2018年电大经济数学基础12期末复习重点资料考试小抄.doc

经济数学基础 12 期末复习资料一、单项选择题1下列函数中为偶函数的是（ ） (A) (B) sinyx=2yx=+(C) (D) 2- cos正确答案：A2下列函数中为奇函数的是（ ） (A) (B) sinyx=1lnxy-=+(C) (D) e-+2正确答案：B3下列各函数对中， （ ）中的两个函数相等A. 2(),()fxgx=B. 1,1f-+C. 2()ln,()lnfxgx=D. sico,()1=正确答案：D4下列结论中正确的是（ ） (A) 周期函数都是有界函数(B) 基本初等函数都是单调函数(C) 奇函数的图形关于坐标原点对称(D) 偶函数的图形关于坐标原点对称正确答案：C5下列极限存在的是（ ） A B 2lim1x01li2xC Dlisnx0liex正确答案：A6已知 ，当（ ）时， 为无()1sif=-)(xf穷小量A. B. C. D. 0xx正确答案：A7当 时，下列变量为无穷小量的是（ ）A B C Dln(1)x+2121ex-sin正确答案： D8函数 在 x = 0 处连12,(),xfxk续，则 k = ( )A-2 B-1 C1 D2 正确答案：B 9.曲线 在点 处的切线斜率是（ ） sinyx)0,(A) (B) (C) (D) 121-正确答案：D 10曲线 在点（0, 1）处的切线斜率为（ yx=+） 。A B C D212-3(1)x+3(1)x-+正确答案：B11若 ，则 （ ） ()cos2fx=()fA0 B1 C 4 D-4 正确答案：C 12下列函数在区间 上单调减少的是（ (,)） (A) (B) (C) (D) xcos2x-x22x正确答案：B 13下列结论正确的是（ ） (A) 若 ，则 必是 的极值点0()fx0x)(f(B) 使 不存在的点 ，一定是 的极值点x(C) 是 的极值点，且 存在，则必有0x)(f 0()f0()f(D) 是 的极值点，则 必是 的驻点x)(f0x)(f正确答案：C14设某商品的需求函数为 ，则当2()1epq-=时，需求弹性为（ ） 6p=A B3 C3 D5e- 2-正确答案：B15若函数 ， 则1()xf-=()1,gx+( )2fg-A-2 B-1 C-1.5 D1.5正确答案：A16函数 的连续区间是（ ） 1ln()yx=-A B 2（ ， ） （ ， ） 2， ） （ ， ）C D1（ ， ） 1， ）正确答案：A17设 ，则 =（ ） ln()dxfc)(xfA B C Dxln21l-2ln正确答案：C18下列积分值为 0 的是（ ） A B-sindx1-ed2xC D1-e2x(cos)x正确答案：C19若 是 的一个原函数，则下列等式成立)(xFf的是( ) A dxafB ()()xaC baFfbD ()d()fxF正确答案：B20.设 ， ， 是单位矩阵，则(12)A=(13)B-I（ ） TI-A B 3526C D12635正确答案：A21.设 为同阶方阵，则下列命题正确的是（ B,）.A.若 ，则必有 或 ABO=ABO=B.若 ，则必有 ,C.若秩 ,秩 ，则秩()()()D. 11-正确答案：B22当条件（ ）成立时， 元线性方程组n有解AXb=A. B. C. D. ()rn= = ()Cq980.536)q+20.5-令 =0，即 =0，得 =140， = -20.-1q2140（舍去） 。=140 是 在其定义域内的唯一驻点，且该问题q1C()确实存在最小值。所以 =140 是平均成本函数 的最小值点，即为1 q()使平均成本最低，每天产量应为 140 件. 此时的平均成本为= =176 （元/件） C()40980.536148已知某产品的销售价格 （单位：元件）是销p量 （单位：件）的函数 ，而总成本为q2q-（单位：元） ，假设生产的产品全部售()105=+出，求产量为多少时，利润最大？最大利润是多少？ 解：由已知条件可得收入函数 2()40qRqp-利润函数2()()(105)LCqq=-+23015-求导得 ()Lq令 得 ，它是唯一的极大值点，因此是最03=大值点 此时最大利润为20(30)15430L即产量为 300 件时利润最大最大利润是 43500 元 9. 设生 产某种产品 个单位时的成本函数为：x（万元）,求：当 时的总成2()106Cx=+10=本和平均成本；当产量 为多少时，平均成本最小？解：因为总成本、平均成本和边际成本分别为：；2()106Cxx=+，所以， ；2()10， 106C 2()x令 ，得 （ 舍去） ，可以验01x=0-证 是 的最小值点，所以当 时，平均成1x=)(Cx本最小10.设生产某产品的总成本函数为 (万()5Cx=+元)，其中 为产量，单位：百吨销售 百吨时的边际x收入为 （万元/百吨） ，求：利润最大时()12R的产量；在利润最大时的产量的基础上再生产 百吨，1利润会发生什么变化？解：因为边际成本为 ，边际利润()Cx()102LxR令 ，得 可以验证 为利润函数05=5x的最大值点. 因此，当产量为 百吨时利润最大. )(x当产量由 百吨增加至 百吨时，利润改变量为6（万元）6255(102)d(10)Lxx1=-即利润将减少 1 万元.11.某厂生产某种产品 q 件时的总成本函数为，单位销售价格为2()4.()Cq元，问产量为多少时可使利润最大？10.(p元 /件最大利润是多少？解：设产量为 q，则收入函数为 2()(140.).014RqLC220.10q因为边际利润 时，利润最大。()L则 ，得()0.41Lq250q产量为 250 时可使利润最大 2max.513最大利润为 1230 元请您删除一下内容，O(_)O 谢谢！2015 年中央电大期末复习考试小抄大全，电大期末考试必备小抄，电大考试必过小抄请您删除一下内容，O(_)O 谢谢！2015 年中央电大期末复习考试小抄大全，电大期末考试必备小抄，电大考试必过小抄The battle for young viewers CCTV is embracing Internet culture and working with independent producers on TV shows to woo audiences under 35. Han Bing bin reports. After charming audiences with his warm smile for 14 years, China Central Television host Li Jiaming recently found himself targeted by a group of young netizens unhappy with his style. The complaints came after Li hosted the premiere of Rising Star on Oct 31. It is a singing competition show that originated in Israel. Many young netizens found his hosting style slow and boring and mocked it as “CCTV evening gala style“. They even initiated an online campaign to replace him. The 40-year-old hosts reaction to the criticism was surprising. During the second episode, he jokingly called himself “the slow Jiaming“ and acted much younger, talking faster and louder. “Its like selling a product. When the customers file a complaint, you must change,“ says Li. “In the Internet age, you get feedback very quickly. These young people are so cute. When youre willing to change for them, they will quickly like you back.“ In order to win more young viewers, CCTV is relying on programs such as Rising Star to embrace Internet culture. In Rising Star, a studio audience and fans watching on television vote for their favorite singers in real time, using the instant-messaging app WeChat. Rising Star was designed to be a live broadcast, but the Chinese version isnt because of policy reasons. Still, WeChat votes by viewers at home are still a major factor in determining which contestants advance to the next round. In the shows latest episode, more than 6.5 million votes were cast via WeChat. “Now the competition among entertainment shows is very fierce. Audiences have more diverse needs. CCTV needs to embrace an open attitude, interact with young audiences and blend with the Internet,“ says Lyu Yitao, director of CCTVs entertainment channel. The producer of Rising Star, Enlight Media, says the program will have “a phenomenal effect“ given CCTVs audience base nationwide. “But it comes with a challenge,“ says Zhang Hang, chief producer of the program and CEO of Enlight Medias TV business. Unlike top-ranking provincial satellite channels such as Hunan TV, which have a large base of young fans thanks to a series of phenomenally popular entertainment and reality shows, CCTV productions are usually more conservative and serious, and thus have a much older audience base. “If we were to run this program on Hunan, we may attract twice as many viewers,“ says Zhang. “But since we didnt make it there, we now have to make the best out of the given conditions. And it means we have to make certain compromises.“ When the current season of Rising Star ends, Zhang says his company will conduct an overall evaluation of the program and make adjustments for future seasons. Although audience ratings havent lived up to Zhangs expectations, he says the program has already helped CCTV attract more young people. According to Enlight Media, the number of people ages 15 to 35 who watched the first episode of Rising Star was 76 percent higher than the usual audience for CCTV entertainment productions. In order to attract young audiences, CCTV has been working with independent production companies. As one of CCTVs closest partners, Enlight Media has produced several entertainment and reality shows for the companys channels, including the Chinese version of The Biggest Loser on CCTVs business channel and an original teenager talent show Shaonian Zhongguoqiang (Strong Young Chinese) on CCTV1. This year CCTV also licensed EE-Media, the producer of the popular Super Girl talent shows, to produce the talk show Hi! 2014, hosted by Taiwan pop star Harlem Yu and one of Chinas most popular TV stars Xie Na. The show is geared toward younger audiences. Canxing Productions, which rose to fame with the success of its Voice of China series on Zhejiang TV, also produced two talent shows for CCTV. One is an original production called Songs of China, which ended up as one of CCTVs most watched programs of 2014. The State Administration of Press, Publication, Radio, Film and Television announced earlier this year that, starting in 2015, only one music talent show can be aired nationwide during prime time each season, and there can be only one program based on foreign formats each year. However, domestic media report that such policies dont apply to CCTV, meaning it will become a highly desired platform by production companies. Wang Changtian, CEO of Enlight Media, confirmed to the Shanghai Securities News that its programs scheduled to air on CCTV next year, which include at least two reality shows, wont be affected. A kung fu-themed reality show, produced by Canxing, is also reportedly scheduled to run on