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高等数学(上册)-第一章教?- 百度文库

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˵ݽԤݿܲȫҪĵҪݣwordʹáword΢ź:xxxxxxxQQxxxxxx ܸṩĵл֧½⡣

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ѧĿҪ 1.⺯ĸպıʾὨӦеĺϵʽ 2.⺯żԡԡԺнԡ

3.⸴Ϻֶκĸ˽ⷴĸ 4.ջȺʼͼΡ

5.⼫޵ĸ⺯Ҽ޵ĸԼ޴Ҽ֮Ĺϵ 6.ռ޵ʼ㷨

7.˽⼫޴ڵ׼򣬲ޣҪ޵ķ 8.СĸСıȽϷõȼСޡ 9.⺯Եĸбϵ͡

10.˽ʺͳȺԣ˽ʣнԡֵСֵֵӦЩʡ

ѧʱ18ѧʱ6ѧʱ2ѧʱϰ⣩

һڣ뺯

һǰоͳΪԪأһЩԪɵмϣƼϾȷԣϵԪرȷģͻԣеԪǻͬģ硰ĽϸߵˡܹɼϣΪԪزȷġ

ͨôĸABCʾϣСдĸabcʾеԪءaǼAеԪأ˵aAaA˵aAa?A

šȫǸɵļϽǸȻN ơɵļϽN+N+ ǡȫɵļϽZ ȡȫɵļϽQ ɡȫʵɵļϽʵR ϵıʾ

šоٷѼϵԪһһоٳáʾ ơüԪصĹͬʾϡ ϼĻϵ

šӼһأABAеһԪضǼBԪأǾ˵ABаϵƼAΪBӼA

?BB ?A

ȣμAǼBӼҼBǼAӼʱAеԪ뼯BеԪȫһ˼A뼯BȣAB

ǡӼμAǼBӼһԪBAdzƼAǼBӼ ȡռǰѲκԪصļϽռ ١κһӼA

?涨ռκμϵӼ

ɡ֮ĻϵԵõĽۣ

?A

ڡڼABCABӼBCӼACӼ ۡǿ԰ȵļϽȼĻӼӼ͡ȼ ϵĻ

šһأڼAڼBԪɵļϳΪABIJAB󲢼ʱǵĹԪڲֻܳһΡ

ABx|xAxB

ơһأڼAڼBԪɵļϳΪABĽAB

1 / 16

ABx|xAxB ǡ

ȫһأһϺо漰ԪأôͳΪȫͨU ڲһAȫUвڼAԪɵļϳΪAȫUIJΪAIJCUA

CUAx|xUx Ԫصĸ

š޼ǰѺ޸ԪصļϽ޼޸ԪصļϽ޼ ơcardʾ޼ԪصĸAa,b,ccard(A)=3 ǡһأABcard(A)+card(B)=card(AB)+card(AB) ҵ⣺

1ѧУ↑˶ᣬAx|xDzμһܵͬѧBx|xDzμӶܵͬѧCx|xDzμİܵͬѧѧУ涨ÿμͬѧֻܲμüϵ˵涨¼ĺ塣šABơAB

2ƽֱϵУC{(x,y)|y=x}ʾֱyxǶȿD={(x,y)|飺2x-y=1,x+4y=5}ʾʲôCD֮ʲôϵֱüԺͼ˵ֹϵ

3֪A={x|1x3}B{x|(x-1)(x-a)=0}жBDzAӼǷʵaʹAB 4޼ABCܲҳԪظ뽻Ԫظ֮Ĺϵأ

5޼A1234nB24682nһֱȽԪظٵķ

2

šĶ壺ڹ۲ijһĹʱֲͬеڹв仯ǰ֮ΪеڹDZ仯ģҲǿȡֵ֮ͬΪעڹлһȻDZ仯ģı仯оĶǼ΢Сģ

ơıʾı仯ģʾ仯Χ˵ָij֮߶ϵȫ塣

IJʽ axb ļǺ [ab] axb ab ϵıʾ ?A

뿪 axbaxb ab][ab Ķ䣬֮⣬䣺 [a+)ʾСaʵȫ壬ҲɼΪax+ޣ (-ޣb)ʾСbʵȫ壬ҲɼΪ-ޣxb (-ޣ+)ʾȫʵҲɼΪ-ޣx+

ע-޺+ޣֱ\\\\Dz,ǼǺš

ǡʵҦģ0.㲻ʽx-ĵʵxȫΪĦ򣬵ΪģijΪİ뾶

ϺĶ壺yuĺy=f(u)uxĺu=(x)u=(x)ĺֵȫ򲿷f(u)ĶڣĩyͨuϵҲxĺdzƺһɺy=f(u)u=(x)϶ɵĺƸϺ

2 / 16

y=f((x))uм

עܸϣϺɸຯɡ ⣺y=arcsinx뺯u=2+xDzܸϳһġ

Ϊu=2+xĶ(-,+)еκxֵӦuֵڻ2ʹy=arcsinuûж塣 4Ⱥ

šȺõֻȺֱǣָݺǺǺñܽһ£

ļǺ ͼ 2

2

ָ a):xΪֵ,yΪ; b):x=0ʱ,y=1. a):ͼλyҲ,(1,0) a=m/n a):mΪżnΪʱ,yż; aΪʵ b):m,nʱ,y溯; c):mnżʱ,y(-,0). ֺֻͼεһ֡ a):Һ2Ϊڵں (Һ) ֻдҺ b):Һ溯 b):a1ʱ,(0,1)ֵΪ(-,+)ֵΪڶڵ. Ǻ a):ڴ˺Ϊֵ,Ǵ(Һ) ֻд˷Һ ֵ[-/2,/2],ΪҺֵ. ơȺɻȺ볣޴ε㼰޴εĺһʽĺΪȺ.

5˫˫䣩

š˫ӦǾ˫ǣ(ñ) ıʽ ͼ 3 / 16

˫ a)䶨Ϊ:(-,+) b)溯 c)ڶǵ ˫ a)䶨Ϊ:(-,+) b)ż c)ͼ(0,1) a)䶨Ϊ:(-,+) ˫ κҵС᣺

1ѧϰ˼ϸ뺯 2ոϺ뷴㷽 ҵP9.1,7,8

b)溯 c)ͼμˮƽֱy=1y=-1֮䣻ڶڵ ڶڣеļ

1

šУһķеһa1ڶa2ȥʹκһnӦһȷanĩdzдa1a2anΪ.еÿһеnanеһͨ.

עҲ԰anԱΪnĺan=ơޣ޵ĸʵľȷġ ǿͨԲڽΣԲ

һԲԲڽΣΪA1ԲڽʮΣΪA2ԲڽʮıΣΪA3ѭȥ(һڽ62εΪAn)ɵһϵڽεA1A2A3AnǾ͹һСǿԷ֣ڽεıʱAnҲ޽ӽijһȷֵ(Բ)ȷֵѧϱΪA1A2A3An n(n)ļޡ

עӾҹŴѧ(Ԫ)ĸԲ 2м޵ĸ

1еļޣһأx1x2x3xn˵(ôС)ܴNʹönNʱһxnʽ

ĩͳƳaxnļޣ߳xna .

n-1

Ķȫ

4 / 16

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