3. 第三章课后习题及答案

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第三章连接课后习题参考答案

第三章连接课后习题参考答案

第三章连接课后习题参考答案第三章连接课后习题参考答案焊接连接参考答案一、概念题3.1 从功能上分类,连接有哪几种基本类型?3.2 焊缝有两种基本类型—对接坡口焊缝和贴角焊缝,二者在施工、受力、适用范围上各有哪些特点?3.3 对接接头连接需使用对接焊缝,角接接头连接需采用角焊缝,这么说对吗?3.4 h和lw相同时,吊车梁上的焊缝采用正f面角焊缝比采用侧面角焊缝承载力高?3.5 为何对角焊缝焊脚尺寸有最大和最小取值的限制?对侧面角焊缝的长度有何要求?为什么?【答】(1)最小焊脚尺寸:角焊缝的焊脚尺寸不能过小,否则焊接时产生的热量较小,致使施焊时冷却速度过快,导致母材开裂。

《规范》规定:h f≥1.5t,式中:t2——较厚焊件厚度,单2位为mm。

计算时,焊脚尺寸取整数。

自动焊熔深较大,所取最小焊脚尺寸可减小1mm;T形连接的单面角焊缝,应增加1mm;当焊件厚度小于或等于4mm时,则取与焊件厚度相同。

(2)最大焊脚尺寸:为了避免焊缝区的主体金属“过热”,减小焊件的焊接残余应力和残余变形,角焊缝的焊脚尺寸应满足12.1t h f式中: t 1——较薄焊件的厚度,单位为mm 。

(3)侧面角焊缝的最大计算长度侧面角焊缝在弹性阶段沿长度方向受力不均匀,两端大而中间小,可能首先在焊缝的两端破坏,故规定侧面角焊缝的计算长度l w ≤60h f 。

若内力沿侧面角焊缝全长分布,例如焊接梁翼缘与腹板的连接焊缝,可不受上述限制。

3.6 简述焊接残余应力产生的实质,其最大分布特点是什么? 3.7 画出焊接H 形截面和焊接箱形截面的焊接残余应力分布图。

3.8 贴角焊缝中,何为端焊缝?何为侧焊缝?二者破坏截面上的应力性质有何区别?3.9 规范规定:侧焊缝的计算长度不得大于焊脚尺寸的某个倍数,原因何在?规范同时有焊缝最小尺寸的规定,原因何在? 3.10 规范禁止3条相互垂直的焊缝相交,为什么。

3.11 举3~5例说明焊接设计中减小应力集中的构造措施。

高等数学第三章课后习题答案

高等数学第三章课后习题答案

第三章 中值定理与导数的应用1. 验证拉格朗日中值定理对函数x x f ln )(=在区间[]e ,1上的正确性。

解:函数()ln f x x =在区间[1,]e 上连续,在区间(1,)e 内可导,故()f x 在[1,]e 上满足拉格朗日中值定理的条件。

又xx f 1)(=',解方程,111,1)1()()(-=--='e e f e f f ξξ即得),1(1e e ∈-=ξ。

因此,拉格朗日中值定理对函数()ln f x x =在区间[1,]e 上是正确的。

2.不求函数)4)(3)(2)(1()(----=x x x x x f 的导数,说明方程0)('=x f 有几个实根,并指出它们所在的区间。

解:函数上连续,分别在区间[3,4][2,3],2],,1[)(x f 上在区间(3,4)(2,3),2),,1(可导,且(1)(2)(3)(4)0f f f f ====。

由罗尔定理知,至少存在),2,1(1∈ξ),3,2(2∈ξ),4,3(3∈ξ使),3,2,1( 0)(=='i f i ξ即方程'()0f x =有至少三个实根。

又因方程'()0f x =为三次方程,故它至多有三个实根。

因此,方程'()0f x =有且只有三个实根,分别位于区间(1,2),(2,3),(3,4)内。

3.若方程 01110=+++--x a x a x a n n n 有一个正根,0x 证明:方程0)1(12110=++-+---n n n a x n a nxa 必有一个小于0x 的正根。

解:取函数()1011nn n f x a x a xa x --=+++。

0()[0,]f x x 在上连续,在0(0,)x 内可导,且0(0)()0,f f x ==由罗尔定理知至少存在一点()00,x ξ∈使'()0,f ξ=即方程12011(1)0n n n a nx a n x a ---+-++=必有一个小于0x 的正根。

信号与系统课后习题与解答第三章

信号与系统课后习题与解答第三章

3-1 求图3-1所示对称周期矩形信号的傅利叶级数(三角形式和指数形式)。

图3-1解 由图3-1可知,)(t f 为奇函数,因而00==a a n2112011201)cos(2)sin(242,)sin()(4T T T n t n T n Edt t n E T T dt t n t f T b ωωωπωω-====⎰⎰所以,三角形式的傅利叶级数(FS )为T t t t E t f πωωωωπ2,)5sin(51)3sin(31)sin(2)(1111=⎥⎦⎤⎢⎣⎡+++=指数形式的傅利叶级数(FS )的系数为⎪⎩⎪⎨⎧±±=-±±==-= ,3,1,0,,4,2,0,021n n jE n jb F n n π所以,指数形式的傅利叶级数为Te jE e jE e jEe jEt f t j t j t j t j πωππππωωωω2,33)(11111=++-+-=--3-2 周期矩形信号如图3-2所示。

若:图3-22τT-2τ-重复频率kHz f 5= 脉宽 s μτ20= 幅度 V E 10=求直流分量大小以及基波、二次和三次谐波的有效值。

解 对于图3-2所示的周期矩形信号,其指数形式的傅利叶级数(FS )的系数⎪⎭⎫⎝⎛=⎪⎭⎫ ⎝⎛====⎰⎰--22sin 12,)(1112212211τωττωππωττωωn Sa T E n n E dt Ee T T dt e t f T F tjn TT t jn n则的指数形式的傅利叶级数(FS )为∑∑∞-∞=∞-∞=⎪⎭⎫⎝⎛==n tjn n tjn ne n Sa TE eF t f 112)(1ωωτωτ其直流分量为T E n Sa T E F n ττωτ=⎪⎭⎫ ⎝⎛=→2lim100 基波分量的幅度为⎪⎭⎫ ⎝⎛⋅=+-2sin 2111τωπEF F 二次谐波分量的幅度为⎪⎭⎫ ⎝⎛⋅=+-22sin 122τωπEF F 三次谐波分量的幅度为⎪⎭⎫ ⎝⎛⋅=+-23sin 32133τωπE F F 由所给参数kHz f 5=可得s T s rad 441102,/10-⨯==πω 将各参数的值代入,可得直流分量大小为V 110210201046=⨯⨯⨯--基波的有效值为())(39.118sin 210101010sin 210264V ≈=⨯⨯⨯- πππ二次谐波分量的有效值为())(32.136sin 251010102sin 21064V ≈=⨯⨯⨯- πππ三次谐波分量的有效值为())(21.1524sin 32101010103sin 2310264V ≈=⨯⨯⨯⨯- πππ3-3 若周期矩形信号)(1t f 和)(2t f 的波形如图3-2所示,)(1t f 的参数为s μτ5.0=,s T μ1= ,V E 1=; )(2t f 的参数为s μτ5.1=,s T μ3= ,V E 3=,分别求:(1))(1t f 的谱线间隔和带宽(第一零点位置),频率单位以kHz 表示; (2))(2t f 的谱线间隔和带宽; (3))(1t f 与)(2t f 的基波幅度之比; (4))(1t f 基波与)(2t f 三次谐波幅度之比。

教育学课后习题及答案

教育学课后习题及答案

1.涂尔干说:“教育史成年一代对社会生活尚未成熟的年轻一代所实施的影响。

其目的在于,使儿童的身体、智力和道德状况都得到激励与发展,以适应整个政治社会在总体上对儿童的要求,并适应儿童将来所处的特定环境的要求。

”这种论断正确地指出了(A.教育具有社会性)。

2.联合国教科文组织在《学会生存》中主张,建设学习化社会的关键在于(C.实施终身教育)。

3.人的发展总是受到社会的制约,这意味着(B.教育要充分考虑社会发展的需要)。

4.人力资本理论认为,人力资本是经济增长的关键,教育是形成人力资本的重要力量。

这一理论的主要缺陷是(C.忽视了劳动力市场中的其他筛选标准)。

二、辨析题教育能推进一个社会的民主化进程。

正确。

教育推进着政治民主化,政治民主化是现代社会政治发展的必然趋势。

一个国家的政治是否民主,与人民的文化素质、教育水平密切相关。

一个国家的教育普及程度越高,公民素质也就越高,就越能具有公民意识,认识民主的价值,推崇民主的措施,同时在政治生活和社会生活中积极履行民主的权利,承担相应的义务。

因此,国民教育的发展和国民素质的不断提高,是推进政治民主化的重要前提和保证。

三、简答题简述教育的个体个性化功能。

1.教育促进人的主体意识和主体能力的发展,培养个体的主体性;2.教育促进人的个体特征的发展,形成个体的独特性;3.教育促进人的个体价值的实现,开发个体的创造性。

四、分析论述题“每逢新学期开始,山西省朔州市平鲁区凤凰镇寄宿制小学的学生……”试结合教育与社会发展的一般原理,对此加以深入分析。

1.教育的经济功能教育能促进经济的发展。

教育经济学的研究表明:当代经济发展已由依靠物质、资金的物力增长模式转变为依靠人力和知识资本增长的模式;人力资本是经济增长的关键,而教育是形成人力资本的重要因素。

教育通过提高国民的人力资本,促进国民收入和经济的增长。

随着社会的发展,教育在经济增长中的作用越来越显著。

现代教育正是通过人的素质的提高和专门劳动力的培养,对经济的发展起着决定性的作用。

大学物理第三章-部分课后习题答案

大学物理第三章-部分课后习题答案

大学物理第三章 课后习题答案3-1 半径为R 、质量为M 的均匀薄圆盘上,挖去一个直径为R 的圆孔,孔的中心在12R 处,求所剩部分对通过原圆盘中心且与板面垂直的轴的转动惯量。

分析:用补偿法〔负质量法〕求解,由平行轴定理求其挖去部分的转动惯量,用原圆盘转动惯量减去挖去部分的转动惯量即得。

注意对同一轴而言。

解:没挖去前大圆对通过原圆盘中心且与板面垂直的轴的转动惯量为:2112J MR =① 由平行轴定理得被挖去部分对通过原圆盘中心且与板面垂直的轴的转动惯量为:2222213()()2424232c M R M R J J md MR =+=⨯⨯+⨯= ②由①②式得所剩部分对通过原圆盘中心且与板面垂直的轴的转动惯量为:2121332J J J MR =-=3-2 如题图3-2所示,一根均匀细铁丝,质量为M ,长度为L ,在其中点O 处弯成120θ=︒角,放在xOy 平面内,求铁丝对Ox 轴、Oy 轴、Oz 轴的转动惯量。

分析:取微元,由转动惯量的定义求积分可得 解:〔1〕对x 轴的转动惯量为:2022201(sin 60)32Lx M J r dm l dl ML L ===⎰⎰ 〔2〕对y 轴的转动惯量为:20222015()(sin 30)32296Ly M L M J l dl ML L =⨯⨯+=⎰〔3〕对Z 轴的转动惯量为:22112()32212z M L J ML =⨯⨯⨯=3-3 电风扇开启电源后经过5s 到达额定转速,此时角速度为每秒5转,关闭电源后经过16s 风扇停止转动,已知风扇转动惯量为20.5kg m ⋅,且摩擦力矩f M 和电磁力矩M 均为常量,求电机的电磁力矩M 。

分析:f M ,M 为常量,开启电源5s 内是匀加速转动,关闭电源16s 内是匀减速转动,可得相应加速度,由转动定律求得电磁力矩M 。

解:由定轴转动定律得:1f M M J β-=,即11252520.50.5 4.12516f M J M J J N m ππβββ⨯⨯=+=+=⨯+⨯=⋅ 3-4 飞轮的质量为60kg ,直径为0.5m ,转速为1000/min r ,现要求在5s 内使其制动,求制动力F ,假定闸瓦与飞轮之间的摩擦系数0.4μ=,飞轮的质量全部分布在轮的外周上,尺寸如题图3-4所示。

高等数学李伟版课后习题答案第三章

高等数学李伟版课后习题答案第三章

⾼等数学李伟版课后习题答案第三章习题3—1(A )1.判断下列叙述是否正确,并说明理由:(1)函数的极值与最值是不同的,最值⼀定是极值,但极值未必是最值;(2)函数的图形在极值点处⼀定存在着⽔平的切线;(3)连续函数的零点定理与罗尔定理都可以⽤来判断函数是否存在零点,⼆者没有差别;(4)虽然拉格朗⽇中值公式是⼀个等式,但将()f ξ'进⾏放⼤或缩⼩就可以⽤拉格朗⽇中值公式证明不等式,不过这类不等式中⼀定要含(或隐含)有某函数的两个值的差.答:(1)不正确.最值可以在区间端点取得,但是由于在区间端点处不定义极值,因此最值不⼀定是极值;⽽极值未必是最值这是显然的.(2)不正确.例如32x y =在0=x 点处取极值,但是曲线在点)00(,却没有⽔平切线.(3)不正确.前者是判断)(x f 是否有零点的,后者是判断)(x f '是否有零点的.(4)正确.⼀类是明显含有)()(a f b f -的;另⼀类是暗含着)()(0x f x f -的. 2.验证函数2)1(e x y -=在区间]20[,上满⾜罗尔定理,并求出定理中的ξ.解:显然2)1(e x y -=在闭区间]20[,上连续,在开区间)20(,内可导,且e )2()0(==y y ,于是函数2)1(ex y -=在区间]20[,上满⾜罗尔定理的条件,2)1(e )1(2)(x x x y ---=',由0)(='ξy ,有0e )1(22)1(=---ξξ,得1=ξ,∈ξ)20(,,所以定理的结论也成⽴.3.验证函数1232-+=x x y 在区间]11[,-上满⾜拉格朗⽇中值定理,并求出公式中的ξ.解:显然1232-+=x x y 在闭区间]11[,-连续,在开区间)11(,-内可导,于是函数1232-+=x x y 在区间]11[,-上满⾜拉格朗⽇中值定理的条件,26)(+='x x y ,2)1(1)1()1(=----y y ,由)()1(1)1()1(ξy y y '=----,有226=+ξ,得0=ξ,∈ξ)11(,-,所以定理的结论也成⽴.4.对函数x x x f cos )(+=、x x g cos )(=在区间]20[π,上验证柯西中值定理的正确性,并求出定理中的ξ.解:显然函数x x x f cos )(+=、x x g cos )(=在闭区间]20[π,上连续,在开区间)20(π,内可导,且x x f sin 1)(-=',x x g sin )(-=',在区间)20(π,内0)(≠'x g ,于是函数x x x f cos )(+=、x x g cos )(=在区间]20[π,上满⾜柯西定理的条件,⼜21)0()2/()0()2/(πππ-=--g g f f ,由)()()0()2/()0()2/(ξξππg f g g f f ''=--,有ξξπsin sin 121--=-,即πξ2sin =,由于∈ξ)20(π,,得πξ2arcsin=,所以定理的结论也成⽴.5.在)(∞+-∞,内证明x x cot arc arctan +恒为常数,并验证2cot arc arctan π≡+x x .证明:设x x x f cot arc arctan )(+=,显然)(x f 在)(∞+-∞,内可导,且-+='211)(x x f 0112≡+x,由拉格朗⽇定理的推论,得在)(∞+-∞,内x x cot arc arctan +恒为常数,设C x f ≡)(,⽤0=x 代⼊,得2π=C ,所以2cot arc arctan π≡+x x .6.不求出函数2()(4)f x x x =-的导数,说明0)(='x f 有⼏个实根,并指出所在区间.解:显然2()(4)f x x x =-有三个零点20±==x x ,,⽤这三点作两个区间]20[]02[,、,-,在闭区间]02[,-上)(x f 连续,在开区间)02(,-内)(x f 可导,⼜0)0()2(==-f f 于是)(x f 在]02[,-满⾜罗尔定理,所以⾄少有∈1ξ)02(,-,使得0)(1='ξf ,同理⾄少有∈2ξ)20(,,使得0)(2='ξf ,所以0)(='x f ⾄少有两个实根.⼜因为)(x f 是三次多项式,有)(x f '时⼆次多项式,于是0)(='x f 是⼆次代数⽅程,由代数基本定理,得0)(='x f ⾄多有两个实根.综上,0)(='x f 恰有两个实根,且分别位于区间)02(,-与)20(,内.7.证明下列不等式:(1)对任何实数b a ,,证明cos cos a b a b -≤-;(2)当0>x 时,x x xx<+<+)1ln(1.证明:(1)当b a =时,cos cos a b a b -≤-显然成⽴.当b a <时,取函数x x f cos )(=,显然)(x f 在闭区间][b a ,上连续,在开间)(b a ,内可导,由拉格朗⽇定理,有∈ξ)(b a ,,使得))(()()(b a f b f a f -'=-ξ,即)(sin cos cos b a b a -?-=-ξ,所以)()(sin cos cos b a b a b a -≤-?-=-ξ.当b a >时,只要将上⾯的区间][b a ,换为][a b ,,不等式依然成⽴.所以,对任何实数b a ,,都有cos cos a b a b -≤-.(2)取函数)1ln()(t t f +=,当0>x 时,函数)1ln()(t t f +=在闭区间]0[x ,上连续,在开区间)0(x ,内可导,根据拉格朗⽇定理,有∈ξ)0(x ,,使得ξξ+='1)(xf .因为x <<ξ0,则x xx x x =+<+<+0111ξ,所以x x x x <+<+)1ln(1. 8.若函数)(x f 在区间),(b a 具有⼆阶导数,且)()()(321x f x f x f ==,其中21x x a <<b x <<3,证明在区间)(3,1x x 内⾄少有⼀点ξ,使得0)(=''ξf .证明:根据已知,函数)(x f 在区间][21x x ,及][32x x ,上满⾜罗尔定理,于是有∈1ξ)(21x x ,,∈2ξ)(32x x ,(其中21ξξ<),所得0)(1='ξf ,0)(2='ξf .再根据已知及)()(21ξξf f '=',函数)(x f '在区间][21ξξ,上满⾜罗尔定理,所以有∈ξ)(21ξξ,?)(3,1x x ,所得0)(=''ξf ,即在区间)(3,1x x 内⾄少有⼀点ξ,使得0)(=''ξf .习题3—1(B )1.在2004年北京国际马拉松⽐赛中,我国运动员以2⼩时19分26秒的成绩夺得了⼥⼦组冠军.试⽤微分中值定理说明她在⽐赛中⾄少有两个时刻的速度恰好为18. 157km/h (马拉松⽐赛距离全长为42.195km ).解:设该运动员在时刻t 时跑了)(t s s =(km ),此刻才速度为)()(t s t v v '==(km/h ),为解决问题的需要,假定)(t s 有连续导数.设起跑时0=t ,到达终点时0t t =,则3238888889.20≈t ,对函数)(t s 在区间]0[0t ,上⽤拉格朗⽇定理,有00t <<ξ,所得)()(0)0()(00ξξv s t s t s ='=--,⽽15706.183238888889.2195.420)0()(00≈=--t s t s km/h ,所以157.1815706.18)(>≈ξv .对)(t v 在区间]0[ξ,及][0t ,ξ上分别使⽤连续函数的介值定理(注意,0)0(=v0)(0=t v ,则数值18. 157分别介于两个区间端点处函数值之间),于是有)0(1ξξ,∈,)0(2,ξξ∈,使得157.18)(1=ξv ,157.18)(2=ξv,这表明该运动员在⽐赛中⾄少有两个时刻的速度恰好为18. 157km/h .2.若函数)(x f 在闭区间][b a ,上连续,在开区间),(b a 内可导,且0)(>'x f ,证明⽅程0)(=x f 在开区间),(b a 内⾄多有⼀个实根.证明:采⽤反证法,若⽅程0)(=x f 在开区间),(b a 有两个(或两个以上)不同的实根21x x <,即0)()(21==x f x f ,根据已知函数)(x f 在][21x x ,上满⾜罗尔定理,于是有∈ξ)()(21b a x x ,,?,使得0)(='ξf ,与在开区间),(b a 内0)(>'x f ⽭盾,所以⽅程0)(=x f 在开区间),(b a 内⾄多有⼀个实根.(注:本题结论也适⽤于⽆穷区间) 3.证明⽅程015=-+x x 只有⼀个正根.证明:设1)(4-+=x x x f ()(∞+-∞∈,x ),则014)(4>+='x x f ,根据上题结果,⽅程015=-+x x 在)(∞+-∞,内⾄多有⼀个实根.取闭区间]10[,,函数1)(4-+=x x x f 在]10[,上连续,且01)0(<-=f ,01)1(>=f ,由零点定理,有)10(,∈ξ,使得0)(=ξf ,从⽽⽅程015=-+x x 在)0(∞+,内⾄少有⼀个实根.综上,⽅程015=-+x x 只有⼀个正根,且位于区间)10(,内. 4.若在),(+∞-∞内恒有k x f =')(,证明b kx x f +=)(.证明:(⽅法1)设函数kx x f x F -=)()(,则0)()(≡-'='k x f x F ,根据拉格朗⽇定理的推论)(x F 恒为常数,设C kx x f x F ≡-=)()(,⽤0=x 代⼊,得)0(f C =,记b f =)0(,则b C kx x f x F ==-=)()(,所以b kx x f +=)(.(⽅法2)记b f =)0(,∈?x ),(+∞-∞,若0=x ,则满⾜b kx x f +=)(;若0≠x ,对函数)(t f 以x t t ==,0为端点的闭区间上⽤拉格朗⽇定理,则有ξ介于0与x 之间,使得)0)(()0()(-'=-x f f x f ξ,即kx b x f =-)(,所以b kx x f +=)(.5.若函数)(x f 在区间)0(∞+,可导,且满⾜0)()(2≡-'x f x f x ,1)1(=f ,证明x x f =)(.证明:设函数xx f x F )()(=(∈x )0(∞+,),则xx x f x f x x x x f x x f x F 2)()(22/)()()(-'=-'=',由0)()(2≡-'x f x f x ,得0)(≡'x F ,根据拉格朗⽇定理的推论)(x F 恒为常数,设C xx f x F ==)()(,⽤1=x 代⼊,且由1)1(=f ,得1=C ,所以1)()(==xx f x F ,即x x f =)(.6.证明下列不等式(1)当0>x 时,证明x x+>1e ;(2)对任何实数x ,证明x x arctan ≥.证明:(1)取函数t t f e )(=(]0[x t ,∈)显然函数)(t f 在区间]0[x ,上满⾜拉格朗⽇定理,则有∈ξ)0(x ,,使得)0)(()0()(-'=-x f f x f ξ,即x xξe 1e =-,所以 x x x+>+=1e 1e ξ.(2)当0=x 时,显然x x arctan ≥.当0≠x 时,取函数t t f arctan )(=,对)(t f 在以x t t ==,0为端点的闭区间上⽤拉格朗⽇定理,则有ξ介于0与x 之间,使得)0)(()0()(-'=-x f f x f ξ,即21arct an ξ+=xx ,所以x x x <+=21arctan ξ.综上,对任何实数x ,都有x x arctan ≥.7.若函数)(x f 在闭区间[1-,1]上连续,在开区间(1-,1)内可导,M f =)0((其中0>M ),且M x f <')(.在闭区间[1-,1]上证明M x f 2)(<.证明:对∈?x [1-,1],当0=x 时,M M f 2)0(<=,.不等式成⽴.当0≠x 时,根据已知,函数)(t f 在以x t t ==,0为端点的区间上满⾜拉格朗⽇定理,则有ξ介于0与x 之间,使得)0)(()0()(-'=-x f fx f ξ,即x f M x f )()(ξ'=-,所以,M x f x f +'=)()(ξ,从⽽M M f M x f M x f x f 2)()()()(<+'≤+'≤+'=ξξξ.综上,在闭区间[1-,1]上恒有M x f 2)(<.8.若函数)(x f 在闭区间]0[a ,上连续,在开区间)0(a ,内可导,且0)(=a f ,证明在开区间)0(a ,内⾄少存在⼀点ξ,使得0)()(='+ξξξf f .证明:设函数)()(x xf x F =(∈x ]0[a ,),则0)(0)0(==a F F ,,再根据已知,函数)(x F 在区间],0[a 满⾜罗尔定理,则有∈ξ)0(a ,,使得0)(='ξf .⽽)()()(ξξξξf f f '+=',于是0)()(='+ξξξf f .所以,在开区间)0(a ,内⾄少存在⼀点ξ,使得0)()(='+ξξξf f .习题3—2(A )1.判断下列叙述是否正确?并说明理由(1)洛必达法则是利⽤函数的柯西中值定理得到的,因此不能利⽤洛必达法则直接求数列极限;(2)凡属“00”,“∞∞”型不定式,都可以⽤洛必达法则来求其的极限值;(3)型如””,“”,“”,“”,““0100∞∞-∞∞?∞型的不定式,要想⽤洛必达法则,需先通过变形.⽐如“0?∞”型要变型成为“00”,“∞∞”型,”,”,““00∞-∞””,““01∞∞型要先通过变型,转化为“0?∞”型的不定式,然后再化为基本类型.答:(1)正确.因为数列是离散型变量,对它是不能求导的,要想对数列的“不定式”极限使⽤洛必达法则,⾸先要根据“海涅定理”将数列极限转换为普通函数极限,然后再使⽤洛必达法则.(2)不正确.如0sin 1sinlim 20=→xx x x (00型)、1cos sin lim -=-+∞→x x x x x (∞∞型)、11lim 2=++∞→x x x (∞∞型)都不能⽤洛⽐达法则求得极限值.(3)正确.可参见本节3.其他类型的不定式极限的求法,但是“∞-∞”型通常是直接化为“00”,“∞∞”型. 2.⽤洛必达法则求下列极限:(1)x x x --→e 1ln lim e ;(2)11lim 1--→n m x x x (0≠mn );(3)x x x 5tan 3sin limπ→;(4)2e e cos 1lim 0-+--→x x x x;(5)1sec tan 2lim0-→x x x x ;(6)xxx 3tan tan lim 2/π→;(7)x x x 2cot lim 0→;(8)x x x cot arc lim +∞→;(9))sin 11(lim 0x x x -→;(10)111lim()ln 1x x x →--;(11)xx x tan 0lim +→;(12))1ln(1)(lim x x x ++∞→;(13)21)(cos lim x x x →;(14)nn n ln lim∞→;解:(1)e11/1lim e 1ln lime e -=-=--→→x x x x x .(2)==----→→1111lim 11lim n m x nm x nx mx x x nm.(3)=-?-==→→22)1(535sec 53cos 3lim 5tan 3sin limx x x x x x ππ53-.(4)=+=-=-+--→-→-→x x x x x x x x x x x x e e cos lim e e sin lim 2e e cos 1lim00021.(5)===-=-→→→→xxx x x x x x x x x x x x tan 4lim tan sec 4lim 1sec 2lim 1sec tan 2lim002004. (6) =---=-=?=→→→→x xx x xx x x x x x x x x sin 3sin 3lim cos 3cos lim )cos 3cos 3sin sin (lim 3tan tan lim2/2/2/2/ππππ3.(7)===→→→x x x x x x x x 2sec 21lim 2tan lim 2cot lim 200021.(8)=+=-+-==+∞→+∞→+∞→+∞→22221lim /1)1/(1lim 1/cot arc lim cot arc lim xx x x x x x x x x x x 1.(9)=-=-=-=-=-→→→→→2sin lim 21cos lim sin lim sin sin lim )sin 11( lim 002000xx x x x x x x x x x x x x x x x 0.(10)xx x x x x x x x x x x x /)1(ln /11lim ln )1(ln 1lim )11ln 1(lim 111-+-=---=--→→→=+=-+-=→→2ln 1lim 1ln 1lim11x x x x x x x 21.(11)设xxy tan =,则x x y ln tan ln =,因为0lim /1/1lim /1ln lim ln lim ln tan lim ln lim 0200=-=-====++++++→→→→→→x xxx x x x x x y x x x x x x ,所以, ==+→0tan 0e lim xx x 1.(12)设)1ln(1)(x x y +=,则)1ln(ln 21)1ln(ln ln x xx x y +=+=,因为 21)11(lim 21)1/(1/1lim 21)1ln(ln lim 21ln lim =+=+=+= +∞→+∞→+∞→+∞→x x x x x y x x x x ,所以 ==++∞→21)1ln(1e )(lim x x x e .(13)设21)(cos x x y =,则2cos ln ln x xy =,因为 21cos 2sin lim cos ln lim ln lim 0200-=-==→→→x x x x x y x x x ,所以==-→2 110e )(cos lim 2x x x e1.(14)根据海涅定理,====+∞→+∞→+∞→∞→xxx xx nn x x x n 2lim2/1/1limln limln lim0.3.验证极限xx xx x cos 2sin 2lim -+∞→存在,并说明不能⽤洛必达法则求得.解:=-+=-+=-+∞→∞→0102/)cos 2(1/)(sin 2lim cos 2sin 2limx x x x x x x x x x 2.因为极限xxx x x x x x sin 21cos 2lim )cos 2()sin 2(lim++='-'+∞→∞→不存在,因为此极限不能⽤洛必达法则求得.4.验证极限x x x x sin )/1sin(lim 20→存在,并说明不能⽤洛必达法则求得.解:=?=?=→→→011sin lim sin lim sin )/1sin(lim0020xx x x x x x x x x 0.因为极限xx x x x x x x x cos )/1sin()/1sin(2lim)(sin ])/1sin([lim 020-=''→→不存在,因为此极限不能⽤洛必达法则求得.习题3—2(B )1.⽤洛必达法则求下列极限:(1)311lnarctan 2limx x xx x -+-→;(2)xx x x 30sin arcsin lim -→(3))tan 11(lim 220xx x -→;(4)]e )11[(lim -+∞→xx x x ; (5) 260)sin (lim x x xx →;(6)n n nn b a )2(lim +∞→(00>>b a ,).解:(1)原式30)1ln()1ln(arctan 2limx x x x x -++-=→=--=--+-+=→→)1(34lim 3111112lim 40220x x x x x x x 34-.(2)原式2220220301311lim 31/11lim arcsin lim xx x x x x x x x x x ---=--=-=→→→=-=--=→→22022032/lim 311lim xx x x x x 61-.(3)原式30022220tan lim tan lim tan tan lim xxx x x x x x x x x x x -?+=-=→→→ ==-=-=→→→22022030tan lim 3231sec lim 2tan lim 2x x xx x x x x x x 32.(4)令t x 1=,则原式21010)1ln()1()1(lim e )1(lim tt t t t t t t t tt ++-+=-+→→ =+-=-+-=++-=→→→t t t t t t t t t t t )1ln(lim 2e 21)1ln(1lim e )1ln()1(lim e 002 02 e -.(5)令6)sin (x x x y =,则2sin ln 6ln x x xy =,因为 30200sin cos lim 3)sin cos 2sin /6(lim ln lim xxx x x x x x x x x y x x x -=-?=→→→ 13sin lim 320-=-=→x x x x ,所以==-→160e )sin (lim x x xx e 1.(6)令=n x nn nb a )2(+,则]2ln )[ln(ln -+=n n n b a n x ,再令x t 1=,因为 tb a b a x x t t t xx x n n 2ln )ln(lim ]2ln )[ln(lim ln lim 011-+=-+=→+∞→∞→ ab b a ba b b a a t t t t t ln 2ln ln ln ln lim 0=+=++=→,所以==+∞→abnn nn b a ln e )2(lim ab .2.当0→x 时,若)(e )(2c bx ax x f x ++-=是⽐2x ⾼阶的⽆穷⼩,求常数c b a 、、.解:根据已知,有0)(e lim220=++-→x c bx ax x x ,由分母极限为零,则有分⼦极限也为零,于是01)]([e lim 2x =-=++-→c c bx ax x ,得1=c ,此时02)2(e lim )(e lim 0220=+-=++-→→x b ax x c bx ax x x x x ,再由分⼦极限为零,同样得1=b ,进⽽022122e lim 2)12(e lim )(e lim 00220=-=-=+-=++-→→→a a x ax x c bx ax x x x x x x ,得21=a ,所以1121===c b a ,,时,当0→x 时,)(e )(2c bx ax x f x ++-=是⽐2x ⾼阶的⽆穷⼩.3.若函数)(x f 有⼆阶导数,且2)0(,1)0(,0)0(=''='=f f f ,求极限2)(limxxx f x -→.解:1)0(210)0()(lim 2121)(lim )(lim002=''=-'-'=-'=-→→→f x f x f x x f x x x f x x x .(注:根据题⽬所给条件,不能保证)(x f ''连续,所以只能⽤⼀次洛⽐达法则,再⽤⼆阶导数的分析定义)习题3—3(A )1.判断下列叙述是否正确?并说明理由:(1)只要函数在点0x 有n 阶导数,就⼀定能写出该函数的泰勒多项式.⼀个函数的泰勒多项式永远都不会与这个函数恒等,⼆者相差⼀个不恒为零的余项;(2)⼀个函数在某点附近展开带有拉格朗⽇余项的n 阶泰勒公式是它的n 次泰勒多项式加上与该函数的n 阶导数有关的所谓拉格朗⽇型的余项;(3)在应⽤泰勒公式时,⼀般⽤带拉格朗⽇型余项的泰勒公式⽐较⽅便.答:(1)前者正确,其根据是泰勒多项式的定义;后者不正确.当)(x f 本⾝是⼀个n 次多项式时,有0)(≡x R n ,这时函数的泰勒多项式恒等于这个函数.(2)不正确.拉格朗⽇型的余项与函数)(x f 的1+n 阶导数有关.(3)不正确.利⽤泰勒公式求极限时就要⽤带有⽪亚诺余项的泰勒公式,⼀般在对余项进⾏定量分析时使⽤带拉格朗⽇型余项的泰勒公式,在对余项进⾏定性分析时使⽤带⽪亚诺型余项的泰勒公式.2.写出函数x x f arctan )(=的带有佩亚诺型余项的三阶麦克劳林公式.解:因为211)(x x f +=',)1(2)(2x x x f +-='',322)1(62)(x x x f ++-=''',于是 2)0(0)0(1)0(0)0(-='''=''='=f f f f ,,,,代⼊到)(!3)0(!2)0()0()0()(332x o x f x f x f f x f +'''+'+'+=中,得 )(3arctan 33x o x x x +-=. 3.按1-x 的乘幂形式改写多项式1)(234++++=x x x x x f .解:因为1234)(23+++='x x x x f ,2612)(2++=''x x x f ,624)(+='''x x f ,24)()4(=x f ,更⾼阶导数都为零,于是,,,20)1(10)1(5)1(=''='=f f f 30)1(='''f ,24)0()4(=f ,将其带⼊到)()1(!4)1()1(!3)1()1(!2)1()1)(1()1()(44)4(32x R x f x f x f x f f x f +-+-'''+-'+-'+=中,得 432)1()1(5)1(10)1(105)(-+-+-+-+=x x x x x f(其中5)5(4)1(!5)()(-=x f x R ξ恒为零). 4.将函数1)(+=x xx f 在1x =点展开为带有佩亚诺型余项的三阶泰勒公式.解:因为111)(+-=x x f ,则2)1(1)(+='x x f ,3)1(2)(+-=''x x f ,4)1(6)(+='''x x f ,于是83)1(41)0(41)1(21)1(='''-=''='=f f f f ,,,,将其带⼊到 ))1(()1(!3)1()1(!2)1()1)(1()1()(332-+-'''+-'+-'+=x o x f x f x f f x f 中,得))1((16)1(8)1(41211332-+-+---+=+x o x x x x x . 5.写出函数xx x f e )(=的带有拉格朗⽇型余项的n 阶麦克劳林公式.解:因为)(e )()(k x x f x k +=(1321+=n n k ,,,,,)(参见习题2.5(B )3),于是,k fk =)0()((n k ,,,,210=),=+=++1)1()!1()()(n n n x n x f x R θ1)!1(e )1(++++n x x n x n θθ,将其带⼊到)(!)0(!2)0()0()0()()(2x R x n f x f x f f x f n nn +++'+'+= ,得 132)!1(e )1()!1(!2e +++++-++++=n x n xx n x n n x x x x x θθ )10(<<θ.6.将函数xx f 1)(=按(1)x +的乘幂展开为带有拉格朗⽇型余项的n 阶泰勒公式.解:因为1)(!)1()(+-=k k k xk x f,于是!)1()(k f k -=-(13210+=n n k ,,,,,,), 1211211)1()1()1()1()!1()!1()1()1()!1()()(+++++++++-=+++-=++=n n n n n n n n n x x n n x n f x R ξξξ,将其代⼊到中)()1(!)1()1(!2)1()1)(1()1()()(2x R x n f x f x f f x f n n n ++-+++-'++-'+-= ,得2112)1()1()1()1()1(11++++-++--+-+--=n n n nx x x x x ξ(ξ介于1-与x 之间).习题3—3(B )1.为了修建跨越沙漠的⾼速公路,测量员测量海拔⾼度差时,必须考虑地球是⼀个球体⽽表⾯不是⽔平,从⽽对测量的结果加以修正.(1)如果R 表⽰地球的半径,L 是⾼速公路的长度.证明修正量为R RLR C -=sec . (2)利⽤泰勒公式证明3422452R L R L C +≈.(3)当⾼速公路长100公⾥时,⽐较(1)和(2)中两个修正量(地球半径取6370公⾥).证明:(1)由αR L =,有R L =α,⼜在直⾓三⾓形ODB 中,CR R+=αcos ,于是R C R L+==1s e cs e c α,由此得R RLR C -=sec .(2)先将x x f sec )(=展开为4阶麦克劳林公式,为此求得x x x f tan sec )(=',x x x x f 32s e c t a n s e c )(+='',x x x x x f tan sec 5tan sec )(33+=''',x x x x x x f5234)4(s e c 5t a n s e c 18tan sec )(++=,,,,,,5)0(0)0(1)0(0)0(1)0()4(=='''=''='=f f f f f 于是 )(245211sec 442x R x x x +++=;当1<2245211sec x x x ++≈,取R L x =,得442224521sec RL R L R L ++≈,于是≈-=R R L R C sec 3422452R L R L +.(3)按公式R RLR C -=sec计算,得修正量为785010135.0)1(≈C ,按公式3422452RL R L C +≈计算,得修正量为785009957.0)2(≈C ,它们相差⼤约为000000178.0)2()1(≈-C C .2.写出函数212e)(x x f -=的带佩亚诺型余项的n 2阶麦克劳林公式.解:由)(!!3!21e 32nn tt o n t t t t ++++++= ,令22x t -=,得 )]2(!2)1(!62!42!221[e eee223624222122n n n nn x x x o n x x x x +?-++?-?+?-==--)(]!)!2()1(!!6!!4!!21[e 22642n n n x o n x x x x +-++-+-= ,按规律,由于nx2项的后⼀项为22+n x,所以余项也可以⽤)(12+n xo .3.写出函数x x f 2sin )(=的带⽪亚诺型余项的m 2阶麦克劳林公式.解:x x 2cos 2121sin 2-=)2()!2()2()1(!6)2(!4)2(!2)2(1[2121222642m m mn x o m x x x x +-++-+--=)()!2(2)1(4523122121642m m m m x o x m x x x +-+-+-=-- ,同上⼀题,余项也可以⽤)(12+m x o .(注意:像2、3题⽤变量代换写泰勒公式的⽅法只使⽤于带有佩亚诺型余项的泰勒公式,不适⽤带有拉格朗⽇型余项的泰勒公式,否则得到的余项不再是拉格朗⽇型余项) 4.应⽤三阶泰勒公式计算下列各数的近似值,并估计误差:(1)330;(2)18sin .解:(1)取函数31)(x x f +=,展开为三阶麦克劳林公式,有31154323)1(3108159311)(x xx x x x x f θ+?-+-+=+=,3339/11332730+?=+=,现取9/1=x ,)59049572912711(3303+-+≈,误差为54431089.19310-?R , 10725.3)000085.0001372.0037037.01(3)59049572912711(3303=+-+≈+-+≈;(2)⽤x sin 的麦克劳林公式,取1018π==x ,得53)10(!5)cos()10(!311018sin πθππx +-=,则3)10(!311018sin ππ-≈,误差为5531055.2)10(!51-?≈<≤πR3090.030899.000517.031416.018sin ≈=-≈.5.利⽤泰勒公式求下列极限:(1)642/012/e cos lim 2x x x x x +--→;(2)x x x x x x x sin )1(sin e lim 20+-→.解:(1)原式64636426 642012/)](!32821[)](!62421[lim xx x o x x x x o x x x x ++?-+--+-+-=→ 3607)(360/7lim 6660=+=→x x o x x .(2)原式3233220)](6/)][(2/1[lim x x x x o x x x o x x x --+-+++=→ 31)(3/lim3330=+=→x x o x x .6.设函数)(x f 在区间][b a ,上有⼆阶连续导数,证明:有)(b a ,∈ξ使得)(4)()2(2)()(2ξf a b b a f b f a f ''-=+-+.证明:将函数)(x f y =在20ba x +=点展开为⼀阶泰勒公式,有 20000)(!2)())(()()(x x f x x x f x f x f -''+-'+=η.(η介于x 与0x 之间)分别⽤b x a x ==、代⼊上式,得 201000)(!2)())(()()(x a f x a x f x f a f -''+-'+=η 4)(!2)(2)2()2(21b a f b a b a f b a f -''+-+'++=η(21b a a +<<η),202000)(!2)())(()()(x b f x b x f x f b f -''+-'+=η 4)(!2)(2)2()2(22a b f a b b a f b a f -''+-+'++=η(b b a <<+22η),上两式相加,得]2)()([4)()2(2)()(212ηηf f a b b a f b f a f ''+''-++=+,由)(x f ''连续,根据习题1-7(B )4,得)(2)()(21ξηηf f f ''=''+''()(b a ,∈ξ),于是,)(4)()2(2)()(2ξf a b b a f b f a f ''-++=+,所以,有)(b a ,∈ξ使得)(4)()2(2)()(2ξf a b b a f b f a f ''-=+-+. 7.若函数)(x f 有⼆阶导数,0)(>''x f ,且1)(lim=→xx f x ,⽤泰勒公式证明x x f ≥)(. 证明:由函数)(x f 可导,及1)(lim=→xx f x ,得1)0(0)0(='=f f ,,将)(x f 展开为⼀阶麦克劳林公式,有22)()(x f x x f ξ''+=(ξ介于0与x 之间),由0)(>''x f ,得x x f x x f ≥''+=22)()(ξ.8.设函数)(x f 在区间]20[,上⼆次可微,)2()0(f f =,且M x f ≤'')(,对任何]20[,∈x ,证明M x f ≤')(.证明:对任何∈x ]20[,,将函数)(t f y =在x t =点展开为⼀阶泰勒公式,有 2)(!2)())(()()(x t f x t x f x f t f -''+-'+=ξ.(ξ介于x 与t 之间)分别⽤20==t t 、代⼊上式,得 21!2)()()()0(x f x x f x f f ξ''+'-=,(x <<10ξ)(1) 22)2(!2)()2)(()()2(x f x x f x f f -''+-'+=ξ,(22<<ξx )(2)(2)-(1),并由条件)2()0(f f =,有 ])()2)(([21)(202122x f x f x f ξξ''--''+'=,即])()2)(([41)(2122x f x f x f ξξ''--''-=',所以M x x M x x M x f =+-?≤+-≤'222])2[(4])2[(4)(.习题3—4(A )1.下列叙述是否正确?并按照你的判断说明理由:(1)设函数()f x 在区间[,]a b 上连续,在(,)a b 内可导,那么()f x 在区间[,]a b 上单调增加(减少)的充分必要条件是对任意的(,)x a b ∈,0)(>'x f (0)(<'x f );(2)函数的极⼤值点与极⼩值点都可能不是唯⼀的,并且在其驻点与不可导点处均取得极值;(3)判定极值存在的第⼀充分条件是根据驻点两侧导数的符号来确定该驻点是否为极值点,第⼆充分条件是根据函数在其驻点处⼆阶导数的符号来判定该驻点是否为极值点;(4)在区间I 上连续的函数,其最⼤值点或最⼩值点⼀定是它的极值点.答:(1)不正确.如3x y =在]11[,-上单调增加,⽽032≥='x y .(2)前者正确,后者不正确.驻点与不可导点是取得极值必要条件不是充分条件,如函数3x y =有驻点0=x ,⽽3x y =在0=x 点不取极值;⼜如函数3x y =有不可导点0=x ,⽽3x y =在0=x 点也不取极值.(3)前者不正确,后者正确.第⼀充分条件对连续函数的不可导点也适⽤.(4)不正确.函数的最⼤(⼩)值点可以是闭区间端点,这时的最值点就不是极值点. 2.证明函数x x x f arcsin )(-=在]11[,-上单调减少.解:在开区间)11(,-内,0111)(2≤--='xx f ,且等号只在0=x 点成⽴,所以)(x f 在开区间)11(,-内单调减少,⼜因为函数x x x f arcsin )(-=在区间]11[,-的左、右端点处分别右连续、左连续,所以x x x f arcsin )(-=在]11[,-上单调减少. 3.求下列函数的单调区间和极值:(1)323y x x =-;(2)xx y 12+=;(3)3232x x y +?=;(4)2exy x =;(5)x x y -+=)1ln(;(6))1ln(2-=x y .解:(1)定义域为)(∞+-∞,,)2(3632-=-='x x x x y ,由0='y ,得驻点0=x ,2=x ,函数没有不可导点.单增区间为:)2[]0(∞+-∞,、,,单减区间为:]20[,,极⼤值为:0)0(=y ,极⼩值为:4)2(-=y .(2)定义域为)0()0(∞+-∞,,,221xx y -=',由0='y ,得驻点1±=x ,在定义域内函数没有不可导点.单增区间为:)1[]1(∞+--∞,、,,单减区间为:]10()01[,、,-,极⼤值为:2)1(-=-y ,极⼩值为:2)1(=y .(3)定义域为)(∞+-∞,,2233)1(2xx y ?+=',由0='y ,得驻点1-=x ,不可导点0=x .单增区间为:)1[∞+-,,单减区间为:]1(--∞,,⽆极⼤值,极⼩值为:1)1(-=-y .(4)定义域为)0()0(∞+-∞,,,3)2(e xx y x -=',由0='y ,得驻点2=x ,在定义域内函数没有不可导点.单增区间为:、,)0(-∞)2[∞+,,单减区间为:]20(,,⽆极⼤值,极⼩值为:4/e )2(2=y .(5)定义域为)1(∞+-,,xxy +-='1,由0='y ,得驻点0=x ,在定义域内函数没有不可导点.单增区间为:]01(,-,单减区间为:)0[∞+,,极⼤值为:0)0(=y ,⽆极⼩值.(6)定义域为)1()1(∞+--∞,,,122-='x xy ,在定义域内0≠'y ,且没有不可导点.单增区间为:)1(∞+,,单减区间为:)1(--∞,,既⽆极⼤值,也⽆极⼩值.4.求下列函数在指定区间的最⼤值M 和最⼩值m :(1)163)(24+-=x x x f ,]20[,∈x ;(2)11)(+-=x x x f ,]40[,∈x .解:(1))1(121212)(23-=-='x x x x x f ,由0)(='x f ,得1=x (10-==x x ,都不在)20(,内),⽐较数值25)2(2)1(1)0(=-==f f f ,,,得163)(24+-=x x x f 在。

会计课后习题答案(第三章)

会计课后习题答案(第三章)
答案: 正确
19 企业计提当年盈余公积的基数,不包括年初未分配利润。
答案: 正确
20 年度终了,“利润分配”账户所属的各明细账户中,除“未分配利润”明细账户可能有余额外,其他明细账户均无余额。
答案: 正确
21 得利与损失是与企业日常活动直接关联的经济利益总流入或总流出。
答案: 错误
8 下列支出不得列入成本费用的是 。
A: 支付给金融机构的手续费
答案: 制造费用
10 “应付职工薪酬”账户可设置 、 、 、 、 和“非货币性福利”等明细分类账户。
答案: 工资 社会保险费 职工福利 工会经费 职工教育经费
11 .直接生产工人的薪酬费用应计入 账户,车间技术及管理人员薪酬费用应计入 账户,销售机构人员的薪酬费用计入 账户,行政管理人员薪酬费用计入 账户。
答案: 正确
15 企业按职工工资总额一定比例计提的工会经费及职工教育经费应记入管理费用。
答案: 错误
16 企业专设销售机构的固定资产修理费用应计入销售费用。
答案: 正确
17 “生产成本”账户若有余额应在借方,反映期末自制半成品的实际生产成本。
答案: 错误
18 企业当年可供分配的利润包括当年实现的净利润和年初未分配利润。
B: 制造费用
C: 本年利润
D: 管理费用
E: 利润分配
答案: B, D
5 工业企业以下收入中应记入其他业务收入的有 。
A: 销售产品
B: 销售材料
C: 固定资产盘盈
D: 固定资产出租收入
E: 处置固定资产净收益
答案: B, D
6 工业企业以下各项应记入营业外支出的是 。

马原,第三章习题及答案

马原,第三章习题及答案

第三章人类社会及其发展规律(课后练习题)一、单项选择题1 .人类社会历史发展的决定力量是( )A .生产方式B .地理条件C .社会意识D .人口因素2 .社会意识相对独立性的最突出表现是它( )A .同社会存在发展的不同步性B .具有历史的继承性C .对社会存在具有能动的反作用D .同社会经济的发展具有不平衡性3 .在生产关系中起决定作用的是( )A .生产资料所有制B .产品的分配和交换C .在生产中人与人的关系D .管理者和生产者的不同地位4 . “手推磨产生的是封建主的社会,蒸汽磨产生的是工业资本家的社会” , 这句话揭示了( )A .生产工具是衡量生产力水平的重要尺度B .科学技术是第一生产力C .社会形态的更替有其一定的顺序性D .物质生产的发展需要建立相应的生产关系5 .十一届三中全会以来,我党制定的一系列正确的路线、方针、政策促进了我国经济的迅猛发展,这说明( )A .经济基础发展的道路是由上层建筑决定的B .上层建筑的发展决定经济基础的发展方向C .上层建筑对经济基础具有积极的能动作用D .社会主义社会的发展不受经济基础决定上层建筑规律的制约6 .一定社会形态的经济基础是( )A .生产力B .该社会的各种生产关系C .政治制度和法律制度D .与一定生产力发展阶段相适应的生产关系的总和7 .上层建筑是指( )A .社会的经济制度B .科学技术C .社会生产关系D .建立在一定社会经济基础之上的意识形态及相应的制度和设施8 .社会形态是( )A .生产力和生产关系的统一B .同生产力发展一定阶段相适应的经济基础和上层建筑的统一体C .社会存在和社会意识的统一D .物质世界和精神世界的统一9 .人类社会发展的一般规律是( )A .生产方式内部的矛盾规律B .生产力和生产关系、经济基础和上层建筑之间的矛盾运动规律C .社会存在和社会意识的矛盾规律D .物质生产和精神生产的矛盾规律10 .阶级斗争对阶级社会发展的推动作用突出表现在( )A .生产力的发展B .生产关系的变革C .社会形态的更替D .科技的进步11 .社会革命根源于( )A .人口太多B .少数英雄人物组织暴动C .先进思想和革命理论的传播D .社会基本矛盾的尖锐化12 .社会主义改革的根本目的在于( )A .改变社会主义制度B .完善社会主义制度C .解放和发展生产力D .实现社会公平13 . “蒸汽、电力和自动纺织机甚至是比巴尔贝斯、拉斯拜尔和布朗基诸位公民更危险万分的革命家。

计算机操作系统(第四版)课后习题答案第三章

计算机操作系统(第四版)课后习题答案第三章

第三章处理机调度与死锁1,高级调度与低级调度的主要任务是什么?为什么要引入中级调度?【解】(1)高级调度主要任务是用于决定把外存上处于后备队列中的那些作业调入内存,并为它们创建进程,分配必要的资源,然后再将新创建的进程排在就绪队列上,准备执行。

(2)低级调度主要任务是决定就绪队列中的哪个进程将获得处理机,然后由分派程序执行把处理机分配给该进程的操作。

(3)引入中级调度的主要目的是为了提高内存的利用率和系统吞吐量。

为此,应使那些暂时不能运行的进程不再占用宝贵的内存空间,而将它们调至外存上去等待,称此时的进程状态为就绪驻外存状态或挂起状态。

当这些进程重又具备运行条件,且内存又稍有空闲时,由中级调度决定,将外存上的那些重又具备运行条件的就绪进程重新调入内存,并修改其状态为就绪状态,挂在就绪队列上,等待进程调度。

3、何谓作业、作业步和作业流?【解】作业包含通常的程序和数据,还配有作业说明书。

系统根据该说明书对程序的运行进行控制。

批处理系统中是以作业为基本单位从外存调入内存。

作业步是指每个作业运行期间都必须经过若干个相对独立相互关联的顺序加工的步骤。

作业流是指若干个作业进入系统后依次存放在外存上形成的输入作业流;在操作系统的控制下,逐个作业进程处理,于是形成了处理作业流。

4、在什么情冴下需要使用作业控制块JCB>其中包含了哪些内容?【解】每当作业进入系统时,系统便为每个作业建立一个作业控制块JCB根据作业类型将它插入到相应的后备队列中。

JCB包含的内容通常有:1)作业标识2)用户名称3)用户账户4)作业类型(CPU 繁忙型、I/O 芳名型、批量型、终端型)5)作业状态6)调度信息(优先级、作业已运行)7)资源要求8)进入系统时间9)开始处理时间10)作业完成时间11)作业退出时间12)资源使用情况等5.在作业调度中应如何确定接纳多少个作业和接纳哪些作业?【解】作业调度每次接纳进入内存的作业数,取决于多道程序度。

【精选】光纤通信课后习题解答第3章习题参考答案

【精选】光纤通信课后习题解答第3章习题参考答案

第三章 光纤的传输特性1.简述石英系光纤损耗产生的原因,光纤损耗的理论极限值是由什么决定的?答:(1)(2)光纤损耗的理论极限值是由紫外吸收损耗、红外吸收损耗和瑞利散射决定的。

2.当光在一段长为10km 光纤中传输时,输出端的光功率减小至输入端光功率的一半。

求:光纤的损耗系数α。

解:设输入端光功率为P 1,输出端的光功率为P 2。

则P 1=2P 2光纤的损耗系数()km dB P P km P P L /3.02lg 1010lg 102221===α 3.光纤色散产生的原因有哪些?对数字光纤通信系统有何危害?答:(1)按照色散产生的原因,光纤的色散主要分为:模式(模间)色散、材料色散、波导色散和极化色散。

(2)在数字光纤通信系统中,色散会引起光脉冲展宽,严重时前后脉冲将相互重叠,形成码间干扰,增加误码率,影响了光纤的传输带宽。

因此,色散会限制光纤通信系统的传输容量和中继距离。

4.为什么单模光纤的带宽比多模光纤的带宽大得多?答:光纤的带宽特性是在频域中的表现形式,而色散特性是在时域中的表现形式,即色散越大,带宽越窄。

由于光纤中存在着模式色散、材料色散、波导色散和极化色散四种,并且模式色散>>材料色散>波导色散>极化色散。

由于极化色散很小,一般忽略不计。

在多模光纤中,主要存在模式色散、材料色散和波导色散;单模光纤中不存在模式色散,而只存在材料色散和波导色散。

因此,多模光纤的色散比单模光纤的色散大得多,也就是单模光纤的带宽比多模光纤宽得多。

光纤损耗吸收损耗本征吸收杂质吸收原子缺陷吸收紫外吸收 红外吸收氢氧根(OH -)吸收 过渡金属离子吸收散射损耗弯曲损耗5.均匀光纤纤芯和包层的折射率分别为n 1=1.50,n 2=1.45,光纤的长度L=10km 。

试求:(1)子午光线的最大时延差;(2)若将光纤的包层和涂敷层去掉,求子午光线的最大时延差。

解:(1) 1sin 21111⎪⎪⎭⎫ ⎝⎛-=-=n n C Ln n C L n CL c M θτ () s 1.72145.150.110350.1105μ=⎪⎭⎫⎝⎛-⨯⨯=km km (2)若将光纤的包层和涂敷层去掉,则n 2=1.01sin 21111⎪⎪⎭⎫ ⎝⎛-=-=n n C Ln n C L n CL c M θτ () s 5210.150.110350.1105μ=⎪⎭⎫⎝⎛-⨯⨯=km km 6.一制造长度为2km 的阶跃型多模光纤,纤芯和包层的折射率分别为n 1=1.47,n 2=1.45,使用工作波长为1.31μm ,光源的谱线宽度Δλ=3nm ,材料色散系数D m =6ps/nm·km ,波导色散τw =0,光纤的带宽距离指数γ=0.8。

概率论与数理统计(理工类_第四版)吴赣昌主编课后习题答案第三章

概率论与数理统计(理工类_第四版)吴赣昌主编课后习题答案第三章

01 1/401/41/2习题4设(X,Y)的联合分布密度为f(x,y)=12πe-x2+y22,Z=X2+Y2,求Z的分布密度.解答:FZ(z)=P{Z≤z}=P{X2+Y2≤z}.当z<0时,FZ(z)=P(∅)=0;当z≥0时,FZ(z)=P{X2+Y2≤z2}=∫∫x2+y2≤z2f(x,y)dxdy=12π∫∫x2+y2≤z2e-x2+y22dxdy=12π∫02πdθ∫0ze-ρ22ρdρ=∫0ze-ρ22ρdρ=1-e-z22.故Z的分布函数为FZ(z)={1-e-z22,z≥00,z<0.Z的分布密度为fZ(z)={ze-z22,z>00,z≤0.习题5设随机变量(X,Y)的概率密度为f(x,y)={12(x+y)e-(x+y),x>0,y>00,其它,(1)问X和Y是否相互独立?(2)求Z=X+Y的概率密度.解答:(1)fX(x)=∫-∞+∞f(x,y)dy={∫0+∞12(x+y)e-(x+y)dy,x>00,x≤0\under2line令x+y=t{∫x+∞12te-tdt=12(x+1)e-x,x>00,x≤0,由对称性知fY(y)={12(y+1)e-y,y>00,y≤0,显然f(x,y)≠fX(x)fY(y),x>0,y>0,所以X与Y不独立.(2)用卷积公式求fZ(z)=∫-∞+∞f(x,z-x)dx.当{x>0z-x>0 即 {x>0x<z时,f(x,z-x)≠0,所以当z≤0时,fZ(z)=0;当z>0时,fZ(z)=∫0z12xe-xdx=12z2e-z.于是,Z=X+Y的概率密度为fZ(z)={12z2e-z,z>00,z≤0.习题6设随机变量X,Y相互独立,若X服从(0,1)上的均匀分布,Y服从参数1的指数分布,求随机变量Z=X+Y的概率密度.解答:据题意,X,Y的概率密度分布为fX(x)={1,0<x<10,其它, fY(y)={e-y,y≥00,y<0,由卷积公式得Z=X+Y的概率密度为fZ(z)=∫-∞+∞fX(x)fY(z-x)dx=∫-∞+∞fX(z-y)fY(y)dy=∫0+∞fX(z-y)e-ydy.由0<z-y<1得z-1<y<z,可见:当z≤0时,有fX(z-y)=0, 故fZ(z)=∫0+∞0⋅e-ydy=0;当z>0时,fZ(z)=∫0+∞fX(z-y)e-ydy=∫max(0,z-1)ze-ydy=e-max(0,z-1)-e-z,即fZ(z)={0,z≤01-e-z,0<z≤1e1-z-e-z,z>1.习题7设随机变量(X,Y)的概率密度为f(x,y)={be-(x+y),0<x<1,0<y<+∞,0,其它.(1)试确定常数b;(2)求边缘概率密度fX(x),fY(y);(3)求函数U=max{X,Y}的分布函数. 解答:(1)由∫-∞+∞∫-∞+∞f(x,y)dxdy=1,确定常数b.∫01dx∫0+∞be-xe-ydy=b(1-e-1)=1,所以b=11-e-1,从而f(x,y)={11-e-1e-(x+y),0<x<1,0<y<+∞,0,其它.(2)由边缘概率密度的定义得fX(x)={∫0+∞11-e-1e-(x+y)dy=e-x1-e-x,0<x<1,0,其它,fY(x)={∫0111-e-1e-(x+y)dx=e-y,0<y<+∞,0,其它(3)因为f(x,y)=fX(x)fY(y),所以X与Y独立,故FU(u)=P{max{X,Y}≤u}=P{X≤u,Y≤u}=FX(u)FY(u),其中FX(x)=∫0xe-t1-e-1dt=1-e-x1-e-1,0<x<1,所以FX(x)={0,x≤0,1-e-x1-e-1,0<x<1,1,x≥1.同理FY(y)={∫0ye-tdt=1-e-y,0<y<+∞,0,y≤0,因此FU(u)={0,u<0,(1-e-u)21-e-1,0≤u<1,1-e-u,u≥1.习题8设系统L是由两个相互独立的子系统L1和L2以串联方式联接而成,L1和L2的寿命分别为X与Y, 其概率密度分别为ϕ1(x)={αe-αx,x>00,x≤0,ϕ2(y)={βe-βy,y>00,y≤0,其中α>0,β>0,α≠β,试求系统L的寿命Z的概率密度.解答:设Z=min{X,Y},则F(z)=P{Z≥z}=P{min(X,Y)≤z}=1-P{min(X,Y)>z}=1-P{X≥z,Y≥z}=1-[1P{X<z}][1-P{Y<z}]=1-[1-F1{z}][1-F2{z}]由于F1(z)={∫0zαe-αxdx=1-e-αz,z≥00,z<0,F2(z)={1-e-βz,z≥00,z<0,故F(z)={1-e-(α+β)z,z≥00,z<0,从而ϕ(z)={(α+β)e-(α+β)z,z>00,z≤0.习题9设随机变量X,Y相互独立,且服从同一分布,试证明:P{a<min{X,Y}≤b}=[P{X>a}]2-[P{X>b}]2.解答:设min{X,Y}=Z,则P{a<min{X,Y}≤b}=FZ(b)-FZ(a),FZ(z)=P{min{X,Y}≤z}=1-P{min{X,Y}>z}=1-P{X>z,Y>z}=1-P{X>z}P{Y>z}=1-[P{X>z}]2,代入得P{a<min{X,Y}≤b}=1-[P{X>b}]2-(1-[P{X>a}]2)=[P{X>a}]2-[P{X>b}]2.证毕.复习总结与总习题解答习题1在一箱子中装有12只开关,其中2只是次品,在其中取两次,每次任取一只,考虑两种试验:(1)放回抽样;(2)不放回抽样.我们定义随机变量X,Y如下:X={0,若第一次取出的是正品1,若第一次取出的是次品, Y={0,若第二次取出的是正品1,若第二次取出的是次品,试分别就(1),(2)两种情况,写出X和Y的联合分布律.解答:(1)有放回抽样,(X,Y)分布律如下:P{X=0,Y=0}=10×1012×12=2536; P{X=1,Y=0}=2×1012×12=536,P{X=0,Y=1}=10×212×12=536, P{X=1,Y=1}=2×212×12=136,(2)不放回抽样,(X,Y)的分布律如下:P{X=0,Y=0}=10×912×11=4566, P{X=0,Y=1}=10×212×11=1066,P{X=1,Y=0}=2×1012×11=1066, P{X=1,Y=1}=2×112×11=166,解答:X可取值为0,1,2,3,Y可取值0,1,2.P{X=0,Y=0}=P{∅}=0,P{X=0,Y=1}=C30C21C33/C84=2/70,P{X=0,Y=2}=C30C22C32/C84=3/70, P{X=1,Y=0}=C31C20C33/C84=3/70,P{X=1,Y=1}=C31C21C32/C84=18/70,P{X=1,Y=2}=C31C22C31/C84=9/70,P{X=2,Y=0}=C32C20C32/C84=9/70,P{X=2,Y=1}=C32C21C31/C84=18/70,P{X=2,Y=2}=C32C22C30/C84=3/70,P{X=3,Y=0}=C33C20C31/C84=3/70,P{X=3,Y=1}=C33C21C30/C84=2/70,P{X=3,Y=2}=P{∅}=0,所以,(X,Y)的联合分布如下:(3)由FX(x)=P{X≤x,Y<+∞}=∑xi<x∑j=1+∞pij, 得(X,Y)关于X的边缘分布函数为:FX(x)={0,x<114+14,1≤x<214+14+16+13,x≥2={0,x<11/2,1≤x<21,x≥2,同理,由FY(y)=P{X<+∞,Y≤y}=∑yi≤y∑i=1+∞Pij, 得(X,Y)关于Y的边缘分布函数为FY(y)={0,y<-12/12,-1≤y<01,y≥0.习题6设随机变量(X,Y)的联合概率密度为f(x,y)={c(R-x2+y2),x2+y2<R0,x2+y2≥R,求:(1)常数c; (2)P{X2+Y2≤r2}(r<R).解答:(1)因为1=∫-∞+∞∫-∞+∞f(x,y)dydx=∫∫x2+y2<Rc(R-x2+y)d xdy=∫02π∫0Rc(R-ρ)ρdρdθ=cπR33,所以有c=3πR3.(2)P{X2+Y2≤r2}=∫∫x2+y2<r23πR3[R-x2+y2]dxdy=∫02π∫0r3πR3(R-ρ)ρdρdθ=3r2R2(1-2r3R).习题7设f(x,y)={1,0≤x≤2,max(0,x-1)≤y≤min(1,x)0,其它,求fX(x)和fY(y).解答:max(0,x-1)={0,x<1x-1,x≥1, min(1,x)={x,x<11,x≥1,所以,f(x,y)有意义的区域(如图)可分为{0≤x≤1,0≤y≤x},{1≤x≤2,1-x≤y≤1},即f(x,y)={1,0≤x≤1,0≤y≤x1,1≤x≤2,x-1≤y≤1,0,其它所以fX(x)={∫0xdy=x,0≤x<1∫x-11dy=2-x,1≤x≤20,其它,fY(y)={∫yy+1dx=1,0≤y≤10,其它.习题8若(X,Y)的分布律为则α,β应满足的条件是¯, 若X与Y独立,则α=¯,β=¯.解答:应填α+β=13;29;19.由分布律的性质可知∑i⋅jpij=1, 故16+19+118+13+α+β=1,即α+β=13.又因X与Y相互独立,故P{X=i,Y=j}=P{X=i}P{Y=j}, 从而α=P{X=2,Y=2}=P{X=i}P{Y=j},=(19+α)(14+α+β)=(19+α)(13+13)=29,β=P{X=3,Y=2}=P{X=3}P{Y=2}=(118+β)(13+α+β)=(118+β)(13+13),∴β=19.习题9设二维随机变量(X,Y)的概率密度函数为f(x,y)={ce-(2x+y),x>0,y>00,其它,(1)确定常数c; (2)求X,Y的边缘概率密度函数;(3)求联合分布函数F(x,y); (4)求P{Y≤X}; (5)求条件概率密度函数fX∣Y(x∣y); (6)求P{X<2∣Y<1}.解答:(1)由∫-∞+∞∫-∞+∞f(x,y)dxdy=1求常数c.∫0+∞∫0+∞ce-(2x+y)dxdy=c⋅(-12e-2x)\vline0+∞⋅(-e-y)∣0+∞=c2=1,所以c=2.(2)fX(x)=∫-∞+∞f(x,y)dy={∫0+∞2e-2xe-ydy,x>00,x≤0={2e-2x,x>00,x≤0,fY(y)=∫-∞+∞f(x,y)dx={∫0+∞2e-2xe-ydx,y>00,其它={e-y,y>00,y≤0.(3)F(x,y)=∫-∞x∫-∞yf(u,v)dvdu={∫0x∫0y2e-2ue-vdvdu,x>0,y>00,其它={(1-e-2x)(1-e-y),x>0,y>00,其它.(4)P{Y≤X}=∫0+∞dx∫0x2e-2xe-ydy=∫0+∞2e-2x(1-e-x)dx=13.(5)当y>0时,fX∣Y(x∣y)=f(x,y)fY(y)={2e-2xe-ye-y,x>00,x≤0={2e-2x,x>00,x≤0.(6)P{X<2∣Y<1}=P{X<2,Y<1}P{Y<1}=F(2,1)∫01e-ydy=(1-e-1)(1-e-4)1-e-1=1-e-4.习题10设随机变量X以概率1取值为0, 而Y是任意的随机变量,证明X与Y相互独立.解答:因为X的分布函数为F(x)={0,当x<0时1,当x≥0时, 设Y的分布函数为FY(y),(X,Y)的分布函数为F(x,y),则当x<0时,对任意y, 有F(x,y)=P{X≤x,Y≤y}=P{(X≤x)∩(Y≤y)}=P{∅∩(Y≤y)}=P{∅}=0=FX(x)FY(y);当x≥0时,对任意y, 有F(x,y)=P{X≤x,Y≤y}=P{(X≤x)∩(Y≤y)}=P{S∩(Y≤y)}=P{Y≤y}=Fy(y)=FX(x)FY(y),依定义,由F(x,y)=FX(x)FY(y)知,X与Y独立.习题11设连续型随机变量(X,Y)的两个分量X和Y相互独立,且服从同一分布,试证P{X≤Y}=1/2.解答:因为X,Y独立,所以f(x,y)=fX(x)fY(y).P{X≤Y}=∫∫x≤yf(x,y)dxdy=∫∫x≤yfX(x)fY(y)dxdy =∫-∞+∞[fY(y)∫-∞yfX(x)dx]dy=∫-∞+∞[fY(y)FY(y)]dy=∫-∞+∞FY(y)dFY(y)=F2(y)2∣-∞+∞=12,也可以利用对称性来证,因为X,Y独立同分布,所以有P{X≤Y}=P{Y≤X},而P{X≤Y}+P{X≥Y}=1, 故P{X≤Y}=1/12.习题12设二维随机变量(X,Y)的联合分布律为若X与Y相互独立,求参数a,b,c的值.解答:关于X的边缘分布为由于X和Y的地位平等,同法可得Y的边缘概率密度是:fY(y)={2R2-y2πR2,-R≤y≤R0,其它.(2)fX∣Y(x∣y)=f(x,y)fY(y)注意在y处x值位于∣x∣≤R2-y2这个范围内,f(x,y)才有非零值,故在此范围内,有fX∣Y(x∣y)=1πR22πR2⋅R2-y2=12R2-y2,即Y=y时X的条件概率密度为fX∣Y(x∣y)={12R2-y2,∣x∣≤R2-y20,其它.同法可得X=x时Y的条件概率密度为fY∣X(y∣x)={12R2-x2,∣y∣≤R2-x20,其它.由于条件概率密度与边缘概率密度不相等,所以X与Y不独立.习题15设(X,Y)的分布律如下表所示求:(1)Z=X+Y; (2)Z=max{X,Y}的分布律.解答:与一维离散型随机变量函数的分布律的计算类似,本质上是利用事件及其概率的运算法则. 注意,Z的相同值的概率要合并.概率(X,Y)X+YXYX/Ymax{X,Y}1/102/103/102/101/101/10 (-1,-1)(-1,1)(-1,2)(2,-1)(2,1)(2,2)--1-2-2241-1-1/2-221-于是(1)max{X,Y} -112pi 1/102/107/10习题16设(X,Y)的概率密度为f(x,y)={1,0<x<1,0<y<2(1-x)0,其他,求Z=X+Y的概率密度.解答:先求Z的分布函数Fz(z),再求概率密度fz(z)=dFz(z)dz.如右图所示.当z<0时,Fz(z)=P{X+Y≤z}=0;当0≤z<1时,Fz(z)=P{X+Y≤z}=∫∫x+y≤zf(x,y)dxdy=∫0zdx∫0z-x1dy=∫0z(z-x)dx=z2-12x2∣0z=12z2;当1≤z<2时,Fz(z)=∫02-zdx∫0z-xdy+∫2-z1dx∫02(1-x)dy=z(2-z)-12(2-z)2+(z-1)2;当z≥2时,∫∫Df(x,y)dxdy=∫01dx∫02(1-x)dy=1.综上所述Fz(z)={0,z<012z2,0≤z<1z(2-z)-12(2-z)2+(z-1)2,1≤z<21,z≥2,故fz(z)={z,0≤z<12-z,1≤z<20,其它.习题17设二维随机变量(X,Y)的概率密度为f(x,y)={2e-(x+2y),x>0,y>00,其它,求随机变量Z=X+2Y的分布函数.解答:按定义FZ(Z)=P{x+2y≤z},当z≤0时,FZ(Z)=∫∫x+2y≤zf(x,y)dxdy=∫∫x+2y≤z0dxdy=0.当z>0时,FZ(Z)=∫∫x+2y≤zf(x,y)dxdy=∫0zdx∫0(z-x)/22e-(x+2y)dy=∫0ze-x⋅(1-ex-z)dx=∫0z(e-x-e-z)dx=[-e-x]∣0z-ze-z=1-e-z-ze-z,故分布函数为FZ(Z)={0,z≤01-e-z-ze-z,z>0.习题18设随机变量X与Y相互独立,其概率密度函数分别为fX(x)={1,0≤x≤10,其它, fY(y)={Ae-y,y>00,y≤0,求:(1)常数A; (2)随机变量Z=2X+Y的概率密度函数.解答:(1)1=∫-∞+∞fY(y)dy=∫0+∞A⋅e-ydy=A.(2)因X与Y相互独立,故(X,Y)的联合概率密度为f(x,y)={e-y,0≤x≤1,y>00,其它.于是当z<0时,有F(z)=P{Z≤z}=P{2X+Y≤z}=0;当0≤z≤2时,有F(z)=P{2X+Y≤z}=∫0z/2dx∫0z-2xe-ydy=∫0z/2(1-e2x-z)dx;当z>2时,有F(z)=P{2X+Y≤2}=∫01dx∫0z-2xe-ydy=∫01(1-e2x-z)dx.利用分布函数法求得Z=2X+Y的概率密度函数为fZ(z)={0,z<0(1-e-z)/2,0≤z<2(e2-1)e-z/2,z≥2.习题19设随机变量X,Y相互独立,若X与Y分别服从区间(0,1)与(0,2)上的均匀分布,求U=max{X,Y}与V=min{X,Y}的概率密度.解答:由题设知,X与Y的概率密度分别为fX(x)={1,0<x<10,其它, fY(y)={1/2,0<y<20,其它,于是,①X与Y的分布函数分别为FX(x)={0,x≤0x,0≤x<11,x≥1, FY(y)={0,y<0y/2,0≤y<21,y≥2,从而U=max{X,Y}的分布函数为FU(u)=FX(u)FY(u)={0,u<0u2/2,0≤u<1u/2,1≤u<21,u≥2,故U=max{X,Y}的概率密度为fU(u)={u,0<u<11/2,1≤u<20,其它.②同理,由FV(v)=1-[1-FX(v)][1-FY)]=FX(v)+FY(v)-FX(v)FY(v)=FX(v)+FY(v)-FU(v),得V=min{X,Y}的分布函数为FV(v)={0,v<0v2(3-v),0≤v<11,v≥1,故V=min{X,Y}的概率密度为fV(v)={32-v,0<v<10,其它.注:(1)用卷积公式,主要的困难在于X与Y的概率密度为分段函数,故卷积需要分段计算;(2)先分别求出X,Y的分布函数FX(x)与FY(y), 然后求出FU(u),再求导得fU(u); 同理先求出FV(v), 求导即得fV(v).。

计算机组成原理第三章课后题参考答案

计算机组成原理第三章课后题参考答案

计算机组成原理第三章课后题参考答案第三章课后习题参考答案1.有⼀个具有20位地址和32位字长的存储器,问:(1)该存储器能存储多少个字节的信息(2)如果存储器由512K×8位SRAM芯⽚组成,需要多少芯⽚(3)需要多少位地址作芯⽚选择解:(1)∵ 220= 1M,∴该存储器能存储的信息为:1M×32/8=4MB (2)(1024K/512K)×(32/8)= 8(⽚)(3)需要1位地址作为芯⽚选择。

3.⽤16K×8位的DRAM芯⽚组成64K×32位存储器,要求:(1) 画出该存储器的组成逻辑框图。

(2) 设DRAM芯⽚存储体结构为128⾏,每⾏为128×8个存储元。

如单元刷新间隔不超过2ms,存储器读/写周期为µS, CPU在1µS内⾄少要访问⼀次。

试问采⽤哪种刷新⽅式⽐较合理两次刷新的最⼤时间间隔是多少对全部存储单元刷新⼀遍所需的实际刷新时间是多少解:(1)组成64K×32位存储器需存储芯⽚数为N=(64K/16K)×(32位/8位)=16(⽚)每4⽚组成16K×32位的存储区,有A13-A0作为⽚内地址,⽤A15 A14经2:4译码器产⽣⽚选信号,逻辑框图如下所⽰:(2)根据已知条件,CPU在1us内⾄少访存⼀次,⽽整个存储器的平均读/写周期为,如果采⽤集中刷新,有64us的死时间,肯定不⾏;所以采⽤分散式刷新⽅式:设16K×8位存储芯⽚的阵列结构为128⾏×128列,按⾏刷新,刷新周期T=2ms,则分散式刷新的间隔时间为:t=2ms/128=(s) 取存储周期的整数倍s的整数倍)则两次刷新的最⼤时间间隔发⽣的⽰意图如下可见,两次刷新的最⼤时间间隔为tMAXt MAX=×2-=(µS)对全部存储单元刷新⼀遍所需时间为tRt R=×128=64 (µS)4.有⼀个1024K×32位的存储器,由128K×8位DRAM芯⽚构成。

大学物理第三章课后习题答案

大学物理第三章课后习题答案

L 时时, (1)摩擦力做功多少? (2)弹性力做功多少? (3)其他力做功多少? (4)外力做的总功是多少? 8. 小球系于细绳的一端,质量为 m ,并以恒定的角速
度 ω 0 在光滑水平面上围绕一半径为 R 的圆周运动。细 绳穿过圆心小孔, 若手握绳的另一端用力 F 向下拉绳,使小球运转的半径减小一半, 求 力对小球所做的功。 9. 如图所示, 一小车从光滑的轨道上某处由
9. 解:由题意知小车飞越 BC 缺口时做斜抛运动,其射程 BC = 2 R sin α 。 设小车在 B 点时的速度为 υ B , 欲使小车 刚 好 越 过 BC , 应 满 足 2υ B ⋅ sin α g
-7-
2 R sin α = υ B ⋅ cos α ⋅
自治区精品课程—大学物理学
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gR (1) cos α 由 A 点运动到 B 点时机械能守恒得: 1 2 mgh = mg ( R + R cos α ) + mυ B (2) 2 由式(1)与(2)得 1 h = (1 + cos α + )R 2 cos α
自治区精品课程—大学物理学
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第三章 功和能
一、 填空 1. 功等于质点受的 和 的标量积,功是 变化的量度。 2. 物理学中用 来描述物体做功的快慢。力的瞬时功率等于 与 的标积。对于一定功率的机械,当速度小时,力就 (填“大”或“小” ) , 速度大时,力必定 (填“大”或“小” ) 。 3. 合外力对质点所做的功等于质点动能的增量,此即 定理。 4. 质点动能定理的微分形式是 。 5. 质点动能定理的积分形式是 。 6. 按做功性质,可以将力分为 和 。 7. 所做的功只取决于受力物体的初末位置,与物体所经过的路径无 关。做功与路径有关的力叫做 。 8. 物体在 力作用下,沿任意闭合路径绕一周所做的功等于零。 9. 保守力做功与物体势能改变量之间的关系是 。 10. 若保守力做正功,则势能 ( “增加”或“减少” ) ,若保守力做负功, 则 势能 ( “增加”或“减少” ) 。 11. 势能的增量与势能零点的选取 (填“有关”或“无关” ) ,势能的大小 与势能零点的选取 (填“有关”或“无关” ) 。 12. 质点系内各质点之间的相互作用力称为 ,质点系以外的其他物体对 质点系内各质点的作用力称为 。 13. 质点系在运动过程中, 所做的功与 所做的功的总 和等于质点系的机械能的增量,此即质点系的 原理。 14. 在只 有 做功 的情 况下, 质点 系的机 械能 保持不 变, 这就是 定律。 15. 行星沿 轨道绕太阳运行, 太阳位于椭圆的一个 上; 对任一行星, 以 太阳 中 心为 参 考点 , 行星 的 位置 矢 量在 相 等的 时 间内 扫 过的 面 积填 ( “相 等 ”或 “ 不 相等 ” ) ; 行星 绕 太阳 运 动的 和 椭圆 轨 道的 成正比。 16. 第一宇宙速度是 所需要 的速度。 17. 第二宇宙速度是 所需要的 最小速度。 18. 第三宇宙速度是 所需的 最小速度。 二、 简答 1. 2. 3. 4. 5. 简述质点动能定理的内容,并写出其微分形式和积分形式。 简述保守力做功与物体势能改变量之间的关系。 简述质点系功能原理的内容。 简述机械能守恒定律的内容。 简述行星运动的三大定律的内容。

计算机操作系统(第四版)课后习题答案第三章

计算机操作系统(第四版)课后习题答案第三章

第三章处理机调度与死锁1,高级调度与低级调度的主要任务是什么?为什么要引入中级调度?【解】(1)高级调度主要任务是用于决定把外存上处于后备队列中的那些作业调入内存,并为它们创建进程,分配必要的资源,然后再将新创建的进程排在就绪队列上,准备执行。

(2)低级调度主要任务是决定就绪队列中的哪个进程将获得处理机,然后由分派程序执行把处理机分配给该进程的操作。

(3)引入中级调度的主要目的是为了提高内存的利用率和系统吞吐量。

为此,应使那些暂时不能运行的进程不再占用宝贵的内存空间,而将它们调至外存上去等待,称此时的进程状态为就绪驻外存状态或挂起状态。

当这些进程重又具备运行条件,且内存又稍有空闲时,由中级调度决定,将外存上的那些重又具备运行条件的就绪进程重新调入内存,并修改其状态为就绪状态,挂在就绪队列上,等待进程调度。

3、何谓作业、作业步和作业流?【解】作业包含通常的程序和数据,还配有作业说明书。

系统根据该说明书对程序的运行进行控制。

批处理系统中是以作业为基本单位从外存调入内存。

作业步是指每个作业运行期间都必须经过若干个相对独立相互关联的顺序加工的步骤。

作业流是指若干个作业进入系统后依次存放在外存上形成的输入作业流;在操作系统的控制下,逐个作业进程处理,于是形成了处理作业流。

4、在什么情冴下需要使用作业控制块JCB?其中包含了哪些内容?【解】每当作业进入系统时,系统便为每个作业建立一个作业控制块JCB,根据作业类型将它插入到相应的后备队列中。

JCB 包含的内容通常有:1) 作业标识2)用户名称3)用户账户4)作业类型(CPU 繁忙型、I/O芳名型、批量型、终端型)5)作业状态6)调度信息(优先级、作业已运行)7)资源要求8)进入系统时间9) 开始处理时间10) 作业完成时间11) 作业退出时间12) 资源使用情况等5.在作业调度中应如何确定接纳多少个作业和接纳哪些作业?【解】作业调度每次接纳进入内存的作业数,取决于多道程序度。

大学物理课后习题答案第三章

大学物理课后习题答案第三章

第3章 力学基本定律与守恒律 习题及答案1.作用在质量为10 kg 的物体上的力为i t F)210(+=N ,式中t 的单位是s ,(1)求4s 后,这物体的动量和速度的变化.(2)为了使这力的冲量为200 N ·s ,该力应在这物体上作用多久,试就一原来静止的物体和一个具有初速度j6-m ·s -1的物体,回答这两个问题. 解: (1)若物体原来静止,则i t i t t F p t 1401s m kg 56d )210(d -⋅⋅=+==∆⎰⎰,沿x 轴正向,ip I imp v111111s m kg 56s m 6.5--⋅⋅=∆=⋅=∆=∆ 若物体原来具有6-1s m -⋅初速,则⎰⎰+-=+-=-=t tt F v m t m F v m p v m p 000000d )d (,于是⎰∆==-=∆t p t F p p p 0102d,同理, 12v v ∆=∆,12I I=这说明,只要力函数不变,作用时间相同,则不管物体有无初动量,也不管初动量有多大,那么物体获得的动量的增量(亦即冲量)就一定相同,这就是动量定理. (2)同上理,两种情况中的作用时间相同,即⎰+=+=tt t t t I 0210d )210(亦即 0200102=-+t t 解得s 10=t ,(s 20='t 舍去)2.一颗子弹由枪口射出时速率为10s m -⋅v ,当子弹在枪筒内被加速时,它所受的合力为 F =(bt a -)N(b a ,为常数),其中t 以秒为单位:(1)假设子弹运行到枪口处合力刚好为零,试计算子弹走完枪筒全长所需时间;(2)求子弹所受的冲量.(3)求子弹的质量. 解: (1)由题意,子弹到枪口时,有0)(=-=bt a F ,得ba t =(2)子弹所受的冲量⎰-=-=tbt at t bt a I 0221d )(将bat =代入,得 ba I 22= (3)由动量定理可求得子弹的质量202bv a v I m == 3.如图所示,一质量为m 的球,在质量为M 半径为R 的1/4圆弧形滑槽中从静止滑下。

成本会计第三章课后练习题题目以及答案

成本会计第三章课后练习题题目以及答案

1、某工业企业生产甲、乙两种产品,共同耗用A和B两种原材料,耗用量无法按产品直接划分。

甲产品投产100件,原材料单件消耗定额为:A料10千克,B料5千克;乙产品投产200件,原材料单间消耗定额为:A料4千克,B料6千克。

甲、乙两种产品实际消耗总量为:A料1782千克,B料1717千克。

原材料计划单价为:A料2元,B料3元。

原材料成本差异率为-2%。

要求:按定额消费量比例分配甲、乙两种产品的原材料费用,编制原材料费用分配表和会计分录。

思考:原材料费用按定额消耗量比例分配比例分配较按定额费用比例分配有何优缺点?它们各自使用什么样的情况?2、某企业设有修理、运输两个辅助生产车间,本月发生辅助生产费用、提供劳务量如下:运输车间修理车间辅助生产车间元待分配辅助生产费用2000019000元公里40000劳务供应数量20000小时小时修理车间1500耗用劳务数1000小时运输车间量公里3000016000小时基本车间公里小时30008500企业管理部门;编制辅助生产费用:采用交付分配法,计算分配辅助生产费用(列示计算过程)要求分配表和编制有关会计分录。

辅助生产车间费用分配表(交互分配法)项交互分对外分运合修合修运辅助车间名待分配辅助生产费劳务供应数费用分配率(单位成本耗用数修理辅助生产分配金间耗耗用数运输分配金耗用数基本生产车间用分配金额企业管理部门耗耗用数量用分配金额分配金额合计思考:对该分配方法如何评价?采用该分配方法时为什么“辅助生产成本”科目的贷方发生额会大于原来的待分配费用额?3、某工业企业辅助生产车间的制造费用通过“制造费用”科目核算。

有关资料如下:辅助生产费用分配表(计划成本分配法)要求:采用计划成本分配法分配辅助生产费用(列出计算分配过程)并填制辅助生产费用分配表和编制有关的会计分录。

思考:比较计划成本分配法与其他辅助生产费用分配方法,其有点何在?适用条件怎样?第3章费用在各种产品以及期间费用之间的归集和分配1.按定额消耗量比例分配原材料费用(1)甲、乙两种产品的原材料定额消耗量。

第3章 酸、碱及离子平衡(课后习题及参考答案)Yao

第3章  酸、碱及离子平衡(课后习题及参考答案)Yao

第三章 酸、碱和离子平衡1)下列各种物质,哪些是酸?哪些是碱?哪些既是酸又是碱?并写出它们的共轭碱或共轭酸。

CO 32-;NH 3;HAc ;HS -;H 2CO 3;NH 4+;H 2O ;H 2PO 4-;S 2-解:酸:HAc ;H 2CO 3;NH 4+; 共轭碱: Ac -;HCO 3-;NH 3碱: CO 32-;S 2-; 共轭酸: HCO 3-;HS-两性: HS -;H 2O ;H 2PO 4-;NH 3共轭酸: H 2S ;H 3O +;H 3PO 4;NH 4+共轭碱:S 2-;OH -;HPO -;NH 2-2) 在某温度下0.5 mol ⋅L 1-蚁酸(HCOOH)溶液的解离度为2%,试求该温度时蚁酸的解离常数。

解:∵cK o ≈α,∴o 2=c K α=(2%)2×0.50=2.00×10-43) 计算0.050 mol ⋅L 1-次氯酸(HClO)溶液中H 3O +的浓度和次氯酸的解离度。

解:查表得:θ-8a (HClO)=2.8810K ⨯∵ θ86a /0.052.8810 1.7410500c K -=⨯=⨯>∴ 3θH O /c c +=53.7910-=⨯∴35H O 3.7910c +-=⨯ mol ⋅L 1-352HClOH O 3.7910100%7.5810%0.05c c α+--⨯==⨯=⨯4)已知氨水溶液的浓度为0.20 mol ⋅L 1-。

① 求该溶液中的OH -的浓度及pH 值。

② 在上述100 mL 溶液中加入1.07gNH 4Cl 晶体(忽略体积变化),求所得溶液的OH -的浓度及pH 值。

比较①、②计算结果,说明了什么?解: ① 查表得:θ-5b 3(NH )=1.7410K ⨯∵ θ-5b/0.201.7410500c K =⨯>∴θOH /c c -= 1.87×103-mol ⋅L 1-pH =14-pOH =14- (-lg OH c -)=11.27② 设加入NH 4Cl 晶体后,溶液中OH -的浓度为x mol ⋅L1-:溶液中NH 4+的浓度为1.07g/ 53.5g ⋅mol 1-/0.1L=0.2 mol ⋅L 1-NH 3 + H 2ONH 4+ + OH -初始浓度/ mol ⋅L 1- 0.20 0.2平衡浓度/ mol ⋅L 1- 0.20-x 0.20+x x 43θ-5b3()()(0.20)(NH )===1.74100.20NH OH NHc c c c x x K c c xθθθ+-∙+⨯-解得:x =-51.7410⨯ mol ⋅L1-pH =14-pOH =14- (-lg OH c -)=9.24比较①、②计算结果,说明由于同离子效应,使NH 3的解离度下降。

物理化学课后习题答案第三章

物理化学课后习题答案第三章

第三章热力学第二定律3.1卡诺热机在的高温热源和的低温热源间工作。

求(1)热机效率;(2)当向环境作功时,系统从高温热源吸收的热及向低温热源放出的热。

解:卡诺热机的效率为根据定义3.5高温热源温度,低温热源。

今有120 kJ的热直接从高温热源传给低温热源,龟此过程的。

解:将热源看作无限大,因此,传热过程对热源来说是可逆过程3.6不同的热机中作于的高温热源及的低温热源之间。

求下列三种情况下,当热机从高温热源吸热时,两热源的总熵变。

(1)可逆热机效率。

(2)不可逆热机效率。

(3)不可逆热机效率。

解:设热机向低温热源放热,根据热机效率的定义因此,上面三种过程的总熵变分别为。

3.7已知水的比定压热容。

今有1 kg,10 C的水经下列三种不同过程加热成100 C的水,求过程的。

(1)系统与100 C的热源接触。

(2)系统先与55 C的热源接触至热平衡,再与100 C的热源接触。

(3)系统先与40 C,70 C的热源接触至热平衡,再与100 C的热源接触。

解:熵为状态函数,在三种情况下系统的熵变相同在过程中系统所得到的热为热源所放出的热,因此3.8已知氮(N2, g)的摩尔定压热容与温度的函数关系为将始态为300 K,100 kPa下1 mol的N2(g)置于1000 K的热源中,求下列过程(1)经恒压过程;(2)经恒容过程达到平衡态时的。

解:在恒压的情况下在恒容情况下,将氮(N2, g)看作理想气体将代替上面各式中的,即可求得所需各量3.9始态为,的某双原子理想气体1 mol,经下列不同途径变化到,的末态。

求各步骤及途径的。

(1)恒温可逆膨胀;(2)先恒容冷却至使压力降至100 kPa,再恒压加热至;(3)先绝热可逆膨胀到使压力降至100 kPa,再恒压加热至。

解:(1)对理想气体恒温可逆膨胀, U = 0,因此(2)先计算恒容冷却至使压力降至100 kPa,系统的温度T:(3)同理,先绝热可逆膨胀到使压力降至100 kPa时系统的温度T:根据理想气体绝热过程状态方程,各热力学量计算如下2.12 2 mol双原子理想气体从始态300 K,50 dm3,先恒容加热至400 K,再恒压加热至体积增大到100 dm3,求整个过程的。

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第三章1. (Q1) Suppose the network layer provides the following service. The network layer in the source host accepts a segment of maximum size 1,200 bytes and a destination host address from the transport layer. The network layer then guarantees to deliver the segment to the transport layer at the destination host. Suppose many network application processes can be running at the destination host.a. Design the simplest possible transport-layer protocol that will get application data to thedesired process at the destination host. Assume the operating system in the destination host has assigned a 4-byte port number to each running application process.b. Modify this protocol so that it provides a “return address” to the destination process.c. In your protocols, does the transport layer “have to do anything” in the core of the computernetwork.Answer:a. Call this protocol Simple Transport Protocol (STP). At the sender side, STP accepts from thesending process a chunk of data not exceeding 1196 bytes, a destination host address, and a destination port number. STP adds a four-byte header to each chunk and puts the port number of the destination process in this header. STP then gives the destination host address and the resulting segment to the network layer. The network layer delivers the segment to STP at the destination host. STP then examines the port number in the segment, extracts the data from the segment, and passes the data to the process identified by the port number.b. The segment now has two header fields: a source port field and destination port field. At thesender side, STP accepts a chunk of data not exceeding 1192 bytes, a destination host address,a source port number, and a destination port number. STP creates a segment which contains theapplication data, source port number, and destination port number. It then gives the segment and the destination host address to the network layer. After receiving the segment, STP at the receiving host gives the application process the application data and the source port number.c. No, the transport layer does not have to do anything in the core; the transport layer “lives” inthe end systems.2. (Q2) Consider a planet where everyone belongs to a family of six, every family lives in its own house, each house has a unique address, and each person in a given house has a unique name. Suppose this planet has a mail service that delivers letters form source house to destination house. The mail service requires that (i) the letter be in an envelope and that (ii) the address of the destination house (and nothing more ) be clearly written on the envelope. Suppose each family has a delegate family member who collects and distributes letters for the other family members. The letters do not necessarily provide any indication of the recipients of the letters.a. Using the solution to Problem Q1 above as inspiration, describe a protocol that thedelegates can use to deliver letters from a sending family member to a receiving family member.b. In your protocol, does the mail service ever have to open the envelope and examine theletter in order to provide its service.Answer:a.For sending a letter, the family member is required to give the delegate the letter itself, theaddress of the destination house, and the name of the recipient. The delegate clearly writes the recipient’s name on the top of the letter. The delegate then puts the letter in an e nvelope and writes the address of the destination house on the envelope. The delegate then gives the letter to the planet’s mail service. At the receiving side, the delegate receives the letter from the mail service, takes the letter out of the envelope, and takes note of the recipient name written at the top of the letter. The delegate than gives the letter to the family member with this name.b.No, the mail service does not have to open the envelope; it only examines the address on theenvelope.3. (Q3) Describe why an application developer might choose to run an application over UDP rather than TCP.Answer:An application developer may not want its application to use TCP’s congestion control, which can throttle the application’s sending rate at times of congestion. Often, designers of IP telephony and IP videoconference applications choose to run their applications over UDP because they want to avoid TCP’s congestion control. Also, some applications do not need the reliable data transfer provided by TCP.4. (P1) Suppose Client A initiates a Telnet session with Server S. At about the same time, Client B also initiates a Telnet session with Server S. Provide possible source and destination port numbers fora. The segment sent from A to B.b. The segment sent from B to S.c. The segment sent from S to A.d. The segment sent from S to B.e. If A and B are different hosts, is it possible that the source port number in the segment fromA to S is the same as that fromB to S?f. How about if they are the same host?Yes.f No.5. (P2) Consider Figure 3.5 What are the source and destination port values in the segmentsflowing form the server back to the clients’ processes? What are the IP addresses in the network-layer datagrams carrying the transport-layer segments?Answer:Suppose the IP addresses of the hosts A, B, and C are a, b, c, respectively. (Note that a,b,c aredistinct.)To host A: Source port =80, source IP address = b, dest port = 26145, dest IP address = a To host C, left process: Source port =80, source IP address = b, dest port = 7532, dest IP address = cTo host C, right process: Source port =80, source IP address = b, dest port = 26145, dest IP address = c6. (P3) UDP and TCP use 1s complement for their checksums. Suppose you have the followingthree 8-bit bytes: 01101010, 01001111, 01110011. What is the 1s complement of the sum of these 8-bit bytes? (Note that although UDP and TCP use 16-bit words in computing the checksum, for this problem you are being asked to consider 8-bit sums.) Show all work. Why is it that UDP takes the 1s complement of the sum; that is , why not just sue the sum? With the 1s complement scheme, how does the receiver detect errors? Is it possible that a 1-bit error will go undetected? How about a 2-bit error?Answer:One's complement = 1 1 1 0 1 1 1 0.To detect errors, the receiver adds the four words (the three original words and the checksum). If the sum contains a zero, the receiver knows there has been an error. All one-bit errors will be detected, but two-bit errors can be undetected (e.g., if the last digit of the first word is converted to a 0 and the last digit of the second word is converted to a 1).7. (P4) Suppose that the UDP receiver computes the Internet checksum for the received UDPsegment and finds that it matches the value carried in the checksum field. Can the receiver be absolutely certain that no bit errors have occurred? Explain.Answer:No, the receiver cannot be absolutely certain that no bit errors have occurred. This is because of the manner in which the checksum for the packet is calculated. If the corresponding bits (that would be added together) of two 16-bit words in the packet were 0 and 1 then even if these get flipped to 1 and 0 respectively, the sum still remains the same. Hence, the 1s complement the receiver calculates will also be the same. This means the checksum will verify even if there was transmission error.8. (P5) a. Suppose you have the following 2 bytes: 01001010 and 01111001. What is the 1scomplement of sum of these 2 bytes?b. Suppose you have the following 2 bytes: 11110101 and 01101110. What is the 1s complement of sum of these 2 bytes?c. For the bytes in part (a), give an example where one bit is flipped in each of the 2 bytesand yet the 1s complement doesn’t change.0 1 0 1 0 1 0 1 + 0 1 1 1 0 0 0 0 1 1 0 0 0 1 0 1 1 1 0 0 0 1 0 1 + 0 1 0 0 1 1 0 0 0 0 0 1 0 0 0 1Answer:a. Adding the two bytes gives 10011101. Taking the one’s complement gives 01100010b. Adding the two bytes gives 00011110; the one’s complement gives 11100001.c. first byte = 00110101 ; second byte = 01101000.9. (P6) Consider our motivation for correcting protocol rdt2.1. Show that the receiver, shown inthe figure on the following page, when operating with the sender show in Figure 3.11, can lead the sender and receiver to enter into a deadlock state, where each is waiting for an event that will never occur.Answer:Suppose the sender is in state “Wait for call 1 from above” and the receiver (the receiver shown in the homework problem) is in state “Wait for 1 from below.” The sender sends a packet with sequence number 1, and transitions to “Wait for ACK or NAK 1,” waiting for an ACK or NAK. Suppose now the receiver receives the packet with sequence number 1 correctly, sends an ACK, and transitions to state “Wait for 0 from below,” waiting for a data packet with sequence number 0. However, the ACK is corrupted. When the rdt2.1 sender gets the corrupted ACK, it resends the packet with sequence number 1. However, the receiver is waiting for a packet with sequence number 0 and (as shown in the home work problem) always sends a NAK when it doesn't get a packet with sequence number 0. Hence the sender will always be sending a packet with sequence number 1, and the receiver will always be NAKing that packet. Neither will progress forward from that state.10. (P7) Draw the FSM for the receiver side of protocol rdt3.0Answer:The sender side of protocol rdt3.0 differs from the sender side of protocol 2.2 in that timeouts have been added. We have seen that the introduction of timeouts adds the possibility of duplicate packets into the sender-to-receiver data stream. However, the receiver in protocol rdt.2.2 can already handle duplicate packets. (Receiver-side duplicates in rdt 2.2 would arise if the receiver sent an ACK that was lost, and the sender then retransmitted the old data). Hence the receiver in protocol rdt2.2 will also work as the receiver in protocol rdt 3.0.11. (P8) In protocol rdt3.0, the ACK packets flowing from the receiver to the sender do not havesequence numbers (although they do have an ACK field that contains the sequence number of the packet they are acknowledging). Why is it that our ACK packets do not require sequence numbers?Answer:To best Answer this question, consider why we needed sequence numbers in the first place. We saw that the sender needs sequence numbers so that the receiver can tell if a data packet is a duplicate of an already received data packet. In the case of ACKs, the sender does not need this info (i.e., a sequence number on an ACK) to tell detect a duplicate ACK. A duplicate ACK is obvious to the rdt3.0 receiver, since when it has received the original ACK it transitioned to the next state. The duplicate ACK is not the ACK that the sender needs and hence is ignored by the rdt3.0 sender.12. (P9) Give a trace of the operation of protocol rdt3.0 when data packets and acknowledgmentpackets are garbled. Your trace should be similar to that used in Figure 3.16Answer:Suppose the protocol has been in operation for some time. The sender is in state “Wait for call fro m above” (top left hand corner) and the receiver is in state “Wait for 0 from below”. The scenarios for corrupted data and corrupted ACK are shown in Figure 1.13. (P10) Consider a channel that can lose packets but has a maximum delay that is known.Modify protocol rdt2.1 to include sender timeout and retransmit. Informally argue whyyour protocol can communicate correctly over this channel.Answer:Here, we add a timer, whose value is greater than the known round-trip propagation delay. We add a timeout event to the “Wait for ACK or NAK0” and “Wait for ACK or NAK1” states. If the timeout event occurs, the most recently transmitted packet is retransmitted. Let us see why this protocol will still work with the rdt2.1 receiver.• Suppose the timeout is caused by a lost data packet, i.e., a packet on the senderto- receiver channel. In this case, the receiver never received the previous transmission and, from the receiver's viewpoint, if the timeout retransmission is received, it look exactly the same as if the original transmission is being received.• Suppose now that an ACK is lost. The receiver will eventually retransmit the packet on atimeout. But a retransmission is exactly the same action that is take if an ACK is garbled. Thus the sender's reaction is the same with a loss, as with a garbled ACK. The rdt 2.1 receiver can already handle the case of a garbled ACK.14. (P11) Consider the rdt3.0 protocol. Draw a diagram showing that if the network connectionbetween the sender and receiver can reorder messages (that is, that two messagespropagating in the medium between the sender and receiver can be reordered), thenthe alternating-bit protocol will not work correctly (make sure you clearly identify thesense in which it will not work correctly). Your diagram should have the sender on theleft and the receiver on the right, with the time axis running down the page, showingdata (D) and acknowledgement (A) message exchange. Make sure you indicate thesequence number associated with any data or acknowledgement segment.Answer:15. (P12) The sender side of rdt3.0 simply ignores (that is, takes no action on) all received packetsthat are either in error or have the wrong value in the ack-num field of anacknowledgement packet. Suppose that in such circumstances, rdt3.0 were simply toretransmit the current data packet . Would the protocol still work? (hint: Consider whatwould happen if there were only bit errors; there are no packet losses but prematuretimeout can occur. Consider how many times the nth packet is sent, in the limit as napproaches infinity.)Answer:The protocol would still work, since a retransmission would be what would happen if the packet received with errors has actually been lost (and from the receiver standpoint, it never knows which of these events, if either, will occur). To get at the more subtle issue behind this question, one has to allow for premature timeouts to occur. In this case, if each extra copy of the packet is ACKed and each received extra ACK causes another extra copy of the current packet to be sent, the number of times packet n is sent will increase without bound as n approaches infinity.16. (P13) Consider a reliable data transfer protocol that uses only negative acknowledgements.Suppose the sender sends data only infrequently. Would a NAK-only protocol bepreferable to a protocol that uses ACKs? Why? Now suppose the sender has a lot ofdata to send and the end to end connection experiences few losses. In this second case ,would a NAK-only protocol be preferable to a protocol that uses ACKs? Why?Answer:In a NAK only protocol, the loss of packet x is only detected by the receiver when packetx+1 is received. That is, the receivers receives x-1 and then x+1, only when x+1 is received does the receiver realize that x was missed. If there is a long delay between the transmission of x and the transmission of x+1, then it will be a long time until x can be recovered, under a NAK only protocol.On the other hand, if data is being sent often, then recovery under a NAK-only scheme could happen quickly. Moreover, if errors are infrequent, then NAKs are only occasionally sent (when needed), and ACK are never sent – a significant reduction in feedback in the NAK-only case over the ACK-only case.17. (P14) Consider the cross-country example shown in Figure 3.17. How big would the windowsize have to be for the channel utilization to be greater than 80 percent?Answer:It takes 8 microseconds (or 0.008 milliseconds) to send a packet. in order for the sender to be busy 90 percent of the time, we must have util = 0.9 = (0.008n) / 30.016 or n approximately 3377 packets.18. (P15) Consider a scenario in which Host A wants to simultaneously send packets to Host Band C. A is connected to B and C via a broadcast channel—a packet sent by A is carriedby the channel to both B and C. Suppose that the broadcast channel connecting A, B,and C can independently lose and corrupt packets (and so, for example, a packet sentfrom A might be correctly received by B, but not by C). Design a stop-and-wait-likeerror-control protocol for reliable transferring packets from A to B and C, such that Awill not get new data from the upper layer until it knows that B and C have correctlyreceived the current packet. Give FSM descriptions of A and C. (Hint: The FSM for Bshould be essentially be same as for C.) Also, give a description of the packet format(s)used.Answer:In our solution, the sender will wait until it receives an ACK for a pair of messages (seqnum and seqnum+1) before moving on to the next pair of messages. Data packets have a data field and carry a two-bit sequence number. That is, the valid sequence numbers are 0, 1, 2, and 3. (Note: you should think about why a 1-bit sequence number space of 0, 1 only would not work in the solution below.) ACK messages carry the sequence number of the data packet they are acknowledging.The FSM for the sender and receiver are shown in Figure 2. Note that the sender state records whether (i) no ACKs have been received for the current pair, (ii) an ACK for seqnum (only) has been received, or an ACK for seqnum+1 (only) has been received. In this figure, we assume that theseqnum is initially 0, and that the sender has sent the first two data messages (to get things going).A timeline trace for the sender and receiver recovering from a lost packet is shown below:Sender Receivermake pair (0,1)send packet 0Packet 0 dropssend packet 1receive packet 1buffer packet 1send ACK 1receive ACK 1(timeout)resend packet 0receive packet 0deliver pair (0,1)send ACK 0receive ACK 019. (P16) Consider a scenario in which Host A and Host B want to send messages to Host C. HostsA and C are connected by a channel that can lose and corrupt (but not reorder)message.Hosts B and C are connected by another channel (independent of the channelconnecting A and C) with the same properties. The transport layer at Host C shouldalternate in delivering messages from A and B to the layer above (that is, it should firstdeliver the data from a packet from A, then the data from a packet from B, and so on).Design a stop-and-wait-like error-control protocol for reliable transferring packets fromA toB and C, with alternating delivery atC as described above. Give FSM descriptionsof A and C. (Hint: The FSM for B should be essentially be same as for A.) Also, give adescription of the packet format(s) used.Answer:This problem is a variation on the simple stop and wait protocol (rdt3.0). Because the channel may lose messages and because the sender may resend a message that one of the receivers has already received (either because of a premature timeout or because the other receiver has yet to receive the data correctly), sequence numbers are needed. As in rdt3.0, a 0-bit sequence number will suffice here.The sender and receiver FSM are shown in Figure 3. In this problem, the sender state indicates whether the sender has received an ACK from B (only), from C (only) or from neither C nor B. The receiver state indicates which sequence number the receiver is waiting for.20. (P17) In the generic SR protocol that we studied in Section 3.4.4, the sender transmits amessage as soon as it is available (if it is in the window) without waiting for anacknowledgment. Suppose now that we want an SR protocol that sends messages twoat a time. That is , the sender will send a pair of messages and will send the next pairof messages only when it knows that both messages in the first pair have been receivercorrectly.Suppose that the channel may lose messages but will not corrupt or reorder messages.Design an error-control protocol for the unidirectional reliable transfer of messages.Give an FSM description of the sender and receiver. Describe the format of the packetssent between sender and receiver, and vice versa. If you use any procedure calls otherthan those in Section 3.4(for example, udt_send(), start_timer(), rdt_rcv(), and soon) ,clearly state their actions. Give an example (a timeline trace of sender and receiver)showing how your protocol recovers from a lost packet.Answer:21. (P18) Consider the GBN protocol with a sender window size of 3 and a sequence numberrange of 1024. Suppose that at time t, the next in-order packet that the receiver isexpecting has a sequence number of k. Assume that the medium does not reordermessages. Answer the following questions:a. What are the possible sets of sequence number inside the sender’s window at timet? Justify your Answer.b .What are all possible values of the ACK field in all possible messages currentlypropagating back to the sender at time t? Justify your Answer.Answer:a.Here we have a window size of N=3. Suppose the receiver has received packet k-1, and hasACKed that and all other preceeding packets. If all of these ACK's have been received by sender, then sender's window is [k, k+N-1]. Suppose next that none of the ACKs have been received at the sender. In this second case, the sender's window contains k-1 and the N packets up to and including k-1. The sender's window is thus [k- N,k-1]. By these arguments, the senders window is of size 3 and begins somewhere in the range [k-N,k].b.If the receiver is waiting for packet k, then it has received (and ACKed) packet k-1 and the N-1packets before that. If none of those N ACKs have been yet received by the sender, then ACKmessages with values of [k-N,k-1] may still be propagating back. Because the sender has sent packets [k-N, k-1], it must be the case that the sender has already received an ACK for k-N-1.Once the receiver has sent an ACK for k-N-1 it will never send an ACK that is less that k-N-1.Thus the range of in-flight ACK values can range from k-N-1 to k-1.22. (P19) Answer true or false to the following questions and briefly justify your Answer.a. With the SR protocol, it is possible for the sender to receive an ACK for a packet thatfalls outside of its current window.b. With CBN, it is possible for the sender to receiver an ACK for a packet that fallsoutside of its current window.c. The alternating-bit protocol is the same as the SR protocol with a sender and receiverwindow size of 1.d. The alternating-bit protocol is the same as the GBN protocol with a sender andreceiver window size of 1.Answer:a.True. Suppose the sender has a window size of 3 and sends packets 1, 2, 3 at t0 . At t1 (t1 > t0)the receiver ACKS 1, 2, 3. At t2 (t2 > t1) the sender times out and resends 1, 2, 3. At t3 the receiver receives the duplicates and re-acknowledges 1, 2, 3. At t4 the sender receives the ACKs that the receiver sent at t1 and advances its window to 4, 5, 6. At t5 the sender receives the ACKs 1, 2, 3 the receiver sent at t2 . These ACKs are outside its window.b.True. By essentially the same scenario as in (a).c.True.d.True. Note that with a window size of 1, SR, GBN, and the alternating bit protocol arefunctionally equivalent. The window size of 1 precludes the possibility of out-of-order packets (within the window). A cumulative ACK is just an ordinary ACK in this situation, since it can only refer to the single packet within the window.23. (Q4) Why is it that voice and video traffic is often sent over TCP rather than UDP in today’sInternet. (Hint: The Answer we are looking for has nothing to do with TCP’s congestion-control mechanism. )Answer:Since most firewalls are configured to block UDP traffic, using TCP for video and voice traffic lets the traffic though the firewalls24. (Q5) Is it possible for an application to enjoy reliable data transfer even when the applicationruns over UDP? If so, how?Answer:Yes. The application developer can put reliable data transfer into the application layer protocol. This would require a significant amount of work and debugging, however.25. (Q6) Consider a TCP connection between Host A and Host B. Suppose that the TCP segmentstraveling form Host A to Host B have source port number x and destination portnumber y. What are the source and destination port number for the segments travelingform Host B to Host A?Answer:Source port number y and destination port number x.26. (P20) Suppose we have two network entities, A and B. B has a supply of data messages thatwill be sent to A according to the following conventions. When A gets a request fromthe layer above to get the next data (D) message from B, A must send a request (R)message to B on the A-to-B channel. Only when B receives an R message can it send adata (D) message back to A on the B-to-A channel. A should deliver exactly one copy ofeach D message to the layer above. R message can be lost (but not corrupted) in the A-to-B channel; D messages, once sent, are always delivered correctly. The delay alongboth channels is unknown and variable.Design(give an FSM description of) a protocol that incorporates the appropriatemechanisms to compensate for the loss-prone A-to-B channel and implementsmessage passing to the layer above at entity A, as discussed above. Use only thosemechanisms that are absolutely necessary.Answer:Because the A-to-B channel can lose request messages, A will need to timeout and retransmit its request messages (to be able to recover from loss). Because the channel delays are variable and unknown, it is possible that A will send duplicate requests (i.e., resend a request message that has already been received by B). To be able to detect duplicate request messages, the protocol will use sequence numbers. A 1-bit sequence number will suffice for a stop-and-wait type of request/response protocol.A (the requestor) has 4 states:• “Wait for Request 0 from above.” Here the requestor is waiting for a call from above to request a unit of data. When it receives a request from above, it sends a request message, R0, to B, starts a timer and make s a transition to the “Wait for D0” state. When in the “Wait for Request 0 from above” state, A ign ores anything it receives from B.• “Wait for D0”. Here the requestor is waiting for a D0 data message from B. A timer is always running in this state. If the timer expires, A sends another R0 message, restarts the timer and remains in this state. If a D0 message is received from B, A stops the time and transits to the “Wait for Request 1 from above” state. If A receives a D1 data message while in this state, it is ignored.• “Wait for Request 1 from above.” Here the requestor is again waiting for a call from above to request a unit of data. When it receives a request from above, it sends a request message, R1, to B, starts a timer and makes a transition to the “Wait for D1” state. When in the “Wait for Request 1 from above” state, A ignores anything it receives from B.• “Wait for D1”. Here the requestor is waiting for a D1 data message from B. A timer is always running in this state. If the timer expires, A sends another R1 message, restarts the timer and remains in this state. If a D1 message is received from B, A stops the timer and transits to the “Wait for Request 0 from above” state. If A receives a D0 data message while in this state, it is ignored.The data supplier (B) has only two states:。

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