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首页 高起专数学复习资料

高起专数学复习资料.doc

高起专数学复习资料

手机一响情绪就乱了
2018-07-11 0人阅读 举报 0 0 暂无简介

简介:本文档为《高起专数学复习资料doc》,可适用于综合领域

高起专数学复习资料成人高考数学知识提纲数学复习资料集合:会用列举法、描述法表示集合会集合的交、并、补运算能借助数轴解决集合运算的问题具体参看课本例、、充分必要条件要分清条件和结论由条件可推出结论条件是结论成立的充分条件由结论可推A,B出条件则条件是结论成立的必要条件。从集合角度解释若则A是B的充分BA,条件若则A是B的必要条件若A=B则A是B的充要条件。例:对“充分必要条件”的理解请看两个例子:x,()“”是“”的什么条件,x,x,x,()是的什么条件,AB,AB,我们知道若则A是B的充分条件若“”则A是B的必要条AB,件但这种只记住定义的理解还不够必须有自己的理解语言:“若即是A能推出B”但这样还不够具体形象因为“推出”指的是什么还不明确即使借助数轴、文氏图也还是“抽象”的如果用“A中的所有元素能满足B”的自然语言去理解,基本能深刻把握“充分必要条件”的内容x,本例中即集合当中的元素{,},不能满足或者说不属于但的元素能满足或者说属于假设{}{}{,},AB,x,x,则满足“”故“”是“”的必要非A,{x|x,},B,{x|x,}x,x,充分条件同理是的必要非充分条件yxyx,,,,直角坐标系注意某一点关于坐标轴、坐标原点、的坐标的写法。如点()关于轴对称坐标为()x点()关于轴对称坐标为()y点()关于原点对称坐标为()yx,点()关于轴对称坐标为()yx,,点()关于轴对称坐标为()函数的三要素:定义域、值域、对应法则如果两个函数三要素相同则是相同函数。会求函数的定义域做页第一大题函数的定义域、值域、解析式、单调性、奇偶性性、周期是重要的研究内容尤其是定义域、一次和二次函数的解析式单调性最重要。函数的奇偶性。()具有奇偶性的函数的定义域的特征:定义域必须关于原点对称~为此确定函数的奇偶性时务必先判定函数定义域是否关于原点对称。()确定函数奇偶性的常用方法(若所给函数的解析式较为复杂应先化简再判断insouthwestofZhejiangProvincialCommitteeoftheparty'sstruggle,developdemocraticUnitedFrontagainstJapan,establishedthearmedforcesandtheantiJapanesebasearea,decidedtoestablishtheCPCZhejiangCommitteeInFebruary,withGuYuliang,SecretaryZhu,asMinister,JieXuintoapropagandaMinister,ZhangZhihuaaswomen'sMinister,HuangyanasyouthMinister,zhexirecorderofPenrhynasmilitarySecretaryoftheestablishmentHanchangorganizationattachedtotherecordersoftheWestAftertheSpringFestival,ZhuXiwasdeterminedtorally,ledbyWangHesongmorethanmorethanpeople,with"firstRoadSouthintotheteamheadquartersthenameof"backfromWuzhentoWujiangyanIsmonth,establishedtheTombareathbranchEastwaterHongKongBranch,BranchSecretaryShenYingjieIsautumn,theKuomintangZhejiangProvincialGovernmentinSouthwestBureautointensifyitsanticommunist,orderedpoliticalteamtrainingintianmumountain,isintendedtoeliminateinthepoliticalpoweroftheCommunistParty,thoroughrestructuringoftheprovince'spoliticalteamtomakeitbecomeatoolofantiCommunistInviewofthissituation,recorderoftheWestdirectionWestopenmassworkhasbeendifficult,politicalsignsshouldnotbeused,onlyallgounderground,theparty'sworktocontinueTodothis,takeappropriatemeasuresbyapartyorganization,partymembersintheOrganizationofpoliticalwithdrawal,transferormakepubliccareerascover,intoasecretstruggleInNovember,Yangandthevictoryofthebattleofthe其奇偶性):fx(),定义法:利用函数奇偶性定义的等价形式:或,,fxfx()(),,,fx()()。图像法:奇函数的图象关于原点对称偶函数的图象关于轴对称。fx(),y常见奇函数:指数是奇数yxyxyxyxyxyx,,,,,,,,,,,sin,tan,常见偶函数:ykyxyxyxyx,,,,,,,,,cos一些规律:两个奇函数相加或者相减还是奇函数两个偶函数相加或者相减还是偶sinx函数但是两种函数加减就是非奇非偶两种函数乘除是奇函数例如yx,,tancosx是奇函数()函数奇偶性的性质:奇函数在关于原点对称的区间上若有单调性则其单调性完全相同偶函数在关于原点对称的区间上若有单调性则其单调性恰恰相反如果奇函数有反函数那么其反函数一定还是奇函数若为偶函数则fx()fxfxfx()()(||),,,奇函数定义域中含有则必有故是为奇函数的既不充分fx()f(),f(),fx()也不必要条件。函数的单调性:一般用来比较大小而且主要用来比较指数函数、对数函数的大小此外反比例函数、一次函数、二次函数的单调性也比较重要要熟记他们的图像的分布和走势。熟记课本第页至页的图和相关结论。一次函数、反比例函数p例p例二次函数表达形式有三种:一般式:顶点式:fxaxbxc(),fxaxmn()(),,零点式:要会根据已知条件的特点灵活地选用二次函数的表达形fxaxxxx()()(),,,式。课本中的p例()例、例例例习题p、、、axb,一元一次不等式的解法关键是化为再把的系数化为注意乘以或者x除以一个负数不等号的方向要改变一元一次不等式组最后取个不等式的交集即数轴上的公共部分。做p、、大题绝对值不等式只要求会做:和||axbccaxbc,,,,,||axbccaxb,,,axbc,,或者一定会去绝对值符号。做p一元二次不等式是重点阅读课文至的图表及至页的例题。做页、、、、a,axbxc,xx,xx,设,是方程的两实根且则其解集如下表:axbxc,axbxc,axbxc,axbxc,,,{|xxx,{|xxx,{|}xxxx,,或或{|}xxxx,,xx,}xx,},,bb,{|}xx,,{|}xx,,Raa,,,,RRaxbxc,a对于方程有实数解的问题。首先要讨论最高次项系数是否为其a,,,b,ac,次若则一定有。insouthwestofZhejiangProvincialCommitteeoftheparty'sstruggle,developdemocraticUnitedFrontagainstJapan,establishedthearmedforcesandtheantiJapanesebasearea,decidedtoestablishtheCPCZhejiangCommitteeInFebruary,withGuYuliang,SecretaryZhu,asMinister,JieXuintoapropagandaMinister,ZhangZhihuaaswomen'sMinister,HuangyanasyouthMinister,zhexirecorderofPenrhynasmilitarySecretaryoftheestablishmentHanchangorganizationattachedtotherecordersoftheWestAftertheSpringFestival,ZhuXiwasdeterminedtorally,ledbyWangHesongmorethanmorethanpeople,with"firstRoadSouthintotheteamheadquartersthenameof"backfromWuzhentoWujiangyanIsmonth,establishedtheTombareathbranchEastwaterHongKongBranch,BranchSecretaryShenYingjieIsautumn,theKuomintangZhejiangProvincialGovernmentinSouthwestBureautointensifyitsanticommunist,orderedpoliticalteamtrainingintianmumountain,isintendedtoeliminateinthepoliticalpoweroftheCommunistParty,thoroughrestructuringoftheprovince'spoliticalteamtomakeitbecomeatoolofantiCommunistInviewofthissituation,recorderoftheWestdirectionWestopenmassworkhasbeendifficult,politicalsignsshouldnotbeused,onlyallgounderground,theparty'sworktocontinueTodothis,takeappropriatemeasuresbyapartyorganization,partymembersintheOrganizationofpoliticalwithdrawal,transferormakepubliccareerascover,intoasecretstruggleInNovember,Yangandthevictoryofthebattleofthe数列的同项公式与前n项的和的关系sn,,,(数列的前n项的和为){}asaaa,?a,,nnnnssn,,,,nn,*等差数列的通项公式aanddnadnN,,,,,()()nnaa()nn(),dn其前n项和公式为,,nadn(),nads,nann,*等比数列的通项公式aaqqnN,,,,()nqn,aaq,aq(),,n,q,,q,,,s,,q其前n项的和公式为或,qs,,n,n,,naq,,,naq,,,等差数列的性质:()当mnpq,时,则有特别地当时则有aa,aaaaa,mnp,mnpqmnp()若、是等差数列{}an„也成等差数列SSSSS,,,,nnnnnnn,()在等差数列中当项数为偶数时项数为奇数时SSnd,,{}an偶奇(这里即)。Sna,,,()aSSkk:(,:)SSa,,an,n奇偶中中中奇偶()如果两等差数列有公共项那么由它们的公共项顺次组成的新数列也是等差数列且新等差数列的公差是原两等差数列公差的最小公倍数注意:公共项仅是公共的项其项数不一定相同即研究ab,nm等比数列前项和公式有两种形式为此在求等比数列前项和时首先要判断nn公比是否为再由的情况选择求和公式的形式当不能判断公比是否为时要qqq对q分和两种情形讨论求解。q,q,等比数列的性质:mnpq,aaa,aaaa,()当时则有特别地当时则有mnp,mnpqmnp()若{}a是等比数列且公比则数列SSSSS,,,,„也是等比数列。q,,nnnnnn当且为偶数时数列SSSSS,,,,„是常数数列它不是等比数nq,,nnnnn列nn,SqS,()在等比数列{}a中当项数为偶数时项数为奇数时n偶奇SaqS,奇偶()数列既成等差数列又成等比数列那么数列是非零常数数列故常数数列{}a{}ann仅是此数列既成等差数列又成等比数列的必要非充分条件。{}an这一章主要是找数字的规律写出数列通项公式但对等差和等比数列要求比较高会有较大的比重出解答题页起的例、、、是基础题例、、、是中档题目例、、是综合题。最要紧做页的题目。,f(x)导数的几何意义:曲线y,f(x)在点P(x,f(x))处的切线的斜率是相应地,y,y,f(x)(x,x)切线方程是导数的应用:insouthwestofZhejiangProvincialCommitteeoftheparty'sstruggle,developdemocraticUnitedFrontagainstJapan,establishedthearmedforcesandtheantiJapanesebasearea,decidedtoestablishtheCPCZhejiangCommitteeInFebruary,withGuYuliang,SecretaryZhu,asMinister,JieXuintoapropagandaMinister,ZhangZhihuaaswomen'sMinister,HuangyanasyouthMinister,zhexirecorderofPenrhynasmilitarySecretaryoftheestablishmentHanchangorganizationattachedtotherecordersoftheWestAftertheSpringFestival,ZhuXiwasdeterminedtorally,ledbyWangHesongmorethanmorethanpeople,with"firstRoadSouthintotheteamheadquartersthenameof"backfromWuzhentoWujiangyanIsmonth,establishedtheTombareathbranchEastwaterHongKongBranch,BranchSecretaryShenYingjieIsautumn,theKuomintangZhejiangProvincialGovernmentinSouthwestBureautointensifyitsanticommunist,orderedpoliticalteamtrainingintianmumountain,isintendedtoeliminateinthepoliticalpoweroftheCommunistParty,thoroughrestructuringoftheprovince'spoliticalteamtomakeitbecomeatoolofantiCommunistInviewofthissituation,recorderoftheWestdirectionWestopenmassworkhasbeendifficult,politicalsignsshouldnotbeused,onlyallgounderground,theparty'sworktocontinueTodothis,takeappropriatemeasuresbyapartyorganization,partymembersintheOrganizationofpoliticalwithdrawal,transferormakepubliccareerascover,intoasecretstruggleInNovember,Yangandthevictoryofthebattleofthe()利用导数判断函数的单调性:设函数y,f(x)在某个区间内可导,,如果那么f(x)为增函数如果那么f(x)为减函数f(x),,f(x),,,如果在某个区间内恒有f(x)为常数f(x),,,,,()求可导函数极值的步骤:求导数求方程的根检验在f(x)f(x),f(x),方程根的左右的符号如果左正右负那么函数y=f(x)在这个根处取得最大值f(x),如果左负右正那么函数y=f(x)在这个根处取得最小值。本章重点是求曲线在一点处的cosxtanxsinx性质切线方程和多项式的导数会求函数最大值最小值和极值。课本页例、、、和页习题要过一过关。三角函数本章出个小题个大题不是重点内容象限角的概念:如果角的终边在坐标轴上就认为这个角不属于任何象限。扇形面积公式:弧长公式:lR,||,,SlRR,,,||,弧度(rad)、任意角的三角函数的定义:设是任意一个角P是的终边上的任意一点(异,,(,)xy于原点),sin,,tan,yxyrxy,,sin,cos,,,,tan,,,,x它与原点的距离是那么xrrxcot,,()y,y特殊角的三角函数值:,cos,insouthwestofZhejiangProvincialCommitteeoftheparty'sstruggle,developdemocraticUnitedFrontagainstJapan,establishedthearmedforcesandtheantiJapanesebasearea,decidedtoestablishtheCPCZhejiangCommitteeInFebruary,withGuYuliang,SecretaryZhu,asMinister,JieXuintoapropagandaMinister,ZhangZhihuaaswomen'sMinister,HuangyanasyouthMinister,zhexirecorderofPenrhynasmilitarySecretaryoftheestablishmentHanchangorganizationattachedtotherecordersoftheWestAftertheSpringFestival,ZhuXiwasdeterminedtorally,ledbyWangHesongmorethanmorethanpeople,with"firstRoadSouthintotheteamheadquartersthenameof"backfromWuzhentoWujiangyanIsmonth,establishedtheTombareathbranchEastwaterHongKongBranch,BranchSecretaryShenYingjieIsautumn,theKuomintangZhejiangProvincialGovernmentinSouthwestBureautointensifyitsanticommunist,orderedpoliticalteamtrainingintianmumountain,isintendedtoeliminateinthepoliticalpoweroftheCommunistParty,thoroughrestructuringoftheprovince'spoliticalteamtomakeitbecomeatoolofantiCommunistInviewofthissituation,recorderoftheWestdirectionWestopenmassworkhasbeendifficult,politicalsignsshouldnotbeused,onlyallgounderground,theparty'sworktocontinueTodothis,takeappropriatemeasuresbyapartyorganization,partymembersintheOrganizationofpoliticalwithdrawal,transferormakepubliccareerascover,intoasecretstruggleInNovember,Yangandthevictoryofthebattleofthe三角函数的恒等变形的基本思路是:一角二图像页图页图页图名三结构。即首先观察角与角之间的关系注的来意角的一些常用变式角的变换是三角函数变源换的核心~第二看函数名称之间的关系通常及图“切化弦”第三观察代数式的结构特点。像基本公式:定义页表格页表格页表格(常见三角不等式域,值域页表格页表格页表格()若则x,(,)单调页表格页表格页表格sintanxxx,,性及,递增()若x,(,)则递减区间sincos,,xx()|sin||cos|xx,周期、页表格、页表页表性及格格同角三角函数的基本关系式奇偶,sintan,=sincos,,,性cos,对称不要求不要求不要求tan,,,,cot轴正弦、余弦的诱导公式(参看课本页)对称不要求不要求不要求注意规律:横不变名竖变名正负看象限中心()负角变正角再写成最值页表格页表格页表格,,,,k,,,及指()转化为锐角三角函数。定区和角与差角公式间的sin()sincoscossin,,,,,,,,,最值cos()coscossinsin,,,,,,,,,简单不要求不要求不要求tantan,,,三角tan(),,,,tantan,,,方程和不absincos,,=(辅助absin(),,等式角所在象限由点的象限决(,)ab,btan,,定,)a二倍角公式sinsincos,,,,coscossincossin,,,,,,,,,,,tan,,tan,,tan,三角函数的周期公式函数xR及函数xR(A,ω,为常数且Aω,)的周期yx,sin(),,yx,cos(),,,,T,,,,xkkZ,,,T,,函数yx,tan(),,(A,ω,为常数且Aω,)的周期,,解三角形就完成模拟试题的相关习题即可。平面向量实数与向量的积的运算律:设λ、μ为实数那么()结合律:λ(μa)=(λμ)a()第一分配律:(λμ)a=λaμa()第二分配律:λ(ab)=λaλb向量的数量积的运算律:insouthwestofZhejiangProvincialCommitteeoftheparty'sstruggle,developdemocraticUnitedFrontagainstJapan,establishedthearmedforcesandtheantiJapanesebasearea,decidedtoestablishtheCPCZhejiangCommitteeInFebruary,withGuYuliang,SecretaryZhu,asMinister,JieXuintoapropagandaMinister,ZhangZhihuaaswomen'sMinister,HuangyanasyouthMinister,zhexirecorderofPenrhynasmilitarySecretaryoftheestablishmentHanchangorganizationattachedtotherecordersoftheWestAftertheSpringFestival,ZhuXiwasdeterminedtorally,ledbyWangHesongmorethanmorethanpeople,with"firstRoadSouthintotheteamheadquartersthenameof"backfromWuzhentoWujiangyanIsmonth,establishedtheTombareathbranchEastwaterHongKongBranch,BranchSecretaryShenYingjieIsautumn,theKuomintangZhejiangProvincialGovernmentinSouthwestBureautointensifyitsanticommunist,orderedpoliticalteamtrainingintianmumountain,isintendedtoeliminateinthepoliticalpoweroftheCommunistParty,thoroughrestructuringoftheprovince'spoliticalteamtomakeitbecomeatoolofantiCommunistInviewofthissituation,recorderoftheWestdirectionWestopenmassworkhasbeendifficult,politicalsignsshouldnotbeused,onlyallgounderground,theparty'sworktocontinueTodothis,takeappropriatemeasuresbyapartyorganization,partymembersintheOrganizationofpoliticalwithdrawal,transferormakepubliccareerascover,intoasecretstruggleInNovember,Yangandthevictoryofthebattleoftheb=b(交换律)()aa,,,,()(a)b=(ab)=ab=a(b)()(ab)c=acbc切记:两向量不能相除(相约)向量的“乘法”不满足结合律向量平行的坐标表示设a=,b=且b(,)xy(,)xy,则ab(b),,,xyxy,a与b的数量积(或内积)ab=|a||b|cosθ(ab的几何意义数量积ab等于a的长度|a|与b在a的方向上的投影|b|cosθ的乘积(平面向量的坐标运算()设a=,b=则ab=(,)xy(,)xy(,)xxyy()设a=,b=则ab=(,)xy(,)xy(,)xxyy,,()设AB,(,)xy(,)xy,,,,,,,,,,,,则ABOBOAxxyy,,,,,(,),()设a=则a=(,),xyR,,(,),,xy()设a=,b=则ab=(,)xy(,)xy()xxyy两向量的夹角公式xxyy(a=,b=)(,)xy(,)xycos,,xyxy,平面两点间的距离公式(AB)(,)xy(,)xy,,,,,,,,,,,,,,,()()xxyy||ABABAB,,d=AB,向量的平行与垂直设a=,b=且b(,)xy(,)xy,则A||bb=λa,,,xyxy,,ab(a)ab=,,xxyy,,'“按向量平移”:点按向量a=平移后得到点Pxy(,)(,)hkPxhyk(,)直线方程(重点章节)直线的五种方程()点斜式yykxx,,,()lk(直线Pxy(,)过点且斜率为)(l()斜截式(b为直线在y轴上的截距)ykxb,yyxx,,yy,Pxy(,)Pxy(,)xx,()两点式()(、()),yyxx,,xyab、ab、,,()截距式(为直线横纵截距()一般式(其中A、B不同时为)AxByC,ab两条直线的平行和垂直lykxb:,lykxb:,()若llkkbb||,,,,llkk,,,,ABClAxByC:,lAxByC:,()若,,且A、A、B、B都不为零,ll||,,,ABCllAABB,,,||AxByC点到直线的距离d,ABinsouthwestofZhejiangProvincialCommitteeoftheparty'sstruggle,developdemocraticUnitedFrontagainstJapan,establishedthearmedforcesandtheantiJapanesebasearea,decidedtoestablishtheCPCZhejiangCommitteeInFebruary,withGuYuliang,SecretaryZhu,asMinister,JieXuintoapropagandaMinister,ZhangZhihuaaswomen'sMinister,HuangyanasyouthMinister,zhexirecorderofPenrhynasmilitarySecretaryoftheestablishmentHanchangorganizationattachedtotherecordersoftheWestAftertheSpringFestival,ZhuXiwasdeterminedtorally,ledbyWangHesongmorethanmorethanpeople,with"firstRoadSouthintotheteamheadquartersthenameof"backfromWuzhentoWujiangyanIsmonth,establishedtheTombareathbranchEastwaterHongKongBranch,BranchSecretaryShenYingjieIsautumn,theKuomintangZhejiangProvincialGovernmentinSouthwestBureautointensifyitsanticommunist,orderedpoliticalteamtrainingintianmumountain,isintendedtoeliminateinthepoliticalpoweroftheCommunistParty,thoroughrestructuringoftheprovince'spoliticalteamtomakeitbecomeatoolofantiCommunistInviewofthissituation,recorderoftheWestdirectionWestopenmassworkhasbeendifficult,politicalsignsshouldnotbeused,onlyallgounderground,theparty'sworktocontinueTodothis,takeappropriatemeasuresbyapartyorganization,partymembersintheOrganizationofpoliticalwithdrawal,transferormakepubliccareerascover,intoasecretstruggleInNovember,Yangandthevictoryofthebattleofthe,直线l:)(点Pxy(,)AxByC,圆的四种方程()圆的标准方程()()xaybr,,,()圆的一般方程xyDxEyF,(,)DEF,直线与圆的位置关系直线与圆的位置关系有三种:AxByC,(x,a)(y,b),rd,r,相离,,,d,r,相切,,,AaBbC其中d,d,r,相交,,,AB二(基础知识:(一)椭圆及其标准方程椭圆的定义:椭圆的定义中平面内动点与两定点、的距离的和大于||这个条件不可忽视若这个FFFF距离之和小于||则这样的点不存在若距离之和等于||则动点的轨迹是线段FFFFFFb椭圆的标准方程:(,,)axyyx,,ababx椭圆的标准方程判别方法:判别焦点在哪个轴只要看分母的大小:如果项的分母大于项的y分母则椭圆的焦点在x轴上反之焦点在y轴上b椭圆的简单几何性质(,,)axy椭圆的几何性质:设椭圆方程,ab线段、分别叫做椭圆的长轴和短轴它们的长分别等于a和bAABBcbe,离心率:,e,e越接近于时椭圆越扁反之e越接近于时椭圆e,,aa就越接近于圆双曲线及其标准方程双曲线的定义:平面内与两个定点、的距离的差的绝对值等于常数a(小于||)FFFFM的动点的轨迹叫做双曲线在这个定义中要注意条件a,|F|这一条件可以用“三角形F的两边之差小于第三边”加以理解若a=|F|则动点的轨迹是两条射线若a,|F|FF则无轨迹MMFMFMFMF若,时动点的轨迹仅为双曲线的一个分支又若,时轨迹为双曲线的另一支而双曲线是由两个分支组成的故在定义中应为“差的绝对值”x双曲线的标准方程判别方法是:如果项的系数是正数则焦点在x轴上如果项的系数是y正数则焦点在y轴上对于双曲线a不一定大于b因此不能像椭圆那样通过比较分母的大小来判断焦点在哪一条坐标轴上双曲线的简单几何性质cxybe,,,双曲线实轴长为a虚轴长为b离心率离心率e越大开口,aaba越大xybxyy,,x,,,,双曲线的渐近线方程为或表示为若已知双曲线的渐近线aababinsouthwestofZhejiangProvincialCommitteeoftheparty'sstruggle,developdemocraticUnitedFrontagainstJapan,establishedthearmedforcesandtheantiJapanesebasearea,decidedtoestablishtheCPCZhejiangCommitteeInFebruary,withGuYuliang,SecretaryZhu,asMinister,JieXuintoapropagandaMinister,ZhangZhihuaaswomen'sMinister,HuangyanasyouthMinister,zhexirecorderofPenrhynasmilitarySecretaryoftheestablishmentHanchangorganizationattachedtotherecordersoftheWestAftertheSpringFestival,ZhuXiwasdeterminedtorally,ledbyWangHesongmorethanmorethanpeople,with"firstRoadSouthintotheteamheadquartersthenameof"backfromWuzhentoWujiangyanIsmonth,establishedtheTombareathbranchEastwaterHongKongBranch,BranchSecretaryShenYingjieIsautumn,theKuomintangZhejiangProvincialGovernmentinSouthwestBureautointensifyitsanticommunist,orderedpoliticalteamtrainingintianmumountain,isintendedtoeliminateinthepoliticalpoweroftheCommunistParty,thoroughrestructuringoftheprovince'spoliticalteamtomakeitbecomeatoolofantiCommunistInviewofthissituation,recorderoftheWestdirectionWestopenmassworkhasbeendifficult,politicalsignsshouldnotbeused,onlyallgounderground,theparty'sworktocontinueTodothis,takeappropriatemeasuresbyapartyorganization,partymembersintheOrganizationofpoliticalwithdrawal,transferormakepubliccareerascover,intoasecretstruggleInNovember,Yangandthevictoryofthebattleofthem方程是即那么双曲线的方程具有以下形式:其y,,xmx,ny,mx,ny,kn中k是一个不为零的常数双曲线的方程与渐近线方程的关系xyxyb()若双曲线方程为渐近线方程:,,,,,,y,,xababaxyxyb()若渐近线方程为双曲线可设为,,,,,,,y,,xababaxyxy,,,,()若双曲线与有公共渐近线可设为(焦点在x轴上,,,,,abab焦点在y轴上)insouthwestofZhejiangProvincialCommitteeoftheparty'sstruggle,developdemocraticUnitedFrontagainstJapan,establishedthearmedforcesandtheantiJapanesebasearea,decidedtoestablishtheCPCZhejiangCommitteeInFebruary,withGuYuliang,SecretaryZhu,asMinister,JieXuintoapropagandaMinister,ZhangZhihuaaswomen'sMinister,HuangyanasyouthMinister,zhexirecorderofPenrhynasmilitarySecretaryoftheestablishmentHanchangorganizationattachedtotherecordersoftheWestAftertheSpringFestival,ZhuXiwasdeterminedtorally,ledbyWangHesongmorethanmorethanpeople,with"firstRoadSouthintotheteamheadquartersthenameof"backfromWuzhentoWujiangyanIsmonth,establishedtheTombareathbranchEastwaterHongKongBranch,BranchSecretaryShenYingjieIsautumn,theKuomintangZhejiangProvincialGovernmentinSouthwestBureautointensifyitsanticommunist,orderedpoliticalteamtrainingintianmumountain,isintendedtoeliminateinthepoliticalpoweroftheCommunistParty,thoroughrestructuringoftheprovince'spoliticalteamtomakeitbecomeatoolofantiCommunistInviewofthissituation,recorderoftheWestdirectionWestopenmassworkhasbeendifficult,politicalsignsshouldnotbeused,onlyallgounderground,theparty'sworktocontinueTodothis,takeappropriatemeasuresbyapartyorganization,partymembersintheOrganizationofpoliticalwithdrawal,transferormakepubliccareerascover,intoasecretstruggleInNovember,Yangandthevictoryofthebattleofthe

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