电大专科《高等数学》复习资料考试小抄.doc

《电大专科《高等数学》复习资料考试小抄.doc》由会员分享，可在线阅读，更多相关《电大专科《高等数学》复习资料考试小抄.doc（6页珍藏版）》请在淘文阁 - 分享文档赚钱的网站上搜索。

1、电大专科高等数学复习资料考试小抄电大高等数学期末复习资料参考 1、求函数的定义域：1）含有平方根的：被开方数0，2）含分式的：分母0 含对数的：真数0 例：1.函数的定义域是2、函数的对应规律 例：设求 解：由于中的表达式是+1，可将等式右端表示为+1的形式 或：令 3、判断两个函数是否相同：定义域相同及对应规律相同 例：1、下列各函数对中，（ B ）中的两个函数相同 A、 B、 C、 D、 4、判断函数的奇偶性：若，则为偶函数；若，则为奇函数， 也可以根据一些已知的函数的奇偶性，再利用“奇函数奇函数、奇函数偶函 数仍为奇函数；偶函数偶函数、偶函数偶函数、奇函数奇函数仍为偶函数”的性质来判断。

2、 奇函数的图像关于原点对称，偶函数的图像关于y轴对称。 例：下列函数中，（ A ）是偶函数 A B C D 5、无穷小量：极限为零的变量。性质：无穷小量和有界变量的积仍是无穷小量 例1）: 当时，下列变量为无穷小量的是（ B ） A、cos B、ln(1+) C、+1 D、 2） 0 6、函数在一点处极限存在的充要条件是左右极限存在且相等 ( D ) A、1 B、1 C、1 D、不存在 7、极限的计算：对于“”形 例1） 2）= 8、导数的几何意义：； 例：曲线在处的切线斜率是 解：= 9、导数的计算：复合函数求导原则：由外向内，犹如剥笋，层层求导 例1）设，求 解： 例2）设，求dy 解;

3、10、判断函数的单调性： 例：.函数的单调减少区间是11、应用题的解题步骤：1）根据题意建立函数关系式，2）求出驻点（一阶导数=0的点），3）根据题意直接回答 例1） 求曲线上的点，使其到点的距离最短 解：曲线上的点到点的距离公式为 与在同一点取到最小值，为计算方便求的最小值点，将代入得 令 令得可以验证是的最小值点，并由此解出，即曲线上的点和点到点的距离最短 2）某制罐厂要生产一种体积为V的无盖圆柱形容器，问容器的底半径与高各为多少时用料最省？ 解：设容器的底半径为，高为，则其表面积为 因为 所以 由，得唯一驻点，此时，由实际问题可知，当底半径和高时可使用料最省 12、不定积分与原函数的关系

4、: 设 ，则称函数是的原函数., 例1）若的一个原函数为，则（ B ） A、 B、 C、 D 、 解： 2）已知，则 （答案：C） A. B. C. D.解： 13、性质： 例1）（B ） A. B. C. D. 例2）+C 14、不定积分的计算：1）凑微分；2）分部积分 1） 常用凑微分： 例1）若，则（B ） A. B. C. D. 解： 例2）计算 解： 例3)计算 解; 2） 分部积分的常见类型： ，再根据分部积分公式计算 例1）计算 解： 例2）计算不定积分 解： 例3）计算 = 15、定积分的牛顿莱布尼兹公式：设F（）是f()的一个原函数，则 例：若是的一个原函数，则下列等式成立的

5、是（ B ） A. B. C. D. 16、奇偶函数在对称区间上的积分： 若是奇函数，则有 若是偶函数，则有 例1)： 分析：为奇函数，所以0 例2） 分析：为偶函数 故： 17、定积分的计算：1）凑微分，2）分部积分； 定积分的凑微分和不定积分的计算相同。 例1） 计算 解：利用凑微分法，得 例2） 计算定积分 解：利用凑微分法，得 定积分的分部积分与不定积分的计算基本相同： 定积分的分部积分公式： 例1） 计算 解： = 例2） 计算 解： 例3） 计算 解： 请您删除一下内容，O()O谢谢！20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()

6、O谢谢！20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 Jiami

7、ng recently found himself targeted by a group of young netizens unhy with his style.The complaints came after Li hosted the premiere of Rising Star on Oct 31.It is a sinng competition show that orinated in Israel.Many young netizens found his hosting style slow and boring and mocked it as “CCTV even

8、ing gala style“.They even initiated an online caign to replace him.The 40-year-old hosts reaction to the critism 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 fi

9、le a complaint, you must change,“ says Li.“In the Internet age, you get feedback very qukly.These young people are so cute.When youre willing to change for them, they will qukly like you back.“ In order to more young viewers, CCTV is relying on programs such as Rising Star to embrace Internet cultur

10、e.In Rising Star, a studio audience and fans watching on television vote for their favorite singers in real time, using the instant-messang WeChat.Rising Star was designed to be a live broadcast, but the Chinese version isnt because of poly reasons.Still, WeChat votes by viewers at home are still a

11、major factor in determining whh contestants advance to the net 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 you

12、ng 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“ ven CCTVs audience base nationwide.“But it comes with a challenge,“ says Zhang Hang, chief producer of the p

13、rogram and CEO of Enlight Medias TV business.Unlike -ranking provincial satellite channels such as Hunan TV, whh 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 muc

14、h older audience base.“If we were to run this program on Hunan, we may attract twe as many viewers,“ says Zhang.“But since we didnt make it there, we now have to make the best out of the ven conditions.And it means we have to make certain compromises.“ When the current season of Rising Star ends, Zh

15、ang 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 epectations, he says the program has already helped CCTV attract more young people.According to Enlight Media, the number of people ages

16、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

17、 entertainment and reality shows for the companys channels, including the Chinese version of The Biggest Loser on CCTVs business channel and an orinal teenager talent show Shaonian Zhongguoqiang (Strong Young Chinese) on CCTV1.This year CCTV also lensed EE-Media, the producer of the popular Super rl

18、 talent shows, to produce the talk show Hi! 20, hosted by Taiwan pop star Harlem Yu and one of Chinas most popular TV stars ie Na.The show is geared toward younger audiences.Caning Productions, whh rose to fame with the success of its Voe of China series on Zhejiang TV, also produced two talent show

19、s for CCTV.One is an orinal production called Songs of China, whh ended up as one of CCTVs most watched programs of 20.The State Administration of Press, Publation, Radio, Film and Television announced earlier this year that, starting in 20, only one mus talent show can be aired nationwide during pr

20、ime time each season, and there can be only one program based on foreign formats each year.However, domest media report that such polies dont ly to CCTV, meaning it will become a highly desired platform by production companies.Wang Changtian, CEO of Enlight Media, confirmed to the Shanghai Securitie

21、s News that its programs scheduled to air on CCTV net year, whh include at least two reality shows, wont be affected.A kung fu-themed reality show, produced by Caning, is also reportedly scheduled to run on CCTV net year.CCTV is “very active.The level of its acceptance of new ideas is even beyond my

22、 imanation,“ says Zhang Hang.“Our cooperation with CCTV will surely continue.“ When ter comes, nothing is more relaing than a hot spring bath.For thousands of years, natural mineral-rh hot spring baths have also been used to relieve health ailments.The water found in natural hot springs contains a v

23、ariety of different minerals, and the most common one is sulfur.It has a “rotten egg“ smell but is ecellent 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 ter arrives.Here we take a look at some of the best natural hot springs China has to offer. 第 6 页 共 6 页