电大专科微积分初步期末复习考试试题资料参考
电大微积分初步复习题 1、填空题（1）函数的定义域是． 答案：且.（2）函数的定义域是． 答案：
（3）函数，则 ． 答案：
（4）若函数在处连续，则 ． 答案：
（5）函数，则 ． 答案：
（6）函数的间断点是
． 答案：
（7）． 答案：1（8）若，则． 答案：
（9）曲线在点的切斜率是． 答案：
（10）曲线在点的切线方程是 ． 答案：
（11）已知，则=． 答案：
=27（（12）已知，则=． 答案：，=（13）若，则 ． 答案：
（14）函数的单调增加区间是
． 答案：
（15）函数在区间内单调增加，则应满足 ． 答案：
（16）若的一个原函数为，则.答案：
（17）若，则． 答案：
（18）若 答案：
（19）
． 答案：
（20）
． 答案：
（21）若，则． 答案：
（22）若，则． 答案：
（23）
答案：
（24）
.答案：0（25）=． 答案：
(26)已知曲线在任意点处切线的斜率为，且曲线过，则该曲线的方程是.答案：
(27)由定积分的几何意义知，=.答案：
(28)微分方程的特解为.答案：
(29)微分方程的通解为.答案：
(30)微分方程的阶数为 ． 答案：4 2．单项选择题（1）设函数，则该函数是（）． A．奇函数 B．偶函数C．非奇非偶函数 D．既奇又偶函数 答案：B（2）下列函数中为奇函数是（）． A． B． C． D． 答案：C（3）函数的定义域为（）． A． B． C．且 D．且 答案：D（4）设，则（）
A． B． C． D． 答案：C（5）当（）时，函数在处连续.A．0
B．1 C． D． 答案：D（6）当（）时，函数，在处连续.A．0
B．1 C． D． 答案：B（7）函数的间断点是（）
A． B． C． D．无间断点 答案：A（8）若，则=（）．
A.2 B.1 C.-1 D.-2 答案：C（9）设，则（）． A． B． C． D． 答案：B（10）设是可微函数，则（）． A． B． C． D． 答案：D（11）若，其中是常数，则（）． A． B． C． D． 答案：C（1）函数在区间是（）A．单调增加 B．单调减少 C．先增后减 D．先减后增 答案：D（12）满足方程的点一定是函数的（）.A．极值点B．最值点 C．驻点D． 间断点 答案：C（13）下列结论中（）不正确． A．在处连续，则一定在处可微.B．在处不连续，则一定在处不可导.C．可导函数的极值点一定发生在其驻点上.D．函数的极值点可能发生在不可导点上.答案：Ａ（14）下列函数在指定区间上单调增加的是（）． A． B． C． D． 答案：B（15）下列等式成立的是（）． A． B． C． D． 答案：C（16）以下等式成立的是（）
A． B． C． D． 答案：D（17）（）
A.B.C.D.答案：A（18）下列定积分中积分值为0的是（）． A． B． C． D． 答案：A（19）设是连续的奇函数，则定积分（）A．0B． C．D． 答案：A（20）下列无穷积分收敛的是（）．
A． B．
C．
D． 答案：D(21)微分方程的通解为（）． A． B． C． D． 答案：C(22)下列微分方程中为可分离变量方程的是（）
A.；
B.；
C.；
D.答案：B 3、计算题（1）． 解：
（2）
解：
（3）
解：
（4）设，求． 解：
（5）设，求.解：
（6）设，求.解：
（7）设，求.解：
（8）
解：
（9）
解：
(10)解：
=(11)解：
(12)解：
(13)解：
4、应用题（1）欲做一个底为正方形，容积为108立方米的长方体开口容器，怎样做法用料最省？ 解：设底边的边长为，高为，用材料为，由已知 令，解得是唯一驻点，且，说明是函数的极小值点，所以当，用料最省.（2）用钢板焊接一个容积为4的正方形的水箱，已知钢板每平方米10元，焊接费40元，问水箱的尺寸如何选择，可使总费最低？最低总费是多少？ 解：设水箱的底边长为，高为，表面积为，且有 所以 令，得，因为本问题存在最小值，且函数的驻点唯一，所以，当时水箱的面积最小.此时的费用为（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 host＇s 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.“It＇s 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 you＇re 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 isn＇t 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 show＇s 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 CCTV＇s entertainment channel.The producer of Rising Star, Enlight Media, says the program will have “a phenomenal effect“ given CCTV＇s audience base nationwide.“But it comes with a challenge,“ says Zhang Hang, chief producer of the program and CEO of Enlight Media＇s 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 didn＇t 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 haven＇t lived up to Zhang＇s 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 CCTV＇s closest partners, Enlight Media has produced several entertainment and reality shows for the company＇s channels, including the Chinese version of The Biggest Loser on CCTV＇s business channel and an original teenager talent show Shaonian Zhongguo－qiang(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 China＇s 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 CCTV＇s 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 don＇t 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, won＇t be affected.A kung fu-themed reality show, produced by Canxing, is also reportedly scheduled to run on CCTV next year.CCTV is “very active.The level of its acceptance of new ideas is even beyond my imagination,“ says Zhang Hang.“Our cooperation with CCTV will surely continue.“ When winter comes, nothing is more relaxing than a hot spring bath.For thousands of years, natural mineral-rich hot spring baths have also been used to relieve health ailments.The water found in natural hot springs contains a variety of different minerals, and the most common one is sulfur.It has a “rotten egg“ smell but is excellent for skin.The sulfur-containing water might be just what the doctor ordered when it comes to relieving pain, stress, itchy skin, arthritis and more.Hot springs resorts are thriving as biting cold winter arrives.Here we take a look at some of the best natural hot springs China has to offer.
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