2017年成人高考(专升本)试题及答案
2017年成人高考(专升本)试题及答案2017年成人高考专升本高等数学模拟试题一 高等数学一. 选择题（1-10小题，每题4分，共40分） 1. 设0lim →x sinaxx=7,则a の值是（ ）A 17B 1C 5D 7 2. 已知函数f(x)在点x 0处可等，且 f ′(x 0)=3,则0lim→h f(x 0+2h )-f(x 0)h等于（ ） A 3 B 0 C 2 D 63. 当x 0时，sin(x 2+5x 3)与x 2比较是（ ） A 较高阶无穷小量 B 较低阶の无穷小量 C 等价无穷小量 D 同阶但不等价无穷小量4. 设y=x -5+sinx ，则y ′等于（ ）A -5x -6+cosx B -5x -4+cosx C -5x -4-cosx D -5x -6-cosx 5. 设y=4-3x 2 ，则f ′(1)等于（ ） A 0 B -1 C -3 D 36. ⎠⎛(2e x-3sinx)dx 等于（ ）A 2e x +3cosx+cB 2e x +3cosxC 2e x -3cosxD 17. ⎠⎜⎛01dx 1-x 2dx 等于（ ）A 0B 1C 2π D π 8. 设函数 z=arctan y x，则x z ∂∂等于（ ）y x z ∂∂∂2A -y x 2+y 2B y x 2+y 2C x x 2+y 2D -x x 2+y 2 9. 设y=e2x+y则yx z∂∂∂2=（ ）A 2ye 2x+yB 2e 2x+yC e 2x+yD –e 2x+y10. 若事件A 与B 互斥，且P （A ）＝0.5 P （AUB ）＝0.8,则P （B ）等于（ ） A 0.3 B 0.4 C 0.2 D 0.1二、填空题（11-20小题，每小题4分，共40分） 11. ∞→x lim (1-1x)2x=12. 设函数f(x)= 在x=0处连续，则 k ＝13. 函数-e -x 是f(x)の一个原函数，则f(x)＝ 14. 函数y=x-e x の极值点x= 15. 设函数y=cos2x ， 求y ″= 16. 曲线y=3x 2-x+1在点（0,1）处の切线方程y=Ke 2xHcosx17. ⎠⎜⎜⎛1x-1dx ＝18. ⎠⎛(2e x-3sinx)dx = 19. xdx x sin cos 203⎰π=20. 设z=e xy ,则全微分dz=三、计算题（21-28小题，共70分） 1. 1lim →x x 2-12x 2-x-12. 设函数 y=x 3e 2x , 求dy3. 计算 ⎠⎛xsin(x 2+1)dx4. 计算 ⎰+10)12ln(dx x5. 设随机变量x の分布列为 (1) 求a の值，并求P(x<1)(2) 求D(x)x y -0.a -0 0.0.1 20.6.求函数y=e x1+xの单调区间和极值7.设函数z=(x,y)是由方程x2+y2+2x-2yz=e z所确定の隐函数，求dz8.求曲线y=e x,y=e-x与直线x=1所围成の平面图形面积2017年成人高考专升本高等数学模拟试题一 答案一、（1-10小题，每题4分，共40分）1. D2. D3. C4. A5. C6. A7. C8.A9. B 10. A 二、（11-20小题，每小题4分，共40分）11. e -2 12. 2 13. e -x 14. 0 15.-4cos2x 16. y=-x+1 17.1ln -x +c 18. 2e x+3cosx+c 19. 14 20. dz=e xy (ydx+xdy)三、（21-28小题，共70分）1. 1lim →x x 2-12x 2-x-1 =(x-1)(x-1)(x-1)(2x+1) =232. y ′=(x 3)′e 2x +(e 2x )′x 3=3x 2e 2x +2e 2x x 3 =x 2e 2x (3+2x) dy=x 2e 2x dx3. ⎠⎛xsin(x 2+1)dx =12 ⎠⎛sin(x 2+1)d(x 2+1) =12cos(x 2+1)+c4. ⎠⎛01ln(2x+1)dx =xln(2x+1)10-⎠⎜⎜⎛012x (2x+1) dx =ln3-{x-12 ln(2x+1)} 10=-1+32ln35. (1) 0.1+a+0.2+0.1+0.3=1 得出a=0.3P(x<1),就是将x<1各点の概率相加即可，即：0.1+0.3+0.2＝0.6(2) E(x)=0.1×(-2)+0.3×(-1)+0.2×0+0.1×1+0.3×2=0.2D(x)=E{xi-E(x)}2=(-2-0.2)2×0.1+(-1-0.2)2×0.3+(0-0.2)2×0.2+(1-0.2)2×0.1+(2-0.2)2×0.3=1.966. 1) 定义域 x ≠-12) y ′=e x (1+x)-e x (1+x)2 =xe x(1+x)2 3）令y ′＝0,得出x=0(注意x=1这一点也应该作为我们考虑单调区间の点) ↓↓↑函数在（-∞，1）U （-1,0）区间内单调递减在（0，+∞）内单调递增该函数在x=0处取得极小值，极小值为17.xf ∂∂ =2x+2, yf∂∂ =2y-2zzf ∂∂ =-2y-e zxz ∂∂=-x f ∂∂÷zf ∂∂ =2(x+1)2y+ez az ay==-y f∂∂÷zf ∂∂=2y-2z -(2y+e z ) =2y-2z 2y+ez dz=2(x+1)2y+e z dx+2y-2z 2y+ez dy 8.如下图：曲线y=e x ,y=e -x,与直为A(1,e),B(1,e -1)则x yy（-∞- - +-（-10 （0，无意无意F(0)=1为小S=dxe ex x)(10--⎰= (e x +e -x ) 10=e+e -1-22017年成人高考专升本高等数学模拟试题二答案必须答在答题卡上指定の位置，答在试卷上无效．．．．．．．。
一、选择题：1~10小题，每小题4分，共40分。
在每小题给出の四个选项中，只有一项是符合题目要求の，将所选项前の字母填涂在答题卡相应题号の信息．．．．．．．．．．点上．．。
(C) 1.2lim(1)x x→+=A ．3B ．2C ．1D ．0 (D) 2．设sin y x x =+，则'y =A ．sin xB ．xC ．cos x x +D ．1cos x + (B) 3．设2xy e =，则dy =A ．2xe dxB ．22xedxC ．212x e dxD ．2xe dx(C) 4．1(1)xdx -=⎰A ．21x C x -+ B ．21x C x ++C ．ln ||x x C -+D ．ln ||x x C ++ (C) 5．设5xy =，则'y =A ．15x - B ．5xC ．5ln 5xD ．15x +(C) 6．0lim xt x e dt x→=⎰A ．xe B ．2e C ．e D ．1(A) 7．设22z x y xy =+，则zx∂=∂ A ．22xy y + B ．22xxy+ C ．4xy D ．22x y +(A) 8．过点(1,0,0)，(0,1,0)，(0,0,1)の平面方程为A ．1x y z ++=B ．21x y z ++=C ．21x y z ++=D ．21x y z ++= (B) 9．幂级数1nn x n∞=∑の收敛半径R =A ．0B ．1C ．2D ．+∞ (B) 10．微分方程''2'3()()sin 0y y x ++=の阶数为A ．1B ．2C ．3D ．4 二、填空题：11~20小题，每小题4分，共40分。
将答案填写在答题卡相应题号后．．．．．．．．。
11．3lim(1)___.xx x→∞-=(1)12．曲线xy e -=在点(0,1)处の切线斜率___.k =(-1/e)13．设2xy x e =，则'___.y =2xe^x+x^2e^x14．设cos y x =，则'___.y =-sinx15．3(1)___.x dx +=⎰x^4/4+x+C16．1___.x e dx ∞-=⎰2/e17．设22z x y =+，则___.dz =2+2y18．设z xy =，则2___.zx y∂=∂∂119．01___.3nn ∞==∑120．微分方程0dy xdx +=の通解为___.y =y=-(x^2/2)三、解答题：21~28小题，共70分。
解答应写出推理、演算步骤，并将其写在答题卡相应题号后．．．．．．．．。
21．（本题满分8分）(1/4) 设函数22()sin 2x a f x xx⎧+⎪=⎨⎪⎩,0,0x x ≤>，在0x =处连续，求常数a の值.22．（本题满分8分） 计算0lim .sin x xx e e x-→-23．（本题满分8分） 设23x t t t⎧=⎪⎨=⎪⎩，（t 为参数），求1t dy dx=.(根号下t-1) 24．（本题满分8分） 设函数32()39f x xx x=--，求()f x の极大值.（-9）25．（本题满分8分）求1(1)dx x x +⎰. 26．（本题满分10分）计算2Dx ydxdy ⎰⎰，其中积分区域D 由2y x =，1x =，0y =围成.27．（本题满分10分）求微分方程2''3'26y y y e ++=の通解.28．（本题满分10分） 证明：当0x >时，(1)ln(1)x x x ++>.。
2017年成人高考专升本政治真题及答案含解析
【考情点拨】本题考查了内因和外因的辩证关系原理。
【应试指导】唯物辩证法认为，内因是事物发展的内在依据，是第一位的原因；外因是事物发展的外部条件，是第二位的原因；外因通过内因而起作用。内外因关系原理是我国独立自主、自力更生、对外开放等一系列政策方针的理论依据。
6．【答案】B
【考情点拨】本题考查了唯物主义认识论和唯心主义认识论。
7．与感性认识相比较，理性认识的特点是【】
A．直接性和形象性
B．生动性和具体性
C．丰富性和多样性
D．抽象性和间接性
8．在一定条件下，人们对客观事物的发展过程及其发展规律的正确认识总是有限的、不完全的。这说明真理具有【】
A．绝对性
B．客观性
C．相对性
D．一元性
9．下列各项属于社会意识形态的是【】
A．政治制度
25．改革、发展、稳定三者关系中，稳定是【】
A．目的
B．动力
C．根本
D．前提
26．邓小平提出的“三步走”发展战略中，第三步战略目标是，到21世纪中叶，国民生产总值再翻两番，达到【】
A．温饱水平
B．中等发达国家水平
C．发达国家水平
D．小康水平
27．我国社会主义初级阶段的个人收入分配制度是【】
A．按劳分配为主体，多种分配方式并存
A．重要武器
B．主要形式
C．战略阵地
D．基本内容
14．毛泽东提出，坚持武装斗争必须建立一支人民的军队，这支军队的唯一宗旨是【】
A．坚持党对军队的绝对领导
B．执行严格的革命纪律
C．注重思想政治教育
D．坚持全心全意为人民服务
15．我国新民主主义社会的重要特征是【】
A．长期性B．稳定性
2017年成人高考(专科起点升本科) 大学语文试题及参考答案
2017年成人高等学校专升本招生全国统一考试大学语文选择题一、 选择题：1—20小题，每小题2分，共40分。
在每小题给出的四个选项中，只有一项是符合题目要求的。
1.陶渊明《饮酒（其五）》的体裁是A. 五言古诗B. 五言律诗 C. 五言绝句 D. 杂言诗2.沈从文《边城》表现的地域风情是A. 闽东风情B. 湘西风情C. 赣南风情D. 北平风情3.下列诗人中，诗风苍凉悲壮的是A. 曹操 B. 陶渊明C. 李白 D. 王维4.下列作品中，借用了乐府旧题的一组是A. 李白《行路难》、杜甫《蜀相》B. 陆游《关山月》、李白《行路难》C. 曹操《短歌行》、陶渊明《饮酒》D. 王昌龄《从军行》、白居易《杜陵叟》5.下列作品中，同属于人物传记的是A. 《张中丞传后叙》《陈情表》 B. 《五代史伶官传序》《马伶传》C. 《李将军列传》《冯谖客孟尝君》 D. 《李将军列传》《马伶传》6. 《苦恼》《猎人笔记》《麦琪的礼物》的作者依次是A. 屠格涅夫、欧·亨利、契诃夫 B. 契诃夫、屠格涅夫、欧·亨利C. 欧·亨利、契诃夫、屠格涅夫 D. 契诃夫、欧·亨利、屠格涅夫7.下列关于作品、作者、体裁搭配完全正确的是A. 《报刘一丈书》——侯方域——书信体议论文B. 《论毅力》——梁实秋——议论文C. 《答司马谏议书》——王安石——书信体驳论文D. 《陈情表》——李斯——奏章8.关于苏轼《前赤壁赋》一文，下列表述错误的是44A. 是一篇文赋B. 文章的语言骈散相间，音韵和谐C. 文章在结构上采用的是主客问答、伸客抑主的方法D. 文章对景物描写体现出作者乐观豁达的人生态度9.关于《陌上桑》一诗，下列表述错误的是44A. 是一首汉乐府民歌B. 是一首叙事诗C. 诗中主人公是罗敷D. 是一首表达青年男女爱情的诗歌10.下列作品中，属于记事散文的是A. 曹禺《日出》 B. 郁达夫《故都的秋》C. 茅盾《香市》 D. 鲁迅《灯下漫笔》11.冰心、郁达夫、徐志摩曾参加的文学社团依次是A. 文学研究会、新月社、创造社B. 创造社、文学研究会、新月社C. 文学研究会、创造社、新月社D. 新月社、文学研究会、创造社12.下列关于“词”的常识表述错误的是44A. 词起始于唐代，盛行于宋代B. 词由五言诗、七言诗和民间歌谣发展而成C. 词有词牌，不同词牌有不同的押韵规则D. 词可分为“婉约”与“豪放”两大流派，并以“豪放派”为正宗13. “天下为公”“狡兔三窟”两个成语依次出自A. 《礼记·大同》《冯谖客孟尝君》 B. 《季氏将伐颛臾》《李将军列传》C. 《冯谖客孟尝君》《季氏将伐颛臾》 D. 《李将军列传》《礼记·大同》14.下列文学常识表述错误的是44A. “初唐四杰”是指王勃、杨炯、卢照邻、骆宾王B. “中唐古文运动”的领袖是韩愈、柳宗元C. “新乐府运动”的倡导者是王维、白居易D. “小李杜”指的是李商隐、杜牧15.下列各句中，同时采用了对偶、夸张的是A. 恨相见得迟，怨归去得疾。
2017年成人高考数学(专升本)试题及答案(三套试卷)
2017年成人高考专升本高等数学模拟试题一一. 选择题（1—10小题,每题4分，共40分）1。
设0lim →x 错误!=7，则a 的值是（ ) A 错误! B 1 C 5 D 72。
已知函数f(x ）在点x 0处可等，且f ′（x 0)=3，则0lim →h 错误!等于（ ） A 3 B 0 C 2 D 63。
当x 0时,sin(x 2+5x 3)与x 2比较是( ）A 较高阶无穷小量B 较低阶的无穷小量C 等价无穷小量D 同阶但不等价无穷小量4. 设y=x —5+sinx ，则y ′等于（ ）A —5x -6+cosxB —5x —4+cosxC —5x —4—cosxD —5x —6—cosx5. 设y=，4—3x 2 ,则f ′（1）等于( )A 0B —1C -3D 36。
错误!等于（ )A 2e x +3cosx+cB 2e x +3cosxC 2e x -3cosxD 17. 错误!等于( )A 0B 1C 2π D π 8。
设函数 z=arctan 错误!，则xz ∂∂等于（ )y x z ∂∂∂2 A 错误! B 错误! C 错误! D 错误!9。
设y=e 2x+y 则yx z ∂∂∂2=( ） A 2ye 2x+y B 2e 2x+y C e 2x+y D –e 2x+y10. 若事件A 与B 互斥，且P （A ）＝0。
5 P(AUB ）＝0。
8，则P （B)等于（ )A 0。
3B 0.4C 0.2D 0.1二、填空题（11-20小题，每小题4分,共40分)11. ∞→x lim （1—错误!)2x =12。
设函数f(x)= 在x=0处连续，则 k ＝13. 函数—e —x 是f(x)的一个原函数，则f （x ）＝14。
函数y=x-e x 的极值点x=15. 设函数y=cos2x , 求y ″=16。
曲线y=3x 2-x+1在点（0，1)处的切线方程y=17. 错误!＝18。
2017年山东成人高考专升本高等数学(二)真题及答案
2017年山东成人高考专升本高等数学(二)真题及答案一、选择题：1－10小题，每小题4分，共40分。
在每小题给出的四个选项中，只有一项是符合题目要求的，将近选项前的字母填涂在答题卡相应题号的信息点上。
确答案：A【解析】根据函数的连续性立即得出结果【点评】这是计算极限最常见的题型。
在教学中一直被高度重视。
正确答案：【解析】使用基本初等函数求导公式【点评】基本初等函数求导公式是历年必考的内容，我们要求考生必须牢记。
正确答案：C【解析】使用基本初等函数求导公式【点评】基本初等函数求导公式是历年必考的内容，我们要求考生必须牢记。
【答案】D【解析】本题考查一阶求导简单题，根据前两个求导公式选D正确答案：D【解析】如果知道基本初等函数则易知答案；也能根据导数的符号确定【点评】这是判断函数单调性比较简单的题型。
正确答案：A【解析】基本积分公式【点评】这是每年都有的题目。
【点评】用定积分计算平面图形面积在历年考试中，只有一两年未考。
应当也一直是教学的重点正确答案：C【解析】变上限定积分求导【点评】这类问题一直是考试的热点。
正确答案：D【解析】把x看成常数，对y求偏导【点评】本题属于基本题目，是年年考试都有的内容【点评】古典概型问题的特点是，只要做过一次再做就不难了。
二、填空题：11－20小题，每小题4分，共40分，把答案写在答题卡相应题号后。
【解析】直接代公式即可。
【点评】又一种典型的极限问题，考试的频率很高。
【答案】0【解析】考查极限将1代入即可，【点评】极限的简单计算。
【点评】这道题有点难度，以往试题也少见。
【解析】求二阶导数并令等于零。
解方程。
题目已经说明是拐点，就无需再判断【点评】本题是一般的常见题型，难度不大。
【解析】先求一阶导数，再求二阶【点评】基本题目。
正确答案：2【解析】求出函数在x=0处的导数即可【点评】考查导数的几何意义，因为不是求切线方程所以更简单了。
【点评】这题有些难度。
很多人不一定能看出头一步。
2017年重庆成人高考专升本大学语文真题及答案
2017年重庆成人高考专升本大学语文真题及答案一、选择题：本大题共20个小题，每小题2分，共40分。
在每小题给出的四个选项中，只有一项是符合题目要求的，把所选项前的字母填在题后的括号内。
1.我国先秦时期著名的语录体散文集是()A.《孟子》B.《论语》C.《庄子》D.《老子》2.“民为贵，社稷次之，君为轻”的提出者是()A.孔子B.孟子C.韩非子D.荀子3.《谏逐客书》中，“弃黔首以资敌国，却宾客以业诸侯”所采用的修辞方法是()A.比喻B.层递C.对偶D.对比4.《五代史伶官传序》一文的中心论点是()A.盛衰之理，虽日天命，岂非人事哉B.祸患常积于忽微，而智勇多困于所溺C.满招损，谦得益D.忧劳可以兴国，逸豫可以亡身5.“譬如为山，未成一篑，止，吾止也;譬如平地，虽复一篑，进，吾往也”这段话所用的逻辑论证方法是()A.演绎、对比B.归纳、对比C.类比、归纳D.对比、比喻6.鲁迅在《灯下漫笔》中，用“人肉的筵宴”为喻是为了说明()A.中国文明的实质B.中国精神文明的核心C.奴化心态D.中国历史的可怕7.《郑伯克段于鄢》中“大都不过参国之一”，“参国之一”的意思是()A.参加国之一B.三个国家中的一个C.三个国都中的一个D.国都的三分之一8.“其身正，不令而行;其身不正，虽令不从”的原出处是()A.《史记》B.《论语》C.《左传》D.《资治通鉴》9.韩愈的《张中丞传后叙》中，与刻画南霁云性格的描写无关的是()A.博闻强记B.拔刀断指C.义不忍食D.射塔明志10.属于唐宋八大家的是()A.白居易B.刘禹锡C.柳宗元D.李白11.茅盾的第一篇长篇小说是()A.《幻灭》B.《子夜》C.《霜叶红似二月花》D.《虹》12.巴金创作的长篇小说三部曲最著名的是()A.《蚀》三部曲B.“爱情三部曲”C.“激流三部曲”D.“抗战三部曲”13.“分崩离析”“贻笑大方”“形影相吊”三个成语依次出自()A.《季氏将伐颛臾》《庄子•秋水》《陈情表》B.《寡人之于国也》《庄子•秋水》《陈情表》C.《季氏将伐颛臾》《寡人之于国也》《庄子•秋水》D.《陈情表》《庄子•秋水》《季氏将伐颛臾》14.《灯下漫笔》中，鲁迅认为青年的使命是()A.崇奉国粹B.热心复古C.创造第三样时代D.赞颂固有精神文明15.下列加点字解释错误的是()A.淇水汤汤，渐车帷裳。
2017年成人高考高数真题及答案解析
2017年成人高等学校专升本招生全国统一考试高等数学（一）一、选择题：每小题4分，共40分，在每小题给出的四个选项中，只有一项是符合题目要求。
1.当0→x 时，下列变量是无穷小量的为（ ） A.21xB.x2 C.x sin D.()e x +ln 2.=⎪⎭⎫⎝⎛+→xx x 21lim 0（ ） A.e B.1-e C.2e D.2-e3.若函数()⎪⎩⎪⎨⎧=≠=-0,0,21x a x e x f x，在x=0处连续，则常数a=（ ） A.0 B.21C.1D.2 4.设函数()x x x f ln =，则()='e f （ ） A.-1 B.0 C.1 D.25.函数()x x x f 33-=的极小值为（ ） A.-2 B.0 C.2 D.46.方程132222=++z y x 表示的二次曲面是（ ） A.圆锥面 B.旋转抛物面 C.球面 D.椭球面7.若()1210=+⎰dx k x ，则常数=k （ ） A.-2 B.-1 C.0 D.18.设函数()x f 在[]b a ,上连续且()0>x f ，则（ ） A.()0>dx x f ba ⎰B.()0<dx x f ba ⎰C.()0=⎰dx x f ba D.()dx x f ba⎰的符号无法确定9.空间直线231231-=-+=-z y x 的方向向量可取为（ ） A.（3，-1,2） B.（1，-2,3） C.（1,1，-1） D.（1，-1，-1）10.一直a 为常数，则幂级数()∑∞=+-121n nan （ ） A.发散 B.条件收敛 C.绝对收敛 D.敛散性与a 的取值有关 二、填空题：11～20小题，每小题4分，共40分。
将答案填写在答题卡相应题号后。
11.()=--→2sin 2lim2x x x _________12.曲线121++=x x y 的水平渐进方程为_________ 13.若函数()x f 满足()21='f ，则()()=--→11lim 21x f x f x _________ 14.设函数()xx x f 1-=，则()='x f _______15.()⎰-=+22cos sin ππdx x x _______16.⎰+∞=+0211dx x __________ 17.一直曲线22-+=x x y 的切线l 斜率为3，则l 的方程为_________ 18.设二元函数()y x z +=2ln ，则=∂∂xz_________ 19.设()x f 为连续函数，则()='⎪⎭⎫ ⎝⎛⎰xdt t f 0__________ 20.幂级数∑∞=03n n nx 的收敛半径为_________三、解答题：21～28题，共70分，接答应写出推理、演算步骤21.求201sin lim x x e x x --→22.设⎪⎩⎪⎨⎧+=+=3211ty tx ，求dx dy23.已知x sin 是()x f 的一个原函数，求()⎰'dx x f x24.计算dx x⎰+401125.设二元函数122+-+=y x y x z ，求yx zx z ∂∂∂∂∂2及26.计算二重积分⎰⎰+Ddxdy y x 22，其中区域(){}4,22≤+=y x y x D27.求微分方程2x dxdyy 的通解28.用铁皮做一个容积为V 的圆柱形有盖桶，证明当圆柱的高等于底面直径时，所使用的铁皮面积最小2017年成人高等学校专升本招生全国统一考试高等数学（一）试题答案解析1.【答案】C【解析】00sin sin lim 0==→x x2.【答案】C【解析】222021lim 21lim e x x xx xx =⎪⎭⎫ ⎝⎛+=⎪⎭⎫ ⎝⎛+⋅→→3.【答案】B【解析】因为函数()x f 在0=x 处连续，则()()21021lim lim 00====-→→f a e x f x x x4.【答案】D【解析】因为()()1ln ln ln +='+='x x x x x f ，所以()21ln =+='e e f 5.【答案】A【解析】因为()332-='x x f ，令()0='x f ，得驻点11-=x ，12=x ，又()x x f 6='' ()0<61-=-''f ，()0>61=''f ，所以()x f 在12=x 处取得极小值，且极小值()2311-=-=f6.【答案】D【解析】可将原方程化为13121222=++z y x ，所以原方程表示的是椭球面。
2017年成人高考专升本英语真题及答案
2017年成人高考专升本英语真题及答案第1卷(选择题，共125分)I.Phonetics(5points)Directions:In each of the following groups of words,there are four underlined letters or letter combinations marked A,B,C and pare the underlined parts and iden-tify the one that is different from the others in pronunciation.Mark your answerby blackening the corresponding letter on the Answer Sheet.1.A.penalty B.moment C.quarrel D.absent2.A.sympathy B.material C.courage D.analysis3.A.starvation B.suggestion C.satisfaction D.situation4.A.donkey B.turkey C.money D.obey5.A.revise B.consist C.advertise D.visitⅡ.Vocabulary and Structure(15points)Directions:There are15incomplete sentences in this section.For each sentence there are four choices marked A,B,C and D.Choose one answer that best completes the sentence and blacken the corresponding letter on the Answer Sheet.6.Jonathan and Joe left the house to go for__after supper.A.walkB.the walkC.wallksD.a walk7.He pointed at the new car and asked,"___is it?Have you ever seen it before?"A.WhyB.WhereC.WhoD.Whose8.My father asked__to help with his work.A.I and TomB.Tom and meC.me and TomD.Tom and I9.Nowadays little knowledge__to be a dangerous thing.A.seemB.seemedC.does seemD.do seem10.If their marketing team succeeds,they__their profits by20percent.A.will increaseB.would be increasingC.will have increasedD.would have been increasing11.You'd better take these documents with you__you need them for the meeting.A.unlessB.in caseC.untilD.so that12.I haven't been to a pop festival before and Mike hasn't__A.tooB.as wellC.neitherD.either13.__is known to the world,Mark Twain was a great American writer.A.AsB.OnceC.ThatD.It14.John complained to the bookseller that there were several pages______in the dictionary.ckingB.losingC.missingD.dropping15.Not until the game had begun__at the sports ground.A.should he have arrivedB.would he have arrivedC.did he arriveD.had he arrived16.Moviegoers know that many special effects are created by computers, they often don'tknow is that these scenes still require a lot of work.A.ThatB.WhomC.WhatD.How17.The president is to give a formal__at the opening ceremony.A.speechB.debateC.discussionD.argument18.When I am confronted with such questions,my mind goes__,and I can hardly remember myown date of birth.A.faintB.blankC.darkD.blind19.If they are willing to lend us the money we need,all our problems will be__A.solvedB.causedC.coveredD.met20.This article__more attention to the problem of cultural conflicts.A.cares forB.allows forC.applies forD.calls forⅢ.Cloze(30points)Directions:For each blank in the following passage,there are four choices marked A, B0Cand D.Choose the one that is most suitable and mark your answer by blackeningthe corresponding letter on the Answer Sheet.What enables some people to get big creative breakthroughs while others only get small and non-creative breakdowns,blaming themselves and society?Are some people"gifted"?Are there other factors21work--factors that we have more control over than we think?While nobody can deny the22that some people seem to be blessed with particular creativity,research shows that anyone can23their chances of coming up with new and original ideas24they would only engage themselves more in the process of25.It's the old Thomas Edison thing about"discovery 2699percent perspiration(汗水)and1percent inspiration."27,the studies prove this:great creative breakthroughs usually happen only 28intense periods of struggle.It is sustained effort towards a specific goal29 eventually prepares for great creative insights.This kind of sustained effort does not always30immediate results,a fact that not only separates the innovators(革新者)from non-innovators,but31 leads some people to conclude that it is just not32for them."Maybe I should have gone to medical school like my mother wanted,"they wonder when thebreakthrough is33to be found.Alas,one forgets during inevitable encounters 34self-doubt,that the big surprise is never35.Indeed,it can happen at any time and place.21.A.to B.in C.at D.by22.A.issue B.problem C.reason D.fact23.A.miss B.reduce C.increase D.lose24.A.because B.if C.while D.whether25.A.creation B.practice C.production D.achievement26.A.being B.be C.was D.were27.A.Sooner or laterB.Some day or otherC.Every now and thenD.Time and again28.A.beyond B.after C.above D. through29.A.that B.who C.what D.as30.A.create B.produce C.inspire D.encourage31.A.too B.once C.again D.also32.A.good B.difficult C.possible D.stupid33.A.anywhere B.everywhere C.somewhere D. nowhere34.A.against B.across C.with D.into35.A.far away ed up C.cleared off D.near by IV.Reading Comprehension(60points)Directions:There are five reading passages in this part.Each passage is followed by four questions.For each question there are four suggested answers marked A,B,C and D.Choose the best answer and blacken the corresponding letter on the Answer Sheet.Passage OneDebate is a valuable way to practise communicating.It can also bring long-lasting rewards,especially for people working with Western businesses.The main activity of debate is presenting one's opinion and suppmting it with evidence,such as statistics or facts.It is a way of persuasive communication. Charles Lebeau helped create the"Discover Debate"method.He says debate is important to understanding how people communicate in Western business. Successful debaters learn how to give their opinkm,reasans and support."What we are trying to do is to develop a kind of thinking or approach to discussion and how to interact(交流)with someone else's opinion,rather than brush their opinion aside."Debate skills are also important in selling a product,he says.In that situation,the judges are the customem."So on Monday,for example,one company may come in and present their case to the customer and they"ll make as strong a ease as theycan.On Tuesday,the next day,another company will come in and present their ease to the ually the party that can present the strongest case wins”Debate also strengthens critical thinking.In other words,it helps students learn to ask questionsand try to understand someone's reasons and evidence.lift-. Lebeau points out that successful debaters learn to listen carefully to what other people are saying.Then,they look for the weak points in someone else's opinion or argument.He says debate teaches a systematic way of questioning.Successful debaters also learn to think from someone else's point of view.Mr.Lebeau says debate can help broaden the mind."There's an expression in English:don't criticize another person before you have walked in their shoes.I think the wonderful thing about debate is,it puts us in another person's shoes."36.According to Paragraph1,what is the purpose of debate?A.To bring long-lasting material rewards.B.To present evidence such as statistics and facts.C.To respond to questions in a systematic way.D.To persuade people to accept your opinions.37.Why is debate important.9A.It helps people understand others better.B.It allows people to present their opinions.C.It develops one's thinking and communicative competence.D.It gives one the opportunity to brush others'opinion aside.38.What does the underlined word"case"in Paragraph3refer to?A.Container.B.Evidence.C.Problem.D.Product.39.What can debaters benefit from"walking in another person's shoes".9A.Becoming more broad-minded.B.Developing critical thinking.C.Finding others'weak points.D.Trying out others'methods.Passage TwoWe all love a hero,and rescue dogs are some of the biggest heroes of all.You will often find them going above and beyond duty to save someone,risking--and at times losing--their lives in the process.Rescue dogs are generally found in the Sporting and Hunting Groups,or from the traditional Herding Group.These types include the Bloodhound,Labrador Retriever,Newfoundland,German Shepherd,Golden Retriever,and Belgian Malinois--all of which are chosen for search-and-rescue duty because of their amazing physical strength,loyalty,and their tendency for mental stability.These types also have a keen sense of hearing and smell--to better locate lost individuals—and are often able to access hard-to-reach areas.As highly trained animals,they serve in many different fields,including specialist search,snow slide rescue,dead body location,and tracking.To overcome obstacles and succeed when performing the demanding duties ofa search-and-rescue worker,a dog must display certain qualities.In addition to intelligence and strength,the dog must be swift,confident,easily trainable, adaptable,and have a high level of stamina(耐力)and endurance.A strong sense of group cooperation and an ability to engage in friendly play during"down"time is also required of search-and-rescue dogs.A rescue dog goes through many,many hours of intensive training to be fit for duty.Training is not for the faint-hearted.Certification training can take from two to three years,working three to four hours a day,three to six days a week,often in group,team-oriented sessions.Each search-and-rescue field requires different types of training.Rescue training,for instance,includes"air scenting"--where dogs are trained to smell the air for the victim's scent(气味)and then follow the scent to the person.This ability is crucial to finding victims trapped under collapsed buildings and snow slide.40.Rescue dogs are chosen probably because__A.they are loyalB.they are braveC.they have amazing appearancesD.they have good eyesight41.What does"faint-hearted"in Paragraph5mean??A.Courageous.B.Cowardly.C.Energetic.D.Slow.42.Which ability is most important for dogs to rescue people trapped in snow?A.Sharp hearing.B.Swift movement.C.Extraordinary smelling.D.A strong memory.43.What is the passage mainly about?A.Selection process of rescue dogs.B.Qualities and training of rescue dogs.C.Risks rescue dogs are faced with.D.Types of tasks rescue dogs can perform.Passage ThreeEating an apple a day doesn't keep the doctor away,but it does reduce the amount of trips you make to the drug store per year.That's according to a new study that investigates whether there's any truth in the old saying.A team of researchers led by Dr Matthew Davis,of the University of Michigan School of Nursing,asked8,399participants to answer survey questions about diet and health.A total of753were apple eaters,consuming at least149g of raw apple per day.The remaining7,646were classed as non-apple eaters.When both groups answered questions on trips to the doctor and trips to the drug store per year,the apple eaters were found to be27%less likely to visit the druggist for drugs.Trips to the doctor were not significantly affected by apple consumption, though."Evidence does not support that an apple a day keeps the doctor away. However,the small number of US adults who eat an apple a day does appear to use fewer prescription medications,"the study concludes.Apple eaters were also found to be less likely to smoke and be more likely tohave a higher educational attainment than non-apple eaters.While apples do not compete with oranges,they docontain some immune(免疫的)system-increasing vitamin C,which may be why apple-eaters visit the druggist less.With over8mg of vitamin C per medium-sized fruit,an apple can provide roughly14%your daily recommended intake.Previous studies have also linked apple consumption to a lower risk of Type2 diabetes(二型糖尿病),improved lung function and a lower risk of colon(结肠) cancer.44.How many non-apple eaters answered survey questions in the research?A.149.B.7,646.C.753.D.8,399.45.What is the conclusion of the study?A.Apple consumption has greatly reduced US adults'trips to the doctor.B.An apple a day does keep the doctor away.C.Apples are far more nutritious than oranges.D.A small number of US adult apple eaters tend to take less medicine.46.What can we learn from the passage?A.Apples are better than oranges.B.Apples do have some vitamin C to increase the immune system.C.Apples can help cure certain diseases.D.Apples can provide people with sufficient daily intake of energy.47.What can be described as the writing style of this passage?A.Objective.B.Creative.C．subjectiveD．persuasivePassage FourSometimes I scratch my head when I read about the government's efforts to improve schools:new standards and tests to be applied,strict teacher evaluations, and threats of school closures and job losses.They frighten the school employees, not to mention the students.Instead of making people unable to solve problems or try new ideas--which is what fear does to us--research on school reform strongly suggests that policy-makers should encourage school leaders to take a more humane approach.In their study on the reform efforts of twelve Chicago public schools,Bryk and Schneider found that enabling positive social relationships between the adults was the key to successful school improvement and that trust was at the heart of those relationships.Trust in schools comes down to one thing:psychological safety or safety to speak one's mind,to discuss with openness and honesty what is and isn't working,to make collective decisions.Yet this kind of safety doesn't come easily to schools.According to Bryk and Schneider,the adults in school rely on each other to do their jobs correctly and with integrity（正直).The challeage is that our expectations are very diverse based on our unique backgrounds.At one school where I taught,each teacher had different expectations about how much effort teachers should put into their work--a big difference between the teachers who left af~the last bell and those who worked into the evening.And when expectations are uncoasci or unspoken,it becomes impossible for others to live up to them.We also make assumptions about the intentions behind a person's behavior. As we all Imam,assumptions are often wrong.For example,parents and teachers my think the principal taml particular decision based on his career advancement rather than hat"s best for the studeata.don't feel psychologically safe to question our assumptions and e~aecmtiatm,trust itiea am the window and our relationships suffer.48.According to Paragraph1,why does the author scratch his head?A.Because he doesn't know what to do once schools are closed.B.Because he is not sure about the practicability of those new tests.C.Because he is concerned that many teachers will lose their jobs.D.Because he is not in favor of the government's reform efforts.49.According to Bryk and Schneider,what was most important for successfulschool improvemt?A.New standards and tests in schools.B.Positive social relationships.C.Strict teacher and student evaluations.D.Assistance of the government.50.What is meant by trust in school?A.Freedom to express one's views,B.Extra effort teachers put into their work.C.Independence of the teachers in schools.D.Unconscious and unspoken expectations.51.What does the author say about the assumptions made about the intentions behind a person's behavior?A.They should be trusted.B.They are often bold.C.They are often incorrect.D.They should be encouraged.Passage FiveAn interesting project called Blue Zones is recording the lifestyle secrets of the communities with the highest,hest concentrations of centenarians in the world.The people in the five regions in Europe,Latin America,Asia and the US that live to be100have a lot going for them.Genes probably play a small role,but thesefolks also have strong social ties,tightly-knit families and lots of opportunities to exercise.As we were examining the dietary secrets of the Blue Zones,as described in author Dan Buettner"s latest book,The Blue Zones Solution,we were struck by how essential tea drinking is in these regions.In fact,Buettner's Blue Zones Beverage Rule--a kind of guideline summarized from his15or so years of studying these places--is:"Drink coffee for breakfast,tea in the afternoon,wine at5p.tm"Science has plenty to say about the healthful virtues of green tea.Researchers are most enthusi-astic almt the components in green tea,as well as foods like cocoa.Why might they help so many Okina~vans in Japan break1007Some components in green tea can lower the risk of stroke,heart disease attd several cancers.One review study also found that drinking green tea can slightly improve metabolism(新陈代谢).If you find yourself on the island of Ikaria,the Greek Blue Zone in the middle of the Aegean,you won't be offered any tea made with tea leaves.Instead,Ikarians typically make their daily cup of tea with just one fresh herb that they have picked themselves that day--either rosemary,wild sage,oregano,nmrjotmn,mint or dandelion,all plants that may have anti-inflammatory(消炎的)properties,which may help lower blood pressure.This could explain Ikaria's very low dementia (痴呆)rate,since high blood pressure is a risk factor for the disease.52.What does the underlined word"centenarians"in Paragraph1refer to?A.People who have secret lifestyles.B.People who enjoy physical exercise.C.People who are one hundred years old or older.D.People who carry the gene for being slim.53.According to Paragraph3,what is the recommended time for tea drinking?A.In the morning.B.Any time of a day.C.In the early evening.D.In the afternoon.54.What may the tea Ikarians drink daily help?A.To improve metabolism.B.To lower blood pressure.C.To lower life stress.D.To improve social relationships.55.What might be the best title of the passage?A.Tea-Drinking TipsB.Lifestyle Secrets of IkariansC.Tea-Drinking Ceremony in OkinawaD.Blue Zones SolutionsⅤ.Daily Conversation(15points)Directions:Pick out appropriate expressions from the eight choices below and complete thefollowing dialoaue by blackenina the corresuondina letter on the Answer Sheet.Woman:Hello,Mr.Johnson's office.Man:Good morning.56？Woman:Sorry,he's in a meeting at the moment.57？Man:Yes.This is Steve Lee from Brightlight Systems.58？Woman:Tomorrow afternoon in your office.Man:59Woman:Okay.60Man:Thank you.第Ⅱ卷(非选择题，共25分)Ⅵ.Writing(25points)Directions:For this part,you are supposed to write an essay in English in100-120 words based on the following information.Remember to write it clearly.61．你(Li Yuan)组织同学进行了一次烧烤野餐(barbecue)。
2017年成人高考专升本大学语文考试文言文试题及答案十一
阅读本⽂内容，回答下⾯试题： 李将军⼴者，陇西成纪⼈也。
其先⽈李信，秦时为将，逐得燕太⼦丹者也。
故槐⾥，徙成纪。
⼴家世世受射。
孝⽂帝⼗四年，匈奴⼤⼊萧关，⽽⼴以良家⼦从军击胡，⽤善骑射，杀⾸虏多，为汉中郎。
⼴从弟李蔡亦为郎，皆为武骑常侍，秩⼋百⽯。
尝从⾏，有所旻陷折关及格猛兽，⽽⽂帝⽈：“惜乎，⼦不遇时!如令⼦当⾼帝时，万户侯岂⾜道哉!” 及孝景初⽴，⼴为陇西都尉，徙为骑郎将。
吴楚军时，⼴为骁骑都尉，从太尉亚夫击吴楚军，取旗，显功名昌⾢下。
以梁王授⼴将军印，还，赏不⾏。
徙为上⾕太守，匈奴⽇以合战。
典属国公孙昆邪为上泣⽈：“李⼴才⽓，天下⽆双，⾃负其能，数与虏敌战，恐亡之。
”於是乃徙为上郡太守。
後⼴转为边郡太守，徙上郡。
尝为陇西、北地、雁门、代郡、云中太守，皆以⼒战为名。
匈奴⼤⼊上郡，天⼦使中贵⼈从⼴勒习兵击匈奴。
中贵⼈将骑数⼗纵，见匈奴三⼈，与战。
三⼈还射，伤中贵⼈，杀其骑且尽。
中贵⼈⾛⼴。
⼴⽈：“是必射雕者也。
”⼴乃遂从百骑往驰三⼈。
三⼈亡马步⾏，⾏数⼗⾥。
⼴令其骑张左右翼，⽽⼴⾝⾃射彼三⼈者，杀其⼆⼈，⽣得⼀⼈，果匈奴射雕者也。
已缚之上马，望匈奴有数千骑，见⼴，以为诱骑，皆惊，上⼭陈。
⼴之百骑皆⼤恐，欲驰还⾛。
⼴⽈：“吾去⼤军数⼗⾥，今如此以百骑⾛，匈奴追射我⽴尽。
今我留，匈奴必以我为⼤军诱，必不敢击我。
”⼴令诸骑⽈：“前!”前未到匈奴陈⼆⾥所，⽌，令⽈：“皆下马解鞍!”其骑⽈：“虏多且近，即有急，柰何?”⼴⽈：“彼虏以我为⾛，今皆解鞍以⽰不⾛，⽤坚其意。
”於是胡骑遂不敢击。
有⽩马将出护其兵，李⼴上马与⼗馀骑饹射杀胡⽩马将，⽽复还⾄其骑中，解鞍，令⼠皆纵马卧。
是时会暮，胡兵终怪之，不敢击。
夜半时，胡兵亦以为汉有伏军於旁欲夜取之，胡皆引兵⽽去。
平旦，李⼴乃归其⼤军。
⼤军不知⼴所之，故弗从。
居久之，孝景崩，武帝⽴，左右以为⼴名将也，於是⼴以上郡太守为未央卫尉，⽽程不识亦为长乐卫尉。
程不识故与李⼴俱以边太守将军屯。
2017年成人高考专升本教育理论考试真题及答案
2017年成人高考专升本教育理论考试真题及答案本试卷共两部分，满分150分，考试时间150分钟。
教育学部分一、选择题：1～12小题，每小题2分，共24分。
在每小题给出的四个选项中，只有一项是符合题目要求的。
1．最早明确提出“长善救失”“教学相长”“不陵节而施”等教学思想的文献是（）。
A．《大学》B．《论语》C．《学记》D．《孟子》2．杜威的《民主主义与教育》中体现的教育理论派别属于（）。
A．实验教育学B．实用主义教育学C．文化教育学D．批判教育学3．在教育起源问题上，历来存在不同的观点。
其中，以美国学者孟禄为代表主张的是（）。
A．生理起源说B．劳动起源说C．心理起源说D．交往起源说4．在影响人身心发展的诸因素中，起主导作用的是（）。
A．遗传B．环境C．教育D．主观能动性5．教育活动开展的出发点和归宿是（）。
A．教育目的B．教育制度C．教育内容D．教育途径6．我国现代学制确立和发展中所沿用的基本类型是（）。
A．单轨学制B．双轨学制C．分支学制D．多轨学制7．人们把教师在教学过程中遇到偶发事件能做出巧妙、恰当处理的行为称为“教育机智”。
这体现了教师劳动的哪一特点？（）。
A．创造性B．主体性C．广延性D．间接性8．我国《基础教育课程改革纲要》规定，在学校课程中设置综合实践活动作为必修课程。
其设置的时段为（）。
A．小学一年级到高中阶段B．小学三年级到初中阶段C．小学三年级到高中阶段D．初中到高中阶段9．中小学教材编写、教学、评估和考试命题的基本依据是（）。
A．教学目标B．课程目标C．课程计划D．课程标准10．王老师在小学语文课上，结合课文内容用生动形象的语言给学生描绘了深秋层林尽染、色彩斑斓的山林风光。
这体现的教学原则是（）。
A．理论联系实际原则B．启发性原则C．直观性原则D．循序渐进原则11．张老师在班主任工作中，经常采用表扬、奖励、批评、处分等方法来提高学生思想品德水平。
这种德育方法是（）。
A．说服教育法B．个人修养法C．榜样示范法D．品德评价法12．每个新人职教师都应学会做班主任工作，而班主任工作的中心是（）。
2017年广东成人高考专升本高等数学(一)真题及答案
♦ 2017年广东成人高考专升本高等数学(一)真题及答案1.当x→0时,下列列变量量是⽆无穷⼩小量量的为 1 A. x 2B. 2xC. sin xD. ln(x e )lim(1 2 )x2. x xA.eB. e1C. e 2D. e2⎧ 1e x , x 0⎫3.若函数 f (x ) ⎪ 2⎪⎩a , x 0, 1⎪ ⎬ ⎪⎭ 在x=0处连续，则常数a=A.0B. 2C.1D.2设函数 f (x ) x ln x ,则 f (e )A.-1B.0C.1.2函数f (x ) x 33x 的极⼩小值为 A.-2 B.0 C.2 D.4⽅方程 x 2 2 y 2 3Z 21 表示的⼆二次曲⾯面是圆锥⾯面 旋转抛物⾯面 球⾯面 椭球⾯面1(2x k ) dx 1 若 0,则常数k=A.-2B.-1C.0D.1设函数f(x)在[a,b]上连续且f(x)>0, 则bf (x ) dx0 abf (x ) dx0 abf (x) dx 0 a∞b f (x ) dx a的符号⽆无法确定x 1 y 2 z 3空间直线 3 A. (3,-1,2)B. (1, -2,3)C. (1,1,-1)D. (1,-1,-1) 1 2 的⽅方向向量量可取为 (1)n已 知 a 为常数,则级数 n 1 n a 2发散 条件收敛 绝对收敛收敛性与a 的取值有关limx 2 11. x 2 sin(x 2) . 曲线yx 12x 1 的⽔水平渐近线⽅方程为 .limf (x )f (1)若函数f(x)满⾜足f’(1)=2，则 x 1 x 21.设函数 f (x ) x 1x ， 则f'(x) =.2(sin x cos x ) dx 2.1+ x ∞12 dx16. 0 .已知曲线 y x 2 x 2 的切线L 斜率为3,则L 的⽅方程为.z设⼆二元函数 z ln(x 2y ) ,则x.设f(x)为连续函数,则 x(f (t ) dt ) 0 .x n幂级数 n 0 3n的收敛半径为 .lim求 x 0 e x sin x 1x 2 ⎧⎪x 1t 2 ,⎫⎪dy⎨y 1t 3 ,⎬22.设⎪⎩⎪⎭ ，求 dx已知sinx 是f(x) 的⼀一个原函数,求xf (x ) dx计算xf(x ) dxz2z百度文库资料店设⼆二元函数z x 2 y2 x y 1,求y 及x y百度文库资料店=计算⼆二重积分 D x 2 y 2 dxdy,其中区域 D(x , y ) | xy 24求微分⽅方程y dy x 2dx的通解28.⽤用铁⽪皮做⼀一个容积为V 的圆柱形有盖桶,证明当圆柱的⾼高等于底⾯面直径时,所使⽤用的 铁⽪皮⾯面积最⼩小.1~5 CCBDA 6~10 DCAABy1 参考答案1111.[答案]112.2 13.1 14.2xx 215.216. 2 17.3x-y-3=0 18. x 2 y19.f(x) 20.3 lim e x sin x 1 2 lim e x cos xlime x sin x 1 21. x 0x x 0 2x x 0 2 2dy2dydt3t3dx dxdtt 2t2因为sinx 是f(x)的⼀一个原函数,所以xf (x ) dx xf (x ) f (x ) dx xf (x )sin x Cx2百度文库资料店设t ,则x t2 , dx 2tdt,0 t 2 .· |r 4 122t1 xdx1 tdx0 02 1 2(1 1 t)dt2 ⎡t | 2 ln(1 t ) |2 ⎤ ⎣ 0 0 ⎦2(2 ln 3) 4 2 ln 3因为 z x 2 y 2x y 1,所以 z 2x 2y 1 y z 2xy 21x2zxy 4xy26.D 可表示为0 2 ,0 r 2x 2 y 2dxdy r ·r dr dDD22dr 2 dr 0 02 13 230 16 3 y dy x 2 , dxydy x 2 dx ,两边同时积分， 1 y 2 1 x 3 C ,2 313y 2 2x 3 Cy2 2x2 C即31设圆柱形的底⾯面半径为r,⾼高为h,则V r 2 h ,令dS4 r 2 h 0,dr2r h d 2 S4dr 2于是由实际问题得,S 存在最⼩小值，即当圆柱的⾼高等于底⾯面直径时,所使⽤用的铁⽪皮⾯面积最 ⼩小.。