最新汕头市东厦中学高二数学选修2-2《导数及其应用》单元测试题人教版名师优秀教案.doc

汕头市东厦中学高二数学(选修2-2)导数及其应用单元测试题(人教版)东厦中学20082009学年度第二学期单元测试 高二级数学(理)科试卷 (选修2-2第二章导数及其应用) 一、选择题(每小题5分共40分) 14t,51运动的方程为，则当的瞬时速率为( ) s,t,34A(5 B. 25 C. 125 D. 625 2.设y=x-lnx，则此函数在区间(0,1)内为( ) A(单调递增， B、有增有减 C、单调递减， D、不确定 f(xh)f(xh)，,00'lim,3(若，则( ) fx()3,0,h0h,3,6,9,12A( B( C( D( 4(已知直线的切线则k=( ) ykxyx,是ln11, A( B( C( D( e,eee3,yxxcos(0)5.曲线与坐标轴围成的面积是 ( ) 25A.4 B. C.3 D.2 26、已知函数的导函数的图象如下图，那么图象可y,f(x),y,g(x)y,f(x),y,g(x)能是( ) 327(已知函数在上是单调函数,则实数的取值范围是a(,，,)f(x),x，ax,x,1( ) A( B( ,3,3(,3:3,，,)C( D( (,3,3)(,3):(3,，,)x8(2008广东9)设a?R，若函数y=e+ax, x?R有大于零的极值点，则( ) 11 A(a, B(a, C(a, D(a, ,1,1ee二、填空题(每小题5分共30分) 322x,1109(函数在时有极值，那么的值分别为 ; a,bfxxaxbxa(),，sinxy,10(函数的导数为_; x11(曲线在点处的切线的方程为_ _; y,lnxMe(,1)8312( xdx, ; ,1tt,021d6xx,13. 已知，若，则 。 t,，,0,14(设函数，若为奇函数，则,=_; fxfx()()，fxx()cos(3)(0),，,三、解答题(共80分) 3215(求垂直于直线并且与曲线相切的直线方程(10分) 2610xy,，,yxx,，,352x,0x,216 . 求由曲线与，所围成的平面图形的面积(画出图形)。yx,3yx,，2(14分) x,x17(求函数的单调区间 (a,o,且a,1)(12分) f(x),a,a18(一艘轮船在航行中的燃料费和它的速度的立方成正比，已知在速度为每小时10公里时的燃料费是每小时6元，而其他与速度无关的费用是每小时96元，问此轮船以多大的速度航行时，能行使每公里的费用最少,(12分) 122x,13232与，试比较与的大19(设函数f(x),xe,x,xgxxx(),fx()gx()33小(14分) 3220(设的图像经过点f(x),ax，bx，cx的极小值为,8,其导函数y,f'(x)2如图所示，(16分) (,2,0),(,0),3(?)求的解析式; f(x)(?)求函数的单调区间和极值; 2 (?)若对恒成立， x,3,3都有f(x),m,14m求实数m的取值范围. 一、选择题CCBCCDBA 二、填空题 xxxcossin,9( 10( 11(x-ey=0 4,11,2x45, 12( 13. 3 14( 46三、解答题 3215(求垂直于直线2610xy,，,并且与曲线相切的直线方程。(10分) yxx,，,3532'2解:设切点为Pab(,)，函数的导数为 yxx,，,35yxx,，36'232a,1kyaa,，,|363切线的斜率，得，代入到 yxx,，,35xa,b,3得，即， P(1,3),。 yxxy，,，,33(1),3602x,0x,216 . 求由曲线与，所围成的平面图形的面积(画出图形)。yx,3yx,，2(14分) 解:如图阴影部分为所求面积 2,y,x，2解方程组 可得x,1或x,2,y,3x,1222 ？S,(x，2),3xdx，3x,(x，2),0132231233xxxx(2)(2) ,，x,，,x013223=1 所以所求图形的面积为1。 x,x17(讨论函数()的单调性(12分) a,0,a,1f(x),a,a解:函数的定义域R x,xx,x f'(x),a,lna,alna,(,x)',lna(a，a)x,x当a0时，lna,0，a，a,0, ？f'(x),0 ？函数f(x)在(,，,)上是增函数x,x当a,0时，lna,0，a，a,0, ？f'(x),0 ？函数f(x)在(,，,)上是减函数18(一艘轮船在航行中的燃料费和它的速度的立方成正比，已知在速度为每小时10公里时的燃料费是每小时6元，而其他与速度无关的费用是每小时96元，问此轮船以多大的速度航行时，能行使每公里的费用最少,(12分) 3解:设船速度为x公里/小时(x>0)时，燃料费用Q为元，则 Q,kx3333由6,k，10可得k,？Q,x 5005003139632y(x96)x？总费用,，,， 500x500x396 ？y',x，,令y',0得x,202500x当x,(0,20)时，y',0，此时函数单调递减当x,(20,，,)时，y',0，此时函数单调递?当x=20时，y取得最小值 ?此轮船以20公里/小时的速度行驶时每公里的费用总和最小。 122132x,3219(设函数fxxxx, 设，试比较与的大gxxx(),()efx()gx()33小(14分) 122132x,32解?fxxxx, gxxx(),()e3321321xx,x,1x,1,故，令，则( fxgxxxxx()()e(e),hxx()e,hx()e1,x,1,令，得，因为x,，1时， hx()0,hx()0?，,x,，1x,，1所以在上单调递减(故时，; hx()hxh()(1)0?,，,x,，,1，x,，,1，因为时，所以在上单调递增( hx()hx()0?，,x,，,1，故时，( hxh()(1)0?,，,2x?0所以对任意，恒有，又，因此， x,，,()，hx()0?fxgx()()0,?故对任意，恒有( x,，,()，fxgx()()?20(本小题满分16分) 32设的图像经过点f(x),ax，bx，cx的极小值为,8,其导函数y,f'(x)2(,2,0),(,0),如图所示， 3(?)求f(x)的解析式; (?)求函数的单调区间和极值; 2 (?)若对恒成立， x,3,3都有f(x),m,14m求实数m的取值范围. 22解(1) ？f'(x),3ax，2bx，c,且y,f'(x)的图像经过点(,2,0),(,0),322b,2，,b,2a,33a32 ？,？f(x),ax，2ax,4ax,2cc,4a,2，,33a,22由图象可知函数上单调递增，在上y,f(x)在(,2)上单调递减,在(,2,)(,，,)33单调递减， 32 由f(x),f(,2),a(,2)，2a(,2),4a(,2),8,解得a,1极小值32 ？f(x),x,2x，4x2(2) 由(1)得f'(x),3x,4x，4,(3x，2)(x,2)2？f'(x),0,则x,2或x, 3222,2x (,2)(,2,)(,，,) 333f'(x)- 0 + 0 - 40单调递减 -8 单调递增 单调递减 f(x) 2722？函数f(x)的单调递减区间是(,2)和(,，,)，单调递增在区间是(,2,)，33 40极小值是-8，极大值是。272 (3)要使对恒成立， x,3,3都有f(x),m,14m2只需 f(x),m,14m即可.min22由(1)可知上单函数y,f(x)在,3,2)上单调递减,在(,2,)上单调递增,在(,333调递减 32 且f(,2),8,f(3),3,2，3，4，3,33,8？f(x),f(3),33min2 ,33,m,14m,3,m,11故所求的实数m的取值范围为 m|3,m,11.(英文版 ) easily blame, to prevent the broken window effect. Supervise the leading cadres to play an exemplary role, take the lead in the strict implementation of the < code > and < rule >, lead to safeguard the solemnity and authority of the party discipline, ensure that the party discipline and the laws and regulations for implementation in place. Throughout the discipline in the daily supervision and management , strengthen supervision and inspection, from the thorough investigation of violations of discipline behavior. Strengthen to key areas, key departments and key projects as well as the masses reflect the concentration of the units and departments for supervision. - strengthening supervision, discipline inspection and supervision of cadres to set an example for compliance with the < code > and < rule > is a man must be hexyl, blacksmith needs its own hardware. Discipline inspection organs as the executor of the party discipline, and supervisor of the defenders, for its supervision must be more strictly, discipline inspection and supervision of cadres to firmly establish the awareness of Party Constitution, sense of discipline and rules consciousness, politics loyalty, sense obey. Action speak Ji Ordinance to set an example of the regulations of the rule of law, strengthen supervision and accept the supervision of the firmness and consciousness, do comply with < > and < >. To firmly establish the discipline must first be disciplined, the supervisor will be subject to the supervision of "concept, and consciously safeguard and implement party compasses party, take the lead in practicing" three strict real strict, so loyal, clean, play. To be good at learning, the Constitution and the < code > as morality, politics and brought to fruition; to implement < >, do not want to, dare not, not with disciplinary ruler to supervision; to discipline a ruler, often the control inspection, and consciously in the ideological red line to draw the row Ming Good accumulation is indeed the bottom line, so that the heart has fear, said to have quit, the line has ended. Attached: indifferent to heart, calmly to the table in our life, there are many unpredictable things will happen, some good, some bad things, we cannot control is powerless to stop, but with time, you will find in life sometimes turns out to be not good, some bad things finally turned out to be a good thing, but then we muddy however did not know, this is the life teach us things. 1, life can be complex, can also be simple. Want simple life of precipitation, to have enough time to reflect, to make Become more perfect. Life is the most important thing is not to win, but the struggle; not to have conquered, but to have fought well. 2, the plain is the background of life. Live a plain life, give up on themselves is not a coward, but the wise answers; not disillusioned after the heart, such as ashes, but experience the storm after the enlightenment; not unrewarding perfunctorily, but calm attitude of life of unrestrained self-confidence. Plain living, there is no noise noisy, no earthly troubles, more did not fill in the discontent of desire, some just a calm, a calm. 3, memory of heart will not good things to erase the, life is a When no movie, pain is a beginning, the struggle is a kind of process, death is a kind of ending. Give up this giving up is the helpless, do not give up the abandoned, do not give up this giving up is ignorance, do not give up should not give up is persistent. 4, a thing figured is heaven, think impassability is hell. Since the living, to live better. Sometimes we because of too narrow-minded, too care around the chores and penny wise and pound foolish, not worth the candle. Some things to attract trouble and worry, completely depends on how we look at and deal with it. Don't always take everything back to things, and don't get into a blind alley, don't want to face, don't be narrow-minded. Poke to care, is a kind of open-minded, a free and easy. 5, I am not afraid of others behind me a knife, I afraid to look back and see stab me, is my intention to treat people; I am not afraid of the truth to tell the best friend, I'm afraid he turned to it as a joke to tell don't 6, when we are in a positive frame of mind, you will find many good things; and when we are in a negative state of mind, you will find many depressed things; life happy and worry, all is you of life attitude, optimistic, good luck; loss of sink, Eritrea company. When you are in adversity, may wish to change a point of view to think everything over to the good Think, because good mentality decided the fate of the! 7, people are tired, rest; heart tired, calm. Grow up, mature, this society read. Tired and sad, squat down, to their a hug. Because the world no one can sympathize with you, have mercy on you. You cry, tears is your own; you pain, no one can understand. Then you only tears to smile. 8, each people have youth, Each youth are a story, the life of the world never gets easier, I want what, wish the world all know, as has been the same; now want anything, for fear that others know, or like to lose the same. 9, the heart move, everything in the world is followed by birth, Rangrang, important thing is often the most difficult to open one's mouth, because words will reduce its importance; to let strangers people care about your life in the good things, the original is not easy 10, do not blame, do not laugh at who, also don't envy who. Like a person is a kind of feeling, not like a person is true. The truth is easy to explain, I feel Is unspeakable. The best travel life is that you in a strange place found a long lost touched. 11, happy life not in the bustling in, and in the peace of mind; no matter how many grievances, how uncomfortable, and ultimately to heal themselves or their own, others may got you to comfort, but never know your heart is how wanjianchuanxin. 12, ma'am, like a movie, learn to appreciate, learn to be grateful, learn tolerance, and goodness, helping others. Instead of accusing the society, as into one; and an exception is better to give than to what 13, don't envy him A sum of, don't lose your life and the life, respectively is: the former is a we experienced cannot escape in a day finally will last minute, while the latter is our persistent, we want to cherish the memory of those people and things. 14, learn to smile, learn to strong, the world you know so many people, so many people and you are, you cannot change also can't let everyone like you, so also do not want to do. Life is too short to go crazy to love to go to waste, to chase the dream to regret. 15, when temper, a blessing to go. A wounding elegant people, the key is to control their own emotions. With the mouth is the most stupid behavior. A control negative emotions than a can take a city more powerful water flow slow, language is expensive. People spent two years of time to learn to speak, but to spend a few years time to shut up. That is a kind of ability, that is a kind of wisdom. 16, life is not perfect, sometimes, growth is not a cry, not an eyeful of tears, there is no trace of emotion, there is no gleam of hope, no desire, no action, no static, there is only one kind of downward sinking feeling, sink A murky? 6? 7? 6? 7 sink? 6? 7? 6? 7 toward the bottom of the sink. 17, in some way, do not go, you will not know the other side scenery is beautiful. To you is not good, you do not mind too much, no one has an obligation to you; you learn knowledge, is you have weapons, you can start from scratch, but not unarmed; how do you treat people, does not represent how others treat you, if cannot see through this point, only inviting worry. 18, time is like a sponge in the water, as long as you are willing to squeeze, the total water is still there. Every life, after the ups and downs The best test of live, to life, survival and continuation, do not stop the struggle in the joys and sorrows of life on the road, so that different soul to bear life beat, acceptance of suffering. 19, indifferent to heart, calmly in table, elegant and comfortable life, do not take what is so important. The pursuit will be disappointed; to be alive, you will have trouble. Life is the most afraid of what all want to care about, but also what all grasp is not firm, without scenery, separated populations, such as not to desire, all docked in the fate of the end. Why is too rigid, the natural, to go stay not to live, let go of obsession, revel is 20, if the fate of the broken Hopes of sailing, please don't despair, the coast is still, if the fate of the withered petals of the beautiful, please do not sink, the spring is still, life will always be endless trouble, please don't helpless, because they are still alive, is still a dream, the sun still, we still. Lost, keep memories; to get, must work to; but the most important is good to cherish their own. 21, life, select the complex, is to choose the pain; choose a simple, is choose to be happy. The complex world like a Significance of pride. Hope is the ornate palace, outside people admiring the magnificent, living in the deep knowledge of living it to pay the price. Simple world as a simple log cabin outside ridiculed shabby, the heart is willing to go live to know the joy. Suffering and joy is their own choice. 22, learn how to use a single powerful heart, let the past be the past, let the future come. Life is really the end of the end of an eagle is flying wings, life is constantly pursuit. Don't miss to regret, don't wait for old just miss. Time to return, seize every moment, again painstakingly again tired also Those struggling to fly. 23, life could not Yimapingchuan, even flat pavement, inevitably there will be a few pieces of roadblocks. Some of the rocks around the past, while others have to move it out. Just move others put the stone is very easy, because the stone from the appearance we can discern; difficult to myself to move away the heart of stone head. Leave time to spend with her, often reflect my heart, so as to remove your heart of stone. 24, everything does not have to be demanding, come to, everything does not have to care about, over the past; failing to do not frown, laugh it laugh. Results Don't demand, do to; life is a simple, calm and peaceful. Always not to choose their own path and regret, life is like a train, the scenery and then the United States will retreat, the passage of time and encounter will eventually drifting further and further away, before is always himself. 25, everyone has a weakness, weakness is true humanity. That has no weakness, a shallow person. That people think there is no weakness, mostly false. Life has shortcomings, there are shortcomings is the real life. That no one regret, or childish or numbness or Self deception. It is in tolerance of weakness and so on to accept, people live happily. Hello, everyone! I am a party member. The title of my speech is: < study and implement the party's two laws, doing practical play highway. 2015 October 18, the Central Committee of the Communist Party of China promulgated the implementation of the < the probity of the Communist Party of China self-discipline criterion > and < Chinese Communist Party discipline and punishment regulations. We Heyuan male passers-by to respond positively to the call of the Central Committee o