电高等数学期末复资料参考
1求函数定义域：1）含方根：开方数≥02）含分式：分母≠0
含数：真数＞0
例： 1函数定义域
2函数应规律
例：设求
解：中表达式x+1等式右端表示x+1形式
：令
3判断两函数否相：定义域相应规律相
例：1列函数中（ B ）中两函数相
A B
C D
4判断函数奇偶性：偶函数奇函数
根已知函数奇偶性利奇函数奇函数奇函数偶函
数奇函数偶函数偶函数偶函数×偶函数奇函数×奇函数偶函数性质判断
奇函数图关原点称偶函数图关y轴称
例：列函数中（ A ）偶函数
A． B．
C． D．
5穷量：极限零变量性质：穷量界变量积穷量
例1） 时列变量穷量（ B ）
Acosx Bln(1+x) Cx+1 D
2） 0
6函数点处极限存充条件左右极限存相等
( D )
A1 B—1 C1 D存
7极限计算：形
例1）
2）
8导数意义：
例：曲线处切线斜率 ．
解：
9导数计算：复合函数求导原：外犹剥笋层层求导
例1）设求．
解：
例2）设求dy
解
10判断函数单调性：
例：函数单调减少区间
11应题解题步骤：1）根题意建立函数关系式2）求出驻点（阶导数0点）3）根题意直接回答
例1） 求曲线点点距离短．
解：曲线点点距离公式
点取值计算方便求值点代入
令
令．验证值点解出曲线点点点距离短．
2）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？
解：设容器底半径高表面积
唯驻点时实际问题知底半径高时料省．
12定积分原函数关系
设 称函数原函数
例1）原函数（ B ）
A B C D
解：
2）已知 （答案：C）
A B C D
解：
13性质：
例1）（ B ）．
A B C D
例2） +C
14定积分计算：1）凑微分2）分部积分
1） 常凑微分：
例1）（ B ）．
A B C D
解：
例2）计算．
解：
例3)计算．
解
2） 分部积分常见类型：
根分部积分公式计算
例1）计算
解：
例2）计算定积分
解：
例3）计算
15定积分牛顿莱布尼兹公式：设F（x）f(x)原函数
例：原函数列等式成立（ B ）
A B
C D
16奇偶函数称区间积分：
奇函数
偶函数
例1)：
分析：奇函数0
例2）
分析：偶函数 ：
17定积分计算：1）凑微分2）分部积分
定积分凑微分定积分计算相
例1） 计算
解：利凑微分法
例2） 计算定积分
解：利凑微分法
定积分分部积分定积分计算基相：
定积分分部积分公式：
例1） 计算
解：
例2） 计算
解：
例3） 计算
解：
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 40yearold 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 instantmessaging 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 65 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 topranking 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 EEMedia 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 futhemed 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 mineralrich 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 sulfurcontaining 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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1求函数定义域：1）含方根：开方数≥02）含分式：分母≠0
含数：真数＞0
例： 1函数定义域
2函数应规律
例：设求
解：中表达式x+1等式右端表示x+1形式
：令
3判断两函数否相：定义域相应规律相
例：1列函数中（ B ）中两函数相
A B
C D
4判断函数奇偶性：偶函数奇函数
根已知函数奇偶性利奇函数奇函数奇函数偶函
数奇函数偶函数偶函数偶函数×偶函数奇函数×奇函数偶函数性质判断
奇函数图关原点称偶函数图关y轴称
例：列函数中（ A ）偶函数
A． B．
C． D．
5穷量：极限零变量性质：穷量界变量积穷量
例1） 时列变量穷量（ B ）
Acosx Bln(1+x) Cx+1 D
2） 0
6函数点处极限存充条件左右极限存相等
( D )
A1 B—1 C1 D存
7极限计算：形
例1）
2）
8导数意义：
例：曲线处切线斜率 ．
解：
9导数计算：复合函数求导原：外犹剥笋层层求导
例1）设求．
解：
例2）设求dy
解
10判断函数单调性：
例：函数单调减少区间
11应题解题步骤：1）根题意建立函数关系式2）求出驻点（阶导数0点）3）根题意直接回答
例1） 求曲线点点距离短．
解：曲线点点距离公式
点取值计算方便求值点代入
令
令．验证值点解出曲线点点点距离短．
2）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？
解：设容器底半径高表面积
唯驻点时实际问题知底半径高时料省．
12定积分原函数关系
设 称函数原函数
例1）原函数（ B ）
A B C D
解：
2）已知 （答案：C）
A B C D
解：
13性质：
例1）（ B ）．
A B C D
例2） +C
14定积分计算：1）凑微分2）分部积分
1） 常凑微分：
例1）（ B ）．
A B C D
解：
例2）计算．
解：
例3)计算．
解
2） 分部积分常见类型：
根分部积分公式计算
例1）计算
解：
例2）计算定积分
解：
例3）计算
15定积分牛顿莱布尼兹公式：设F（x）f(x)原函数
例：原函数列等式成立（ B ）
A B
C D
16奇偶函数称区间积分：
奇函数
偶函数
例1)：
分析：奇函数0
例2）
分析：偶函数 ：
17定积分计算：1）凑微分2）分部积分
定积分凑微分定积分计算相
例1） 计算
解：利凑微分法
例2） 计算定积分
解：利凑微分法
定积分分部积分定积分计算基相：
定积分分部积分公式：
例1） 计算
解：
例2） 计算
解：
例3） 计算
解：
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 40yearold 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 instantmessaging 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 65 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 topranking 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 EEMedia 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 futhemed 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 mineralrich 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 sulfurcontaining 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
文档香网(httpswwwxiangdangnet)户传
《香当网》用户分享的内容，不代表《香当网》观点或立场，请自行判断内容的真实性和可靠性！
该内容是文档的文本内容，更好的格式请下载文档