电大《微积分初步》(15春)期末复习考试试题及参考答案


    电微积分初步(15春)期末复考试试题参考答案
    填空题
     ⒈函数 .
    ⒉   1  .
     ⒊曲线处切线斜率  .
    ⒋原函数  .
    ⒌ 4 阶微分方程
    6函数 .
    7函数处连续 3 .
     8曲线点处切线方程 1 .
    9 .
    10微分方程阶数 3 .
    11函数定义域   .
    12  2 .
     13曲线点处切线方程 .
    14 0 .
    15微分方程特解 .
    16函数定义域    .
    17函数间断点  .
     18函数单调增加区间  .
    19 .
    20微分方程阶数 .
    21函数定义域    .
    23函数处连续 2 .
     24曲线点处斜率 .
    25 .
    26微分方程满足初始条件特解 .
     27函数 .
    28   0  时穷量
    29y x (x – 1)(x – 2)(x – 3)(1) .
    30     .
    31微分方程特解
    32函数定义域     .
    33函数处连续 1 .
     34曲线点处切线方程 .
    35 .
    36微分方程阶数 .
    37函数 .
    38     .
    39曲线点处切线方程 .
    40     .
    51微分方程阶数 5 .
    二单项选择题
    ⒈函数图形关(B )称.
      A坐标原点        B轴
      C.轴          D
    ⒉( C )时函数处连续
    A.0    B.1 C.    D.
    ⒊函数区间( D ) 
    A.单调减少   B.单调增加
    C.先减增  D.先增减
    ⒋列等式成立(A ).
      A.       B.
    C.      D.
    ⒌微分方程通解(B )
    A    B
    C D
    6设函数该函数(A ).
      A.奇函数  B.偶函数  C.非奇非偶函数 D.奇偶函数
    7已知( D )时穷量
    A.    B. C.  D.
    8函数区间( C ) 
    A.单调增加   B.单调减少
    C.先增减  D.先减增
    9等式成立( A )
    A. B.
    C. D.
    10列微分方程中分离变量方程(B )
    A    B
    C D
    11设函数该函数(A ).
    A.偶函数 B.奇函数  C.非奇非偶函数 D.奇偶函数
    12( C )时函数处连续
    A.0    B.1 C.    D.
    14列结中( C )正确.
    A.处连续定处微
    B.函数极值点定发生驻点
    C.处连续定处导
    D.函数极值点定发生导点
    15列等式中正确(D ).
      A      B
      C        D
    16微分方程阶数(B )
    A 2   B 3 C 4 D 5
    ⒈设函数该函数(B ).
      A.奇函数  B.偶函数  C.非奇非偶函数 D.奇偶函数
    17时列变量中穷量(C )
    A.    B. C.    D.
    18设( D ).
    A. B. C. D.
    19切线斜率2x积分曲线族中通点(1 4)曲线( C ).
    A. B.
    C.y x2 + 3 D. y x2 + 4

    20微分方程通解(A )
    A  B  C D
    21设( D )
    A.   B.  
    C.    D.
    22函数f (x)点x0处导( B )错误.
    A.函数f (x)点x0处定义 B.
    C.函数f (x)点x0处连续 D.函数f (x)点x0处微
    33函数区间( A ) 
    A.先减增  B.先增减
    C.单调减少   D.单调增加
    34( B )
    A B
    C D
    35微分方程阶数( C)
    A 1   B 2 C 3 D 5
    36函数定义域(C ).
    A.  B.  
    C. D.
    37曲线处切线斜率( D ).
    A. B. C. D.
    38列结正确( B ).
    A.(x0) 0x0必f (x)极值点
    B.x0f (x)极值点(x0)存必(x0) 0
    C.x0f (x)极值点x0必f (x)驻点
    D.存点x0定f (x)极值点
    39列穷积分收敛( A ).
      A.       B.
      C.         D.
    40微分方程阶数(D ).
    A 1 B 2 C 3 D 4
    41设( C )
    A.   B.  
    C.    D.
    42函数f (x)点x0处导( B)错误.
    A.函数f (x)点x0处定义 B.
    C.函数f (x)点x0处连续 D.函数f (x)点x0处微
    43函数区间( D) 
    A.单调增加   B.单调减少
    C.先增减  D.先减增
    44( A )
    A B
    C D
    45列微分方程中分离变量方程(B)
    A    B
    C D
    46设函数该函数( d).
    A.非奇非偶函数 B.奇偶函数  C.偶函数 D.奇函数
    47时列变量中穷量( c )
    A.    B. C.    D.
    48列函数指定区间单调减少( b ).
    A. B. C. D.
    49设(c ).
    A B C D
    50列微分方程中(a )线性微分方程.
    A. B.
    C. D.


     三计算题
    ⒈计算极限.


     ⒉设求


    ⒊计算定积分


    ⒋计算定积分

    5计算极限.


     6设求

    7计算定积分

    8计算定积分

    9计算极限.
    解:原式
     10设求
    解:

    11计算定积分
    解:
    12计算定积分
    解:
    13计算极限.
    解:原式
     14设求
    解: 9分

    15计算定积分
    解:
    16计算定积分
    解:
    17计算极限.
    解:原式
     18设求
    解:

    19计算定积分
    解:
    20计算定积分
    解:
    21计算极限.
    解:
     22设求
    解:

    23计算定积分
    解:
    24计算定积分
    解:
    25计算极限.
    解:原式
     26设求
    解: 9分

    27计算定积分
    解:
    28计算定积分
    解:
    29计算极限.
    解:原式
     30设求
    解:

    31计算定积分
    解:
    32计算定积分
    解:
    四应题
    1某制罐厂生产种体积V盖圆柱形容器问容器底半径高少时料省?



    2欲做底正方形容积32立方米长方体开口容器样做法料省?


    3欲做底正方形容积108立方米长方体开口容器样做法料省?
    解:设底边边长高材料已知

    令解唯驻点

    说明函数极值点时料省

    4欲做底正方形容积32立方米长方体开口容器样做法料省?
    解:设底边边长高材料已知

    令解惟驻点易知函数极值点时时料省. 16分

    5钢板焊接容积4底正方形盖水箱已知钢板方米10元焊接费40元问水箱尺寸选择总费低?低总费少?
    解:设水箱底边长高表面积



    问题存值函数驻点唯时水箱面积
    时费 (元)

    6钢板焊接容积4底正方形盖水箱已知钢板方米10元焊接费40元问水箱尺寸选择总费低?低总费少?
    解:设水箱底边长高表面积



    问题存值函数驻点唯时水箱表面积
    时费 (元)

    7欲做底正方形容积32立方米长方体开口容器样做法料省?
    解:设底边边长高材料已知

    令解惟驻点易知函数极值点时时料省. 16分

    8欲做底正方形容积108立方米长方体开口容器样做法料省?
    解:设长方体底边边长高材料已知

    令解唯驻点
    问题存值驻点唯函数极值点时料省
















    微积分初步考试仿真试题

    填空题(题4分题20分)
     ⒈函数 .
    ⒉     时穷量
    ⒊y x (x – 1)(x – 2)(x – 3)(1) .
    ⒋     .
    ⒌微分方程特解

    二单项选择题(题4分题20分)
    ⒈函数定义域( ).
    A.  B.  
    C. D.
    ⒉曲线处切线斜率( ).
    A. B. C. D.
    ⒊列结正确( ).
    A.(x0) 0x0必f (x)极值点
    B.x0f (x)极值点(x0)存必(x0) 0
    C.x0f (x)极值点x0必f (x)驻点
    D.存点x0定f (x)极值点
    ⒋列穷积分收敛( ).
      A.       B.
      C.         D.
    ⒌微分方程阶数( ).
    A 1 B 2 C 3 D 4
     三计算题(题44分题11分)
    ⒈计算极限.
     ⒉设求
    ⒊计算定积分
    ⒋计算定积分
    四应题(题16分)
    钢板焊接容积4底正方形盖水箱已知钢板方米10元焊接费40元问水箱尺寸选择总费低?低总费少?


    微积分初步模拟试题答案

    (供参考)


    填空题(题4分题20分)
     ⒈ ⒉0 ⒊ ⒋  ⒌
    二单项选择题(题4分题20分)
     ⒈C  ⒉ D  ⒊B   ⒋A  ⒌ D
    三(题44分题11分)
    ⒈解:
    ⒉解:

    ⒊解:
    4.解:
    四应题(题16分)
    解:设水箱底边长高表面积



    问题存值函数驻点唯时水箱表面积
    时费 (元)

    微积分初步 期末复指导
    考试方式:
    闭卷笔试90分钟
    考核形式考核成绩确定
    考核形式:作业考核期末考试相结合
    考核成绩:满分100分60分格中时作业成绩占考核成绩30%期末
    考试成绩占考核成绩70%
    考题试卷中学生提供导数积分基公式
    函数极限连续考核求
    1.解常量变量概念理解函数概念解初等函数分段函数概念熟练掌握求函数定义域函数值方法掌握复合函数分解成较简单函数方法
    2.解极限概念会求简单极限
    3.解函数连续概念会判断函数连续性会求函数间断点
    二 导数微分部分考核求
    1.解导数概念会求曲线切线方程
    2.熟练掌握求导数方法(导数基公式导数四运算法复合函数求导法)会求简单隐函数导数
    3.解微分概念掌握求微分方法
    4.解高阶导数概念掌握求显函数二阶导数方法
    三导数应考核求
    1.掌握函数单调性判方法
    2.解极值概念极值存必条件掌握极值判方法
    3.掌握求函数值值方法
    四元函数积分考核求
    1.理解原函数定积分概念性质掌握积分基公式掌握直接积分法第换元积分法分部积分法求定积分方法
    2.解定积分概念性质会计算简单定积分
    3.解广义积分概念会计算简单穷限积分
    五积分应考核求
    1.会定积分计算简单面曲线围成图形面积(直角坐标系)绕坐标轴旋转生成旋转体体积
    2.解微分方程概念掌握变量分离微分方程阶线性微分方程解法

    请您删容O(∩_∩)O谢谢2015年中央电期末复考试抄全电期末考试必备抄电考试必抄After earning his spurs in the kitchens of The Westin The Sheraton Sens on the Bund and a sprinkling of other topnotch venues Simpson Lu fi nally got the chance to become his own boss in November 2010 Sort of The Shanghaiborn chef might not actually own California Pizza Kitchen (CPK) but he is in sole charge of both kitchen and frontof house at this Sinan Mansions'stalwart  It’s certainly a responsibility to be the head chef and then to have to manage the rest of the restaurant as well the 31yearold tells Enjoy Shanghai In hotels for example these jobs are strictly demarcated so it’s a great opportunity to learn how a business operates across the board  It was a task that management back in sunny California evidently felt he was ready for and a vote of confi dence from a company that to date has opened 250 outlets in 11 countries And for added pressure the Shanghai branch was also CPK’s China debut  For sure it was a big step and unlike all their other Asia operations that are franchises they decided to manage it directly to begin with says Simpson  Two years ago a private franchisee took over the lease but the links to CPK headquarters are still strong with a mainlandbased 'brand ambassador’ on hand to ensure the business adheres to its ethos of creating innovative hearthbaked pizzas a slice of PR blurb that Simpson insists lives up to the hype  They are very innovative he says The problem with most fast food places is that they use the same sauce on every pizza and just change the toppings Every one of our 16 pizza sauces is a unique recipe that has been formulated to complement the toppings perfectly  The largely local customer base evidently agrees and on Saturday and Sunday at least the place is teeming The kidseatforfree policy at weekends is undoubtedly a big draw as well as is the spacious secondfl oor layout overlooked by a canopy of green from Fuxing Park over the road  The company is also focusing on increasing brand recognition and in recent years has taken part in outside events such as the regular California Week Still the sta are honest enough to admit that business could be better as good in fact as in CPK’s second outlet in the popular Kerry Parkside shopping mall in Pudong  Sinan Mansions has really struggled to get the number of visitors that were envisaged when it first opened and it hasn’t been easy for any of the tenants here adds Simpson We’re planning a third outlet in the city in 2015 and we will probably choose a shopping mall again because of the better foot traffic The tearooms once frequented by Coco Chanel and Marcel Proust are upping sticks and coming to Shanghai Xu Junqian visits the Parisian outpost with sweet treats One thing the centuryold Parisian tearoom Angelina has shown is that legendary fashion designer Coco Chanel not only had style and glamor but also boasted great taste in food pastries in particular One of the most popular tearooms in Paris Angelina is famous for having once been frequented by celebrities such as Chanel and writer Marcel Proust Now Angelina has packed up its French ambience efficient service and beautiful comforting desserts and flown them to Shanghai At the flagship dinein and takeout space in Shanghai everything mimics the original tearoom designed from the beginning of the 20th century in Paris the height of Belle Epoque The paintings on the wall for example are exactly the same as the one that depicts the landscape of southern France the hometown of the owner and the small tables are intentional imitations of the ones that Coco Chanel once sat at every afternoon for hot chocolate The famous hot chocolate known as L’Africain is a luxurious mixture of four types of cocoa beans imported from Africa blended in Paris and then shipped to Shanghai It’s sinfully sweet rich and thick as if putting a bar of melting chocolate directly on the tongue and the fresh whipped cream on the side makes a light but equally gratifying contrast It is also sold in glass bottles as takeaway The signature MontBlanc chestnut cake consists of three parts the pureed chestnut on top the vanilla cream like stuffing and the meringue as base Get all three layers in one scoop not only for the different textures but also various flavors of sweetness The dessert has maintained its popularity for a century even in a country like France perhaps the world’s most competitive place for desserts A much overlooked pairing is the ParisNew York choux pastry and N226 chocolate flavored tea The choux pastry is a mouthful of airy pecanflavored whipped cream while the tea a blend of black teas from China and Ceylon cocoa and rose petals offers a more subtle fragrance of flowers and chocolate Ordering these two items featuring a muted sweetness makes it easier for you to fit into your little black dress Breakfast brunch lunch and light supper are also served at the tearoom a hub of many cultures and takes in a mix of different styles of French cuisines according to the management team The semicooked foie gras terrine is seductive and deceptive It’s generously served at the size and shape of a toast while the actual brioche toast is baked into a curved slice dipped with fig chutney The flavor however is honest strong smooth and sublime And you don’t actually need the toast for crunchiness This is the season for high teas with dainty cups of fine china and little pastries that appeal to both visual and physical appetites But there is one high tea with a difference and Pauline D Loh finds out just exactly why it is special Earl Grey tea and macarons are all very well for the crucial recuperative break inbetween intensive bouts of holiday season shopping And for those who prefer savory to sweet there is still the selection of classic Chinese snacks called dim sum to satisfy and satiate High tea is a meal to eat with eye and mouth an inbetween indulgence that should be light enough not to spoil dinner but sufficiently robust to take the edge off the hunger that strikes hours after lunch The afternoon tea special at ShangXi at the Four Seasons Hotel Pudong has just the right elements It is a pampering meal with touches of luxury that make the high tea session a treat in itself Whole baby abalones are braised and then topped on a shortcrust pastry shell a sort of Chinese version of the Western volauvent but classier Even classier is the dim sum staple shrimp dumpling or hargow upgraded with the addition of slivers of midnight dark truffles This is a master touch and chef Simon Choi who presides unchallenged at ShangXi has scored a winner again Sweet prawns and aromatic truffles — what’s not to love His masterful craftsmanship is exhibited in yet another pastry — a sweet pastry that is shaped to look like a walnut but which you can put straight into the mouth It crumbles immediately and the slightly sweet nutty morsel is so easy to eat you’ll probably reach straight for another My favorite is the dessert that goes by the name yangzhi ganlu or ambrosia from the gods The hotel calls it chilled mango cream with sago pomelo and bird’s nest – made with ingredients that resonate with every female soul It does taste like ambrosia with the sweetsour fragrance of the mango forming the first layer of taste and sensation and the pomelo sacs and sago pearls providing the tactile contrast The bird’s nest — it’s the ingredient that gilds the lily since it is supposed to nourish and nurture a perfect complexion For those unfamiliar with this exotic ingredient the bird’s nest is not a bundle of twigs but is instead the dried secretion that cave swifts use to build their nest Technically it’s bird saliva but the Chinese believe that it has collagenboosting properties essential to beauty To me it just tastes good adding a slight gelatinous crunch to the back of the teeth There is also a baked mushroom puff pastry that includes the highly prized Matsutake or pine mushroom You also get a choice of teas but I strongly recommend the aged Pu’er from Yunnan province It is a mellow tea that will go perfectly with the rich little nuggets and will warm you up on a cold afternoon Incidentally the general guide is green tea such as Longjing or Dragonwell for the hot season semifermented teas like Wulong or Iron Buddha for autumn and more warming teas like Pu’er for winter The ShangXi afternoon tea costs 228 yuan (37) per person and 388 yuan for the more opule

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