最新汕头市东厦中学高二数学选修2-2《导数及其应用》单元测试题人教版优秀名师资料.doc
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1、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),,00lim,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l
2、n11, 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3
3、0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,x1
4、7(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 (?)
5、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,,,35322解:设切点为Pab(,),函数的导数为 yxx,,,35yxx,,36232a,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
6、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
7、),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(x0)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
8、 ?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)
9、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,4a
10、x,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-
11、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 exe
12、mplary role, take the lead in the strict implementation of the and , 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 , s
13、trengthen 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
14、inspection and supervision of cadres to set an example for compliance with the and 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 i
15、nspection 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
16、 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
17、 loyal, clean, play. To be good at learning, the Constitution and the 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 t
18、o 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 power
19、less 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 ha
20、ve 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 disill
21、usioned 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 c
22、alm, 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
23、 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, c
24、ompletely depends on how we look at and deal with it. Dont always take everything back to things, and dont get into a blind alley, dont want to face, dont 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
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