应公式所在列的每
一取值全为0，这说明该公式在它的所有解释下都为假，因此是恒假的。 真值表法比较烦琐，但只要认真仔细，不会出错。 例2.2.1 说明G= (P∧Q→R)∧(P→Q)→(P→R)是恒真、恒假还是可满足。 解：该公式的真值表如下： 表2.2.1 由于表2.2.1中对应公式G所在列的每一取值全为1，故
G恒真。 方法二.以基本等价式为基础，通过反复对一个公式的等价代换，使之最后转化为一个恒真式或恒假式，从而实现公式恒真或恒假的证明。 例2.2.2 说明G= ((P→R) ∨? R)→ (? (Q→P) ∧ P)是恒真、恒假还是可满足。 解：由(P→R) ∨? R=?P∨ R∨? R=1，以及 ? (Q→P) ∧ P= ?（?Q∨ P）∧ P = Q∧? P∧ P=0 知，((P→R) ∨? R)→ (? (Q→P) ∧ P)=0，故G恒假。 方法三.设命题公式G含n个原子，若求得G的主析取范式包含所有2n个极小项，则G是恒真的；若求得G的主合取范式包含所有2n个极大项，则G是恒假的。 方法四. 对任给要判定的命题公式G，设其中有原子P1，P2，…，P n，令P1取1值，求G的真值，或为1，或为0，或成为新公式G1且其中只有原子P2，…，P n，再令P1取0值，求G真值，如此继续，到最终只含0或1为止，若最终结果全为1，则公式G恒真，若最终结果全为0，则公式G
教材练习答案及听力原文 Unit 1 WARMING UP ?Answers: 1 Archimedes, Ancient Greek (287-21 2 BC) He was a mathematician. He found that if you put an object into water the water pushes the object up. It rises and partly floats. The force of the water pushing it up is the same as the weight of the object. 2 Charles Darwin, British (1808-1882) The Origin of Species was published in 1859. It explained how plants and animals had changed over time to fit in with a changing environment. At the time it was published it was very controversial. Many people believed the Bible when it said that God made the first two people (Adam and Eve) and that all other people came from these two. Darwin’s book showed that people had developed from apes instead. So this caused a lot of ar gument between religious and scientific people. However Darwin’s idea became very influential and is still accepted today. 3 Thomas Newcomen, British (1663-1729) He improved the first steam pump built by Thomas Savery in 1698 and turned it into a steam engine for taking water out of mines in 1712. James Watt improved it still further in the 1770s turning it into the first modern steam engine used on the railways. 4 Gregor Mendel, Czech (1822-1884) He grew pea plants and developed ideas on heredity and inherited characteristics. He concentrated on cross-fertilising pea plants and analyzing the results. Between 1856-1863 he grew 28,000 pea plants. He examined seven kinds of seed and plant characteristics and developed some laws of inheritance. The first is that inheritance factors do not combine but are passed to the next generation intact. Second, he found that each partner gives half the inherited factors to the young. Third, some of these factors show up in the offspring (and so are dominant). The other factors are masked by the dominant ones (and so are recessive). 5 Marie Curie, Polish and French (1867-1934) She was born in Poland and came to study in France in 1891 and she lived there for the rest of her life. In 1898 she discovered radium. She received two Nobel prizes, one (with Pierre Curie) for physics (1903) and one for chemistry (1911). She is the only person to have been so honoured. On the death of her husband she took over his job at the Sorbonne in Paris. Her work on radioactivity and the discovery of radium meant that she began a new scientific area of research. She was the first woman to receive a Nobel Prize and the first woman to teach at the Sorbonne. 6 Thomas Edison, American (1847-1931) He was already an inventor of other electrical devices (phonograph, electric light bulb) when in 1882 he designed a system for providing New York with electricity from a central power station. This was a tremendous achievement, which had previously been thought impossible.
U1 Vocabulary work 一 1.given 2.at a glance 3.fluency 4.Given 5.hopefully 6.For its part 7.define 8.looked him up 9.no good 10.quoted, context 11.guidance 12.immediate 13.disgust
https://www.doczj.com/doc/843576622.html,e across 15.put into practice 16.scope 二 1.washed his hands of 2.given 3.putting…into practice 4.was confronted with 5.countering 6.were reduced to eating 7.at a glance 8.took refuge in 9.less practicable 10.countered 11.dedication 12.in disgust
14.for their part 15.gave up 三 1.Without suitable entertainment, these young people often get bored and take refuge in drinking and taking drugs. 2.The school washed its hands of the students’ beha vior during the spring recess. 3.The innocent girl was reduced to crying at his cruel remarks. 4.Many difficult words are out of the scope of his learner’s dictionary. 5.The thief admitted his guilt as soon as he was confronted with evidence. 6.The incident should be viewed in the wider context of the political turmoil of that time. 四 1.has come down 2.came to
《数学分析》练习题1 一、单项选择题（本大题共4小题，每小题5分，共20分）在每小题列出的四个备选项中只有一个是符合题目要求的，请将其代码填写在题后的括号内。错选、多选或未选均无分。 1、广义积分dx x ? -2 2 211的奇点的是 【 】 A ．0 B ．2 C ．2 D ．2± 2、下列关于定积分的说法正确的是 【 】 A ．函数)(x f 在[]b a ,有界，则)(x f 在[]b a ,一定可积； B ．函数)(x f 在[]b a ,可积，则)(x f 在[]b a ,一定有界； C ．函数)(x f 在[]b a ,不可积，则)(x f 在[]b a ,一定无界； D ．函数)(x f 在[]b a ,无界，则)(x f 在[]b a ,可能可积。 3、函数()x f 在闭区间[]b a ,可积是函数()x f 在闭区间[]b a ,连续的__ __条件。 【 】 A ．充分非必要 B ．必要非充分 C ．充分必要 D ．即不充分，又非必要 4、若级数∑∞ =1 n n u 收敛，则下列级数中，为收敛级数的是 【 】 A ．()∑∞=-1 1n n n u B ．()∑∞=-1 1n n n u C ．∑∞=+1 1n n n u u D ．∑ ∞ =++1 1 2 n n n u u 二、填空题（本大题共4小题，每小题5分，共20分）请在每小题的横线上给出正确的答案. 1、(){}x f n 在X 一致收敛的定义是： . 2、函数2 x e -在0=x 处的幂级数展开式为, . 3、积分()1012 <x 的收敛性。 解: 5、求级数∑ ∞ =1 3n n n n x 的收敛半径与收敛域。 解: 6、求dx e x ?+∞ 1。 解： 四、综合题（本大题共3小题，每小题8分，共24分）请在每小题后的空白处写出必要的 证明过程。 1、证明：积分?+∞ 02cos dx x 收敛。 证： 2、设()x f 在R 上连续，()()()dt t x t f x F x 20 -= ?。 证明：(1)若()x f 为偶函数，则()x F 也是偶函数；（2）若()x f 为单调函数，则()x F 也是单调函数。 证： 3、若{}n na 收敛， ()∑∞ =--1 1n n n a a n 收敛，证明级数∑∞ =1 n n a 收敛。 证：
第一章 解三角形 一、选择题 1．在A B C ?中，a =03,30;c C == (4) 则可求得角045A =的是（ ） A ．（1）、（2）、（4） B ．（1）、（3）、（4） C ．（2）、（3） D ．（2）、（4） 2．在ABC ?中，根据下列条件解三角形，其中有两个解的是（ ） A ．10=b ， 45=A ， 70=C B ．60=a ，48=c ， 60=B C ．14=a ，16=b ， 45=A D ． 7=a ，5=b ， 80=A 3．在ABC ?中，若， 45=C ， 30=B ，则（ ） A ； B C D 4．在△ABC ，则cos C 的值为（ ） A. D. 5．如果满足 60=∠ABC ，12=AC ，k BC =的△ABC 恰有一个，那么k 的取值范围是（ ） A B ．120≤ 三、解答题 11. 已知在ABC ?中,cos A = ,,,a b c 分别是角,,A B C 所对的边. (Ⅰ)求tan 2A ； (Ⅱ)若sin()2 B π += ,c =求ABC ?的面积. 解: 12. 在△ABC 中，c b a ,,分别为角A 、B 、C 的对边，5 82 22bc b c a - =-，a =3, △ABC 的面积为6， D 为△ABC 内任一点，点D 到三边距离之和为d 。 ⑴求角A 的正弦值； ⑵求边b 、c ； ⑶求d 的取值范围 解： Lesson 1 Vocabulary 1. Manhood:the state of being human 2. White lie:harmless or trivial lie，esp．one told in order to avoid hurting sb． 3. black sheep：person regarded as a disgrace or a failure by other members of his family or group 4. To upset: to defeat 5. Affirmation:stating sth．as truth firmly and forcefully 6. To strain: to make the greatest possible effort 7. Off base: mistaken 8. (a) want (of) : lack of 9. Ringing cry: rallying call Paragraph 1. The job of arousing manhood within a people that have been taught for so many centuries that they are nobody is not easy. It is no easy job to educate a people who have been told over centuries that they were inferior and of no importance to see that they are humans, the same as any other people. 2. Psychological freedom, a firm sense of self-esteem, is the most powerful weapon against the long night of physical slavery. If you break the mental shackles imposed on you by white supremacists, if you really respect yourself, thinking that you are a Man, equal to anyone else, you will be able to take part in the struggle against racial discrimination. 3. The Negro will only be free when he reaches down to the inner depths of his own being and signs with the pen and ink of assertive manhood his own emancipation proclamation. The liberation of mind can only be achieved by the Negro himself/herself. Only when a negro is fully convinced that he/she is a Man/Woman and is not inferior to anyone else, can he/she throw off the manacles of self-abnegation and become free. 4. Power at its best is love implementing the demands of justice, and justice at its best is power correcting everything that stands against love. Power in its best form of function is the carrying out of the demands of justice with love and justice in the best form of function is the overcoming of everything standing in the way of love with power. ability and 5. At that time economic status was considered the measure of the individual’s talents. At that time, the way to evaluate how capable and resourceful a person was to see how much money he had made (or how wealthy he was). 6. …the absence of worldly goods indicated a want of industrious habits and moral fiber. A person was poor because he was lazy and not hard-working and lacked a sense of right and wrong. 7. It is not the work of slaves driven to their tasks either by the task, by the taskmaster, or by animal necessity. This kind of work cannot be done by slaves who work because the work has to be done, because 人教版生物生物必修二教材课后习题答案 第1章遗传因子的发现 第1节《孟德尔的豌豆杂交实验（一）》 （一）问题探讨 1. 粉色。因为按照融合遗传的观点，双亲遗传物质在子代体内混合，子代呈现双亲的中介性状，即红色和白色的混合色——粉色。 2. 提示：此问题是开放性问题，目的是引导学生观察、分析身边的生物遗传现象，学生通过对遗传实例的分析，辨析融合遗传观点是否正确。有些学生可能举出的实例是多个遗传因子控制生物性状的现象（如人体的高度等），从而产生诸多疑惑，教师对此可以不做过多的解释。只要引导学生能认真思索，积极探讨，投入学习状态即可。 （二）实验 1. 与每个小组的实验结果相比，全班实验的总结果更接近预期的结果，即彩球组合类型数量比DD ∶Dd ∶dd=1∶2∶1，彩球代表的显性与隐性类型的数值比为3∶1。因为实验个体数量越大，越接近统计规律。 如果孟德尔当时只统计10株豌豆杂交的结果，则很难正确地解释性状分离现象，因为实验统计的样本数目足够多，是孟德尔能够正确分析实验结果的前提条件之一。当对10株豌豆的个体做统计时，会出现较大的误差。 2. 模拟实验的结果与孟德尔的假说是相吻合的。因为甲、乙小桶内的彩球代表孟德尔实验中的雌、雄配子，从两个桶内分别随机抓取一个彩球进行组合，实际上模拟雌、雄配子的随机组合，统计的数量也足够大，出现了3∶1的结果。但证明某一假说还需实验验证。 （三）技能训练 提示：将获得的紫色花连续几代自交，即将每次自交后代的紫色花选育再进行自交，直至自交后代不再出现白色花为止。 （四）旁栏思考题 不会。因为满足孟德尔实验条件之一是雌、雄配子结合机会相等，即任何一个雄配子（或雌配子）与任何一个雌配子（或雄配子）的结合机会相等，这样才能出现3∶1的性状分离比。 （五）练习 基础题1.B。2.B。 3. （1）在F1水稻细胞中含有一个控制合成支链淀粉的遗传因子和一个控制合成直链淀粉的遗传因子。在F1形成配子时，两个遗传因子分离，分别进入不同配子中，含支链淀粉遗传因子的配子合成支链淀粉，遇碘变橙红色；含直链淀粉遗传因子的配子合成直链淀粉，遇碘变蓝黑色，其比例为1∶1。 （2）孟德尔的分离定律。即在F1形成配子时，成对的遗传因子发生分离，分离后的遗传因子分别进入不同的配子中。（3）2。 4. （1）白色；黑色。 （2）性状分离；白毛羊为杂合子，杂合子在自交时会产生性状分离现象。 拓展题 1. （1）将被鉴定的栗色公马与多匹白色母马配种，这样可在一个季节里产生多匹杂交后代。 （2）杂交后代可能有两种结果：一是杂交后代全部为栗色马，此结果说明被鉴定的栗色公马很可能是纯合子；二是杂交后代中既有白色马，又有栗色马，此结果说明被鉴定的栗色公马为杂合子。 2. 提示：选择适宜的实验材料是确保实验成功的条件之一。孟德尔在遗传杂交实验中，曾使用多种植物如豌豆、玉米、山柳菊做杂交实验，其中豌豆的杂交实验最为成功，因此发现了遗传的基本规律。这是因为豌豆具有适于研究杂交实验的特点，例如，豌豆严格自花受粉，在自然状态下是纯种，这样确保了通过杂交实验可以获得真正的杂种；豌豆花大，易于做人工 第一课 Vocabulary work 一 1. given 2. at a glance 3. fluency 4. Given 5. hopefully 7. define 8. looked him up 9. no good 10. quoted, context 11. guidance 12. immediate 13. disgust 14. come across 15. put into practice 16. scope 二 1. washed his hands of 2. given 3. putting…into practice 4. was confronted with 5. countering 6. were reduced to eating 7. at a glance 8. took refuge in 9. less practicable 10. countered 11. dedication 12. in disgust 13. relied on 14. for their part 15. gave up 三 1. Without suitable entertainment, these young people often get bored and take refuge in drinking and taking drugs. 2. The school washed its hands of the students’ behavior during the sp ring recess. 3. The innocent girl was reduced to crying at his cruel remarks. 4. Many difficult words are out of the scope of his learner’s dictionary. 5. The thief admitted his guilt as soon as he was confronted with evidence. 6. The incident should be viewed in the wider context of the political turmoil of that time. 四 1. has come down 2. came to 3. comes out 4. come up with 5. come in 6. came across 7. has come about 8. come off 9. come to 10. give up 11. was given back 12. gave away 13. gave out 14. give in 15. gives off/out cloze 1. express 2. both 3. intended 4. still 5. where 6. personal 7. of 8. them 9. make 10. before 11. still 12. before 13. fluent 14. while 15. enough 16. on 17. in 18. In 19. Find 20. Who 21. carefully 22. to 《高数》试卷1（上） 一．选择题（将答案代号填入括号内，每题3分，共30分）. 1．下列各组函数中，是相同的函数的是（ B ）. （A ）()()2ln 2ln f x x g x x == 和 （B ）()||f x x = 和 ()2g x x = （C ）()f x x = 和 ()()2 g x x = （D ）()|| x f x x = 和 ()g x =1 2．函数()()sin 42 0ln 10x x f x x a x ?+-≠? =+?? =? 在0x =处连续，则a =（ B ）. （A ）0 （B ）1 4 （C ）1 （D ）2 3．曲线ln y x x =的平行于直线10x y -+=的切线方程为（ A ）. （A ）1y x =- （B ）(1)y x =-+ （C ）()()ln 11y x x =-- （D ）y x = 4．设函数()||f x x =，则函数在点0x =处（ C ）. （A ）连续且可导 （B ）连续且可微 （C ）连续不可导 （D ）不连续不可微 5．点0x =是函数4 y x =的（ D ）. （A ）驻点但非极值点 （B ）拐点 （C ）驻点且是拐点 （D ）驻点且是极值点 6．曲线1 || y x = 的渐近线情况是（ C ）. （A ）只有水平渐近线 （B ）只有垂直渐近线 （C ）既有水平渐近线又有垂直渐近线 （D ）既无水平渐近线又无垂直渐近线 7． 211 f dx x x ??' ???? 的结果是（ C ）. （A ）1f C x ?? -+ ??? （B ）1f C x ?? --+ ??? （C ）1f C x ?? + ??? （D ）1f C x ?? -+ ??? 8． x x dx e e -+?的结果是（ A ）. （A ）arctan x e C + （B ）arctan x e C -+ （C ）x x e e C --+ （ D ）ln()x x e e C -++ 9．下列定积分为零的是（ A ）. Lesson1 1.The job of arousing manhood within a people that have been taught for so many centuries that they are nobody is not easy. It is no easy job to educate a people who have been told over centuries that they were inferior and of no importance to see that they are humans, the same as any other people. 2.Psychological freedom, a firm sense of self-esteem, is the most powerful weapon against the long night of physical slavery. If you break the mental shackles imposed on you by white supremacists, if you really respect yourself, thinking that you are a Man, equal to anyone else, you will be able to take part in the struggle against racial discrimination. 3.The Negro will only be free when he reaches down to the inner depths of his own being and signs with the pen and ink of assertive manhood his own emancipation proclamation. The liberation of mind can only be achieved by the Negro himself/herself. Only when he/she is fully convinced that he/she is a Man/Woman and is not inferior to anyone else, can he/she throw off the manacles of self-abnegation and become free. 4.Power at its best is love implementing the demands of justice, and justice at its best is power correcting everything that stands against love. Power in the best form of function is the carrying out of the demands of justice with love and justice in the best form of function is the overcoming of everything standing in the way of love with power. 5.At that time economic status was considered the measure of the individual’s ability and talents. At that time, the way to evaluate how capable and resourceful a person was to see how much money he had made (or how wealthy he was). 6.…the absence of worldly goods indicated a want of industrious habits and moral fiber. A person was poor because he was lazy and not hard-working and lacked a sense of right and wrong. 7.It is not the work of slaves driven to their tasks either by the task, by the taskmaster, or by animal necessity. This kind of work cannot be done by slaves who work because the work has to be done, because they are forced to work by slave-drivers or because they need to work in order to be fed and clothed. 8.…when the unjust measurement of human worth on the scale of dollars is eliminated. …when the unfair practice of judging human value by the amount of money a person has is done away with. 9.He who hates does not know God, but he who has love has the key that unlocks the door to the meaning of ultimate reality. Those who harbor hate in their hearts cannot grasp the teachings of God. Only those who have love can enjoy the ultimate happiness in Heaven. 10.Let us be dissatisfied until America will no longer have a high blood pressure of creeds and an anemia of deeds. Let us be dissatisfied until America no longer only talk about racial equality but is unwilling or reluctant to take action to end such evil practice as racial discrimination. 中南大学网络教育课程考试复习题及参考答案 高等数学(专科) 一、填空题： 1.函数1 1 42-+ -= x x y 的定义域是 。 解：),2[]2,(∞+--∞ 。 2.若函数52)1(2 -+=+x x x f ，则=)(x f 。 解：62 -x 3.sin lim x x x x →∞-= 。 答案：1 正确解法：101sin lim 1lim )sin 1(lim sin lim =-=-=-=-∞→∞→∞→∞→x x x x x x x x x x x 4.已知22 lim 2 22=--++→x x b ax x x ，则=a _____, =b _____。 由所给极限存在知，024=++b a ，得42--=a b ， 又由234 12lim 2lim 22 22=+=+++=--++→→a x a x x x b ax x x x , 知8,2-==b a 5.已知∞=---→) 1)((lim 0x a x b e x x ，则=a _____, =b _____。 ∞=---→)1)((lim 0x a x b e x x , 即01)1)((lim 0=-=---→b a b e x a x x x ，∴0,1a b =≠ 6.函数????? ≥+<=0 1 01sin )(x x x x x x f 的间断点是x = 。 解：由)(x f 是分段函数，0=x 是)(x f 的分段点，考虑函数在0=x 处的连续性。 因为 1)0(1)1(lim 01 sin lim 00 ==+=+-→→f x x x x x 所以函数)(x f 在0=x 处是间断的， 又)(x f 在)0,(-∞和),0(+∞都是连续的，故函数)(x f 的间断点是0=x 。 7.设()()()n x x x x y -??--= 21, 则() =+1n y (1)!n + 人教版高中数学必修5课后习题解答 第一章 解三角形 1．1两角和与差的正弦、余弦和正切公式 练习（P4） 1、（1），，； （2）cm ，cm ， . 2、（1），，；或，，； （2），，. 练习（P8） 1、（1）； （2）. 2、（1）； （2）. 习题1.1 A 组（P10） 1、（1）； （2） 2、（1） （2）； （3）； 3、（1）； （2）； （3）； 4、（1）； （2）； 习题1.1 A 组（P10） 1、证明：如图1，设的外接圆的半径是， ①当时直角三角形时，时， 的外接圆的圆心在的斜边上. 在 中，， 即， 所以 ， 又 所以 ②当时锐角三角形时，它的外接圆的圆心在三角形内（图2）， 作过的直径，连接， 则直角三角形，，. 在 中，， 即 ， 所以， 同理：， ③当时钝角三角形时，不妨假设为钝角， 它的外接圆的圆心在外（图3） 作过的直径，连接. 则直角三角形，且， 在中，， 即 即 同理：， 综上，对任意三角形，如果它的外接圆半径等于， 则 2、因为， 所以，即 因为， （第1题图1） （第1题图2） （第1题图3） 所以，或，或. 即或. 所以，三角形是等腰三角形，或是直角三角形. 在得到后，也可以化为 所以 ，或 即，或，得到问题的结论. 1．2应用举例 练习（P13） 1、在中，n mile，， 根据正弦定理， 得 ∴到直线的距离是（cm）. ∴这艘船可以继续沿正北方向航行. 2、顶杆约长1.89 m. 练习（P15） 1、在中，， 在中，根据正弦定理， 所以，山高为 2、在中，m， 根据正弦定理， m 井架的高约9.8m. 3、山的高度为m 练习（P16） 1、约. 练习（P18） 1、（1）约；（2）约；（3）约. 2、约 3、右边 左边【类似可以证明另外两个等式】 习题1.2 A组（P19） 1、在中，n mile， ， 根据正弦定理， 第一课 大学英语精读第五册课后习题答案（1u）(2010-07-20 13:49:10)转载 标签：答案教育分类：大学英语 V ocabulary work 一 1. given 2. at a glance 3. fluency 4. Given 5. hopefully 7. define 8. looked him up 9. no good 10. quoted, context 11. guidance 12. immediate 13. disgust 14. come across 15. put into practice 16. scope 二 1. washed his hands of 2. given 3. putting…into practice 4. was confronted with 5. countering 6. were reduced to eating 7. at a glance 8. took refuge in 9. less practicable 10. countered 11. dedication 12. in disgust 13. relied on 14. for their part 15. gave up 三 1. Without suitable entertainment, these young people often get bored and take refuge in drinking and taking drugs. 2. The school washed its hands of the students’ behavior during the spring recess. 3. The innocent girl was reduced to crying at his cruel remarks. 4. Many difficult words are out of the scope of his learner’s dictionary. 5. The thief admitted his guilt as soon as he was confronted with evidence. 6. The incident should be viewed in the wider context of the political turmoil of that time. 四 1. has come down 2. came to 3. comes out 4. come up with 5. come in 6. came across 7. has come about 8. come off 9. come to 10. give up 11. was given back 12. gave away 13. gave out 14. give in 15. gives off/out cloze 1. express 2. both 3. intended 4. still 5. where 6. personal 7. of 8. them 9. make 10. before 11. still 12. before 13. fluent 14. while 15. enough 16. on 17. in 18. In现代大学英语精读5(第二版)课后答案
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