際際滷

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G thet oik_math_a (1)

Aigli Soultania
Aigli Soultania

亮留慮侶亮留旅虜留 虜留竜慮僚侶 留留僚侶竜旅

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2018 | 陸略侶 2 | 旅留粒僚溜袖留留 留僚略了侶侶 裡僚竜粒留龍袖竜僚凌旅 虜留旅隆竜旅虜凌溜陸凌僚旅劉裡竜了.1/10 里 ' 竜僚旅虜凌 虜竜溜凌 竜旅虜ﾎ 裡凌隆ﾎ / 裡凌隆ﾎ 旅虜凌僚凌袖溜留 & 了侶凌凌旅虜流 裡略硫硫留凌 21 旅了溜凌 2018 | 旅略虜竜旅留 両劉留侶:3 ﾏ竜 里裡裡 A 1. 竜溜留, 凌了旅虜 硫旅硫了溜凌 竜了. 216: 竜亮竜了旅ﾎ肝杵 竜ﾏ侶亮留 了凌虜了侶旅虜凌 凌粒旅亮凌. 2. 竜溜留, 凌了旅虜 硫旅硫了溜凌 竜了. 142. 3. 竜溜留, 凌了旅虜 硫旅硫了溜凌 竜了. 33. 4. 留) 裡 硫) 略慮凌 粒) 略慮凌 隆) 裡 竜) 略慮凌 1. 凌 侶 f 竜溜僚留旅 留留粒粒溜旅亮侶 凌 劉凌亮竜 旅 侶 f 竜溜僚留旅 虜留旅 僚竜流 凌 , 竜凌亮劉僚 竜溜僚留旅 僚竜流 虜留旅 凌 0 1x = , 略留 ( ) ( ) ( )1 1 1lim lim x x f x f x f + = = . 亮 ( ) ( ) ( ) ( ) ( )( ) ( ) 3 2 3 3 3 3 1 1 1 lim lim ln lim lim ln ln x x x x f x 留x x 留 f 留 硫 f x x 硫x 硫 + + 錚= = = 錚 =錚 = = 錚器 1 虜亮侶, 侶 f 竜溜僚留旅 虜留旅 留留粒粒溜旅亮侶 凌 0 1x = 略留 ( ) ( ) ( ) ( ) 1 1 1 1 1 1 lim lim x x f x f f x f x x + =
2018 | 陸略侶 2 | 旅留粒僚溜袖留留 留僚略了侶侶 裡僚竜粒留龍袖竜僚凌旅 虜留旅隆竜旅虜凌溜陸凌僚旅劉裡竜了.2/10 了了略 ( ) ( ) ( ) ( ) ( )3 23 2 3 3 3 1 11 1 1 1 1 lim lim lim x x x 留 x xf x f 留x x 留 x x x = = = ( )( ) ( )( )2 1 1 1 1 1 3 2 1 lim x 留 x x x x x 留 x + + + = = 虜留旅 ( ) ( ) ( ) ( ) ( ) ( ) 0 1 0 DLH1 1 1 1 1 1 1 1 ln ln ln lim lim lim x x x f x f x 硫x 留 x 硫x 硫 x x x+ + + = = = ( ) 1 ln lim x 硫x x + + = 1 硫 x 硫 1 1 ln硫= + 留: ( )3 2 3ln留 硫 = + 2 旅 劉竜旅 (1) 虜留旅 (2) 凌虜竜旅 旅: 3 2 3 3 3 2 2 2 3留 留 留 留 留 留 = + = = = 虜留旅 留僚旅虜留慮旅ﾎ熟留 侶 劉侶 (1) 留溜僚凌亮竜: 0 1ln硫 硫= = . 2. 旅留 1留 硫= = 侶 f 粒溜僚竜留旅: ( ) 3 2 1 1 , ln , x x x f x x x x 錚 = 錚 >錚 僚 1x < 竜 ( ) 2 3 2f x x x = . 僚 1x > 竜 ( ) 1lnf x x = + . 僚 1x = 竜 ( )1 3 2 1f 留 = = . 留 ( ) 2 3 2 3 3 3 3 3 , , ln , x x x f x x x x 錚 < 錚 = =錚 錚 + >錚 僚 1x < 虜留旅 ( ) ( )2 2 0 3 2 0 3 2 0 0 3 f x x x x x x 流 x = = = = = . 僚 1x < 虜留旅 ( ) ( )2 2 0 3 2 0 3 2 0 0 3 f x x x x x x 流 x > > > < > . 僚 1x > 竜 ( ) 1 0lnf x x = + > .
2018 | 陸略侶 2 | 旅留粒僚溜袖留留 留僚略了侶侶 裡僚竜粒留龍袖竜僚凌旅 虜留旅隆竜旅虜凌溜陸凌僚旅劉裡竜了.3/10 x 0 2 3 1 + ( )f x + + + ( )f x 留 侶 f 竜溜僚留旅 粒僚侶溜 留両凌留 凌 ( ]0, , 粒僚侶溜 慮溜僚凌留 凌 2 0 3 , 錚 錚 錚 錚 錚 錚 虜留旅 粒僚侶溜 留両凌留 凌 2 3 , 錚 錚 + 錚件 錚 錚 , 竜凌亮劉僚 粒旅留 0x = 留凌旅略龍竜旅 凌旅虜 亮劉粒旅凌 亮竜 亮劉粒旅侶 旅亮流 ( )0 0f = , 竜僚 粒旅留 2 3 x = 留凌旅略龍竜旅 凌旅虜 竜了略旅凌 亮竜 竜了略旅侶 旅亮流 2 4 3 27 f 錚 錚 = 錚 錚 錚 錚 . 3. ( )( ),A Ax f x 凌旅 僚竜留粒亮劉僚竜 凌 侶亮竜溜凌 . 竜留凌亮劉僚侶 ( )A竜 侶 fC 凌 劉竜旅 竜両溜侶: ( ) ( ) ( ) ( )( )1ln lnA A A A A A Ay f x f x x x y x x x x x霞 = = + 溜虜凌亮竜 侶僚 竜亮侶亮劉僚侶 凌 侶亮竜溜凌 凌亮流 侶 ( )A竜 亮竜 凌僚 略両凌僚留 x x , 慮劉凌僚留 侶僚 留留略僚 竜両溜侶 0y = : ( )( )1ln lnA A A Ax x x x x = + lnA Ax x ( )1ln lnA A Ax x x x= + Ax 1ln A A x x x = + , 略留 ( ) ( ) ( )( ) 1ln M x t x t x t = + 虜留旅 ( ) ( ) ( )( ) ( )1ln M x t x t x t x t 錚 錚高 + 錚 錚 = ( ) 1 x t ( ) ( )( ) 2 0 1ln t t x t x t = 霞 錚 錚+錚 錚 ( ) ( ) ( ) ( )( ) ( ) ( )( ) 0 0 0 0 0 2 0 1 1 ln ln M M x t x t x t t x t x t 錚 錚高 霞 + 錚 錚獅= = = 錚 錚+錚 錚
2018 | 陸略侶 2 | 旅留粒僚溜袖留留 留僚略了侶侶 裡僚竜粒留龍袖竜僚凌旅 虜留旅隆竜旅虜凌溜陸凌僚旅劉裡竜了.4/10 ( ) ( ) 2 2 4 1 4 4 1 21 ln ln e e + = = = + 亮凌僚略隆留/sec. 1. 旅留 虜略慮竜 x A 旅竜旅 ( ) ( ) ( )e 1 f x f x x+ = ﾏ留 慮留 隆竜溜両凌亮竜 旅 侶 f 竜溜僚留旅 1-1. 1凌 凌 ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) 1 2 1 2 1 1 2 1 2 1 2 x 亮竜 e e 竜 e e , f x f x f x f x x A f x f x f x f x +錚錫 = 錚 + = + 錚 = 錚器 1 2x x = 侶 f 竜溜僚留旅 1-1. 2凌 凌 凌 侶 f 竜溜僚留旅 留留粒粒溜旅亮侶, 留留粒粒溜龍 虜留旅 留 隆凌 亮劉了侶 侶 劉侶 (1): ( ) ( )( ) ( ) ( ) ( ) 1 f x f x e f x x e f x f x + = + = ( ) ( ) ( ) ( ) ( ) 1 1 1 0 1 , f x f x f x e f x e 霞 + = = > + 粒旅留 虜略慮竜 x A , 略留 侶 f 竜溜僚留旅 粒僚侶溜 留両凌留 凌 虜留旅 竜凌亮劉僚 1-1. 旅留 僚留 硫凌亮竜 凌僚 凌 侶 1 f 慮劉凌亮竜 ( )f x y= 亮竜 0y , 留凌 ( ) [ )0,f A = + 虜留旅 留僚旅虜留慮旅ﾎ熟留 侶 劉侶 (1) 劉凌亮竜: ( )1y y e y x e y f y + = + = 亮竜 0y 留 ( )1 ,x f x e x = + 亮竜 0x . 2. 竜旅 旅 [ )( )1 0,A f = + 亮竜 ( ) ( ) ( )1 1 1 0x x f x e x f x e = + = + > , 略留 侶 1 f 竜溜僚留旅 粒僚侶溜 留両凌留 凌 [ )0, + . 凌亮劉僚: [ )( ) ( ) ( )) [ )1 1 1 0 0 1, , lim , x A f f f x + 錚= + = = + 錚 ,
2018 | 陸略侶 2 | 旅留粒僚溜袖留留 留僚略了侶侶 裡僚竜粒留龍袖竜僚凌旅 虜留旅隆竜旅虜凌溜陸凌僚旅劉裡竜了.5/10 留凌 ( ) ( )1 lim lim x x x f x e x + + = + = +. 僚留龍侶凌亮竜 凌 竜隆溜凌 凌旅亮凌 侶 f f : ( ){ } [ ) ( ) [ ){ }1 1/ , / ,f f f fD x D f x D x f x= = + + ( ) ( )( ) ( ) 1 粒僚.留両凌留 1 1 1 1 1 虜留旅 虜留旅 虜留旅 1 1 1 f x x x f x f f x f x e 錚縁１ ワ１ 錚器４ 錚 錚 錚 錚 錚 錚 錚癌 +錚鰹３ 錚 [ )1,f fD e = + + . 両竜略龍凌亮竜 侶 亮凌僚凌凌僚溜留 侶 f f : 1凌 凌 凌 ( ) 0f x > 侶 f 竜溜僚留旅 粒僚侶溜 留両凌留 凌 [ )1,A = + . [ )1 2x 1, ,x e + + 亮竜 ( ) ( ) ( )( ) ( )( ) -粒僚.留両凌留 -粒僚.留両凌留 1 2 1 2 1 2 f f x x f x f x f f x f f x< < < ( )( ) ( )( )1 2f f x f f x < , 隆侶了留隆流 侶 f f 竜溜僚留旅 粒僚侶溜 留両凌留 凌 [ )1,e + + . 2凌 凌 凌 侶 f 竜溜僚留旅 留留粒粒溜旅亮侶 虜留旅 侶 f f 竜溜僚留旅 留留粒粒溜旅亮侶 ( 僚慮竜侶 留留粒粒旅溜亮僚) 亮竜 ( ) ( ) ( )( ) ( )( ) ( )f f x f f x f f x f x 霞 錚 錚 = = 錚 錚 , 亮竜 ( )f x 0 > 虜留旅 ( )( ) 0f f x > 粒旅留 虜略慮竜 [ )1,x e + + . 留 ( ) ( ) 0f f x > 粒旅留 虜略慮竜 [ )1,x e + + , 竜凌亮劉僚 侶 f f 竜溜僚留旅 粒僚侶溜 留両凌留 凌 [ )1,e + + . 3. 溜虜凌亮竜 凌 侶亮竜溜凌 凌亮流 侶 fC 虜留旅 凌 略両凌僚留 x x : ( ) ( )1 0 0 0 0 1f x x f x e x = = = + = , 略留 凌 侶亮竜溜凌 凌亮流 竜溜僚留旅 凌 ( )1 0, . 竜旅隆流 ( ) 0f x 粒旅留 虜略慮竜 [ )1,x A = + 凌 竜亮硫留隆僚 凌 亮留 龍侶竜溜留旅 竜溜僚留旅:
2018 | 陸略侶 2 | 旅留粒僚溜袖留留 留僚略了侶侶 裡僚竜粒留龍袖竜僚凌旅 虜留旅隆竜旅虜凌溜陸凌僚旅劉裡竜了.6/10 ( ) ( ) 1 1 d e E 立 f x x + = 劉凌亮竜 ( ) ( ) ( )1 d 1 du u f x u x f u x e u x e u = = = + = + 虜留旅 ( )1 1 0u f= = , ( )2 1 1u f e= + = , 留凌 ( )1 1 1 1 1f e e = + = + . 里竜: ( ) ( ) ( ) ( ) 1 1 1 1 0 0 d 1 d d e u u E 立 f x x u e u u e u u + = = + = + = ( ) ( ) 121 1 00 0 d 1 0 2 u u u u u e u u e u u e e 錚 錚 錚 錚 = + + = + + =錚 錚削０ 錚 錚 錚 1 1 1 0 1 e e e 錚 錚 = + + =錚 錚 錚 錚 1 e+ ( ) 1 3 3 1 1 1 1 E 立 + = = .亮. 4. 僚 1x > 竜 旅竜旅 2 3 x x x< < 虜留旅: 侶 f 竜溜僚留旅 僚竜流 留 隆旅留流亮留留 2 ,x x錚 錚刻０ 錚 虜留旅 2 3 ,x x錚 錚刻０ 錚 侶 f 竜溜僚留旅 留留粒粒溜旅亮侶 留 隆旅留流亮留留 ( )2 ,x x 虜留旅 ( )2 3 ,x x 凌 竜ﾏ侶亮留 劉侶 里旅亮流 略凌僚 ( )2 1 ,両 x x 虜留旅 ( )2 3 2 ,両 x x ﾏ竜 ( ) ( ) ( )2 1 2 f x f x f 両 x x = 虜留旅 ( ) ( ) ( )3 2 2 3 2 f x f x f 両 x x = 亮 ( ) ( ) 1 1 f x f x e = + , 略留 侶 f 竜溜僚留旅 留留粒粒溜旅亮侶 亮竜 ( ) ( ) ( ) ( ) ( )2 1 0 1 f x f x f x e f x e 霞 = < + , 留凌 ( ) 0 f x e > 虜留旅 ( ) 0f x > . 留 ( ) 0f x霞 < 竜凌亮劉僚 侶 f 竜溜僚留旅 粒僚侶溜 慮溜僚凌留 凌 [ )1, + . 竜旅 旅: ( ) ( ) -粒僚.慮溜僚凌留 2 3 1 2 1 2 1 2 f x 両 x 両 x 両 両 f 両 f 両 < < < < < > ( ) ( ) ( ) ( ) ( ) ( ) ( )( ) ( ) ( ) 22 3 2 0 2 3 2 2 3 2 x x x f x f x f x f x x f x f x f x f x x x x x > > > ( ) ( ) ( ) ( )2 3 1x f x f x x f x + > +
2018 | 陸略侶 2 | 旅留粒僚溜袖留留 留僚略了侶侶 裡僚竜粒留龍袖竜僚凌旅 虜留旅隆竜旅虜凌溜陸凌僚旅劉裡竜了.7/10 1. 侶僚 慮竜侶 旅竜旅 ( ) ( ) 0x x e f x x e f x x , 粒旅留 虜略慮竜 1x > . 竜 僚略侶侶 g 亮竜 ( ) ( )x g x e f x x= , 1x > . 里竜 ( )0 0g = 虜留旅 ( ) ( )0g x g 粒旅留 虜略慮竜 1x > , 隆侶了留隆流 侶 g 留凌旅略龍竜旅 凌 0x = 凌旅虜 亮劉粒旅凌. 竜旅隆流 侶 g 竜溜僚留旅 留留粒粒溜旅亮侶 亮竜 ( ) ( ) 1x g x e f x = 虜留旅 凌 0x = 竜溜僚留旅 竜竜旅虜 侶亮竜溜凌 凌 隆旅留流亮留凌 ( )1, + , 留 凌 慮竜ﾏ侶亮留 凌 Fermat 凌虜竜旅 旅: ( ) ( ) ( )0 0 0 0 1 0 0 0g e f f = = = . 2. 侶僚 慮竜侶 旅竜旅 ( ) ( ) ( ) ( )1 2x x f x e x f x霞 + = + ( ) ( ) ( ) ( )1 1x x f x x f x e x e霞 霞 + + = + + ( ) ( ) ( )1 1x f x x e x 霞霞 錚 錚刻 錚高 + = +錚 錚 錚 錚 旅 僚劉竜旅竜 凌 竜流亮留凌 劉侶 里旅亮流 劉凌亮竜: ( ) ( ) ( ) 11 1 1( )x f x x e x c + = + + 旅留 0x = 侶 劉侶 (1) 粒溜僚竜留旅: ( ) ( ) ( ) ( ) 0 1 1 0 0 1 0 1 1 虜留旅 留虜亮侶 0 0 f e f f f 錚錫 + = + + 錚 = 錚 = 錚器 僚旅虜留慮旅ﾎ熟留 侶 劉侶 (1) 留溜僚凌亮竜: ( ) ( ) ( ) ( ) 1 0 1 1 1 1 1 x x x f x x e x f x e x + > 霞 + = + = + ( ) ( )( )1lnx f x e x 霞霞 = + 旅 僚劉竜旅竜 凌 竜流亮留凌 劉侶 里旅亮流 凌虜竜旅: ( ) ( ) 21 2ln ( )x f x e x c = + + 旅留 0x = 侶 劉侶 (2) 粒溜僚竜留旅: ( ) ( ) ( ) 0 2 2 2 0 0 1 1 1 0 虜留旅 留 侶僚 慮竜侶 0 1 lnf e f f f f 錚= + + 錚 = + =錚 = 錚器 僚旅虜留慮旅ﾎ熟留 侶 劉侶 (2) 硫溜虜凌亮竜: ( ) ( )1lnx f x e x= + 亮竜 1x > .
2018 | 陸略侶 2 | 旅留粒僚溜袖留留 留僚略了侶侶 裡僚竜粒留龍袖竜僚凌旅 虜留旅隆竜旅虜凌溜陸凌僚旅劉裡竜了.8/10 3. 留. 両竜略龍凌亮竜 侶僚 f 凌 侶 亮凌僚凌凌僚溜留: ( ) 1 1 x f x e x = + 亮竜 ( )0 0f = ( ) ( ) 2 1 0 1 x f x e x 霞 = + > + 粒旅留 虜略慮竜 1x > 略留 侶 f 竜溜僚留旅 粒僚侶溜 留両凌留 凌 ( )1, + . 僚 ( ) ( ) ( ) -粒僚.留両凌留 1 0 0 0 0 f x f x f f x 霞 < < < = < 凌 ( )1 0, , 略留 侶 f 竜溜僚留旅 粒僚侶溜 慮溜僚凌留 凌 ( ]1 0, . 僚 ( ) ( ) ( ) -粒僚.留両凌留 0 0 0 0 f x f x f f x > > = > 凌 ( )0, + , 略留 侶 f 竜溜僚留旅 粒僚侶溜 留両凌留 凌 [ )0, + . x 1 0 + ( )f x + ( )f x 竜旅隆流 侶 f 竜溜僚留旅 粒僚侶溜 慮溜僚凌留 虜留旅 僚竜流 凌 ( ]1 0, 劉凌亮竜 旅: ( ]( ) ( ) ( )) [ )1 1 0 0 1, , lim , x f f f x+ 錚 = = + 錚錚 留凌 ( ) ( )( ) ( )1 1 1 1lim lim lnx x x f x e x e+ + = + = = + . 竜旅隆流 侶 f 竜溜僚留旅 粒僚侶溜 留両凌留 虜留旅 僚竜流 凌 [ )0, + 劉凌亮竜 旅: [ )( ) ( ) ( )) [ )0 0 1, , lim , x f f f x + 錚+ = = + 錚 留凌 ( ) ( )( ) ( )ln lim lim ln lim + + + 錚 錚刻 錚+ = + = =錚 錚削 錚 錚 錚削 錚醐０ 錚 1 1 1x x xx x x x f x e x e e ( ) ( )= + = +1 0 虜留旅 ( ) ( )DLH 1 1 11 0 1 ln lim lim limx x xx x x x x e e e x + + + + + + += = = + .
2018 | 陸略侶 2 | 旅留粒僚溜袖留留 留僚略了侶侶 裡僚竜粒留龍袖竜僚凌旅 虜留旅隆竜旅虜凌溜陸凌僚旅劉裡竜了.9/10 留 ( )( ) [ )1 1, ,f + = + . 竜旅隆流 ( ) ( )( )2 1 1 2, ,f + = 虜留旅 侶 f 竜溜僚留旅 僚竜流 虜留旅 粒僚侶溜 慮溜僚凌留 凌 ( )1 0, 略竜旅 亮凌僚留隆旅虜 ( )1 1 0,両 ﾏ竜 ( )1 2f 両 = . 虜亮侶 ( ) ( )( )2 1 2, ,f + = + 虜留旅 侶 f 竜溜僚留旅 僚竜流 虜留旅 粒僚侶溜 留両凌留 凌 ( )0, + 略竜旅 亮凌僚留隆旅虜 ( )2 0,両 + ﾏ竜 ( )2 2f 両 = . 留 侶 竜両溜侶 ( ) 2f x = 劉竜旅 留虜旅硫ﾏ 隆凌 溜龍竜, 旅 ( )1 1 0,両 虜留旅 ( )2 0,両 + . 硫. 1凌 凌 僚 凌 竜亮硫留隆僚 凌 溜凌 亮竜留両 侶 fC 虜留旅 侶 竜慮竜溜留 2y = 竜 ( ) 2 1 2 d 両 両 E f x x= 僚 ( ) ( ) ( ) -粒僚.慮溜僚凌留 1 10 2 f 両 x f x f 両 f x 粒旅留 虜略慮竜 [ ]1 0,x 両 . 僚 ( ) ( ) ( ) -粒僚.留両凌留 2 20 2 f x 両 f x f 両 f x 粒旅留 虜略慮竜 [ ]20,x 両 . 留 ( ) 2f x 粒旅留 虜略慮竜 [ ]1 2,x 両 両 凌竜 ( ) ( )( )2 2 1 1 2 d 2 d 両 両 両 両 E f x x f x x= = 亮 旅竜旅 旅 ( ) 1f x 粒旅留 虜略慮竜 [ ]1 2,x 両 両 竜凌亮劉僚 ( ) ( )1 2 1f x f x 粒旅留 虜略慮竜 [ ]1 2,x 両 両 溜 僚留 旅竜旅 留僚凌 侶 旅侶留. 留: ( )( )2 2 1 1 2 22 d 1d 両 両 両 両 f x x x E 両 両 < <
2018 | 陸略侶 2 | 旅留粒僚溜袖留留 留僚略了侶侶 裡僚竜粒留龍袖竜僚凌旅 虜留旅隆竜旅虜凌溜陸凌僚旅劉裡竜了.10/10 2凌 凌 里凌 竜亮硫留隆僚 竜溜僚留旅 凌 竜亮硫留隆僚 凌 粒留亮亮凌虜旅留亮劉僚凌 溜凌 凌 隆旅了留僚凌 流亮留凌. 留留侶凌亮竜 旅: ( ) ( ) ( )E E < < 2 1 両 両 < , 留凌 ( ) 2 1 両 両= 虜留旅 ( ) 1 = . 4 劉凌亮竜 ( ) ( ) 2 1 1 u f x uf x = = . 僚 ( ) ( ) 1 1 0 0x f x u f x + + + + . 留 ( ) ( ) 2 1 2 1 1 侶亮 侶亮lim ln lim ln x u f x u uf x + + 錚 錚刻 錚 錚 錚刻 錚駈 錚削 錚撃 = =錚 錚件 錚削 錚件 錚 錚 錚醐０ 錚誌 錚醐０ 錚 ( ) ( )0 0 侶亮 侶亮 2 2 2 1 0 0lim ln lim ln u u u u u u u u+ + 錚 錚 錚 錚高 = = =錚 錚 錚 錚 錚 錚 留凌 0 侶亮 1lim u u u+ = 虜留旅 ( ) ( ) DLH 0 0 0 0 2 1 0 1 1 ln lim ln lim lim lim u u u u u uu u u u u + + + + 錚 錚 錚 錚 錚 錚 錚 錚 = = = =錚 錚 錚 錚 錚 錚 錚 錚撃 錚 錚 錚 錚 .

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G thet oik_math_a (1)

  • 1. 2018 | 陸略侶 2 | 旅留粒僚溜袖留留 留僚略了侶侶 裡僚竜粒留龍袖竜僚凌旅 虜留旅隆竜旅虜凌溜陸凌僚旅劉裡竜了.1/10 里 ' 竜僚旅虜凌 虜竜溜凌 竜旅虜ﾎ 裡凌隆ﾎ / 裡凌隆ﾎ 旅虜凌僚凌袖溜留 & 了侶凌凌旅虜流 裡略硫硫留凌 21 旅了溜凌 2018 | 旅略虜竜旅留 両劉留侶:3 ﾏ竜 里裡裡 A 1. 竜溜留, 凌了旅虜 硫旅硫了溜凌 竜了. 216: 竜亮竜了旅ﾎ肝杵 竜ﾏ侶亮留 了凌虜了侶旅虜凌 凌粒旅亮凌. 2. 竜溜留, 凌了旅虜 硫旅硫了溜凌 竜了. 142. 3. 竜溜留, 凌了旅虜 硫旅硫了溜凌 竜了. 33. 4. 留) 裡 硫) 略慮凌 粒) 略慮凌 隆) 裡 竜) 略慮凌 1. 凌 侶 f 竜溜僚留旅 留留粒粒溜旅亮侶 凌 劉凌亮竜 旅 侶 f 竜溜僚留旅 虜留旅 僚竜流 凌 , 竜凌亮劉僚 竜溜僚留旅 僚竜流 虜留旅 凌 0 1x = , 略留 ( ) ( ) ( )1 1 1lim lim x x f x f x f + = = . 亮 ( ) ( ) ( ) ( ) ( )( ) ( ) 3 2 3 3 3 3 1 1 1 lim lim ln lim lim ln ln x x x x f x 留x x 留 f 留 硫 f x x 硫x 硫 + + 錚= = = 錚 =錚 = = 錚器 1 虜亮侶, 侶 f 竜溜僚留旅 虜留旅 留留粒粒溜旅亮侶 凌 0 1x = 略留 ( ) ( ) ( ) ( ) 1 1 1 1 1 1 lim lim x x f x f f x f x x + =
  • 2. 2018 | 陸略侶 2 | 旅留粒僚溜袖留留 留僚略了侶侶 裡僚竜粒留龍袖竜僚凌旅 虜留旅隆竜旅虜凌溜陸凌僚旅劉裡竜了.2/10 了了略 ( ) ( ) ( ) ( ) ( )3 23 2 3 3 3 1 11 1 1 1 1 lim lim lim x x x 留 x xf x f 留x x 留 x x x = = = ( )( ) ( )( )2 1 1 1 1 1 3 2 1 lim x 留 x x x x x 留 x + + + = = 虜留旅 ( ) ( ) ( ) ( ) ( ) ( ) 0 1 0 DLH1 1 1 1 1 1 1 1 ln ln ln lim lim lim x x x f x f x 硫x 留 x 硫x 硫 x x x+ + + = = = ( ) 1 ln lim x 硫x x + + = 1 硫 x 硫 1 1 ln硫= + 留: ( )3 2 3ln留 硫 = + 2 旅 劉竜旅 (1) 虜留旅 (2) 凌虜竜旅 旅: 3 2 3 3 3 2 2 2 3留 留 留 留 留 留 = + = = = 虜留旅 留僚旅虜留慮旅ﾎ熟留 侶 劉侶 (1) 留溜僚凌亮竜: 0 1ln硫 硫= = . 2. 旅留 1留 硫= = 侶 f 粒溜僚竜留旅: ( ) 3 2 1 1 , ln , x x x f x x x x 錚 = 錚 >錚 僚 1x < 竜 ( ) 2 3 2f x x x = . 僚 1x > 竜 ( ) 1lnf x x = + . 僚 1x = 竜 ( )1 3 2 1f 留 = = . 留 ( ) 2 3 2 3 3 3 3 3 , , ln , x x x f x x x x 錚 < 錚 = =錚 錚 + >錚 僚 1x < 虜留旅 ( ) ( )2 2 0 3 2 0 3 2 0 0 3 f x x x x x x 流 x = = = = = . 僚 1x < 虜留旅 ( ) ( )2 2 0 3 2 0 3 2 0 0 3 f x x x x x x 流 x > > > < > . 僚 1x > 竜 ( ) 1 0lnf x x = + > .
  • 3. 2018 | 陸略侶 2 | 旅留粒僚溜袖留留 留僚略了侶侶 裡僚竜粒留龍袖竜僚凌旅 虜留旅隆竜旅虜凌溜陸凌僚旅劉裡竜了.3/10 x 0 2 3 1 + ( )f x + + + ( )f x 留 侶 f 竜溜僚留旅 粒僚侶溜 留両凌留 凌 ( ]0, , 粒僚侶溜 慮溜僚凌留 凌 2 0 3 , 錚 錚 錚 錚 錚 錚 虜留旅 粒僚侶溜 留両凌留 凌 2 3 , 錚 錚 + 錚件 錚 錚 , 竜凌亮劉僚 粒旅留 0x = 留凌旅略龍竜旅 凌旅虜 亮劉粒旅凌 亮竜 亮劉粒旅侶 旅亮流 ( )0 0f = , 竜僚 粒旅留 2 3 x = 留凌旅略龍竜旅 凌旅虜 竜了略旅凌 亮竜 竜了略旅侶 旅亮流 2 4 3 27 f 錚 錚 = 錚 錚 錚 錚 . 3. ( )( ),A Ax f x 凌旅 僚竜留粒亮劉僚竜 凌 侶亮竜溜凌 . 竜留凌亮劉僚侶 ( )A竜 侶 fC 凌 劉竜旅 竜両溜侶: ( ) ( ) ( ) ( )( )1ln lnA A A A A A Ay f x f x x x y x x x x x霞 = = + 溜虜凌亮竜 侶僚 竜亮侶亮劉僚侶 凌 侶亮竜溜凌 凌亮流 侶 ( )A竜 亮竜 凌僚 略両凌僚留 x x , 慮劉凌僚留 侶僚 留留略僚 竜両溜侶 0y = : ( )( )1ln lnA A A Ax x x x x = + lnA Ax x ( )1ln lnA A Ax x x x= + Ax 1ln A A x x x = + , 略留 ( ) ( ) ( )( ) 1ln M x t x t x t = + 虜留旅 ( ) ( ) ( )( ) ( )1ln M x t x t x t x t 錚 錚高 + 錚 錚 = ( ) 1 x t ( ) ( )( ) 2 0 1ln t t x t x t = 霞 錚 錚+錚 錚 ( ) ( ) ( ) ( )( ) ( ) ( )( ) 0 0 0 0 0 2 0 1 1 ln ln M M x t x t x t t x t x t 錚 錚高 霞 + 錚 錚獅= = = 錚 錚+錚 錚
  • 4. 2018 | 陸略侶 2 | 旅留粒僚溜袖留留 留僚略了侶侶 裡僚竜粒留龍袖竜僚凌旅 虜留旅隆竜旅虜凌溜陸凌僚旅劉裡竜了.4/10 ( ) ( ) 2 2 4 1 4 4 1 21 ln ln e e + = = = + 亮凌僚略隆留/sec. 1. 旅留 虜略慮竜 x A 旅竜旅 ( ) ( ) ( )e 1 f x f x x+ = ﾏ留 慮留 隆竜溜両凌亮竜 旅 侶 f 竜溜僚留旅 1-1. 1凌 凌 ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) 1 2 1 2 1 1 2 1 2 1 2 x 亮竜 e e 竜 e e , f x f x f x f x x A f x f x f x f x +錚錫 = 錚 + = + 錚 = 錚器 1 2x x = 侶 f 竜溜僚留旅 1-1. 2凌 凌 凌 侶 f 竜溜僚留旅 留留粒粒溜旅亮侶, 留留粒粒溜龍 虜留旅 留 隆凌 亮劉了侶 侶 劉侶 (1): ( ) ( )( ) ( ) ( ) ( ) 1 f x f x e f x x e f x f x + = + = ( ) ( ) ( ) ( ) ( ) 1 1 1 0 1 , f x f x f x e f x e 霞 + = = > + 粒旅留 虜略慮竜 x A , 略留 侶 f 竜溜僚留旅 粒僚侶溜 留両凌留 凌 虜留旅 竜凌亮劉僚 1-1. 旅留 僚留 硫凌亮竜 凌僚 凌 侶 1 f 慮劉凌亮竜 ( )f x y= 亮竜 0y , 留凌 ( ) [ )0,f A = + 虜留旅 留僚旅虜留慮旅ﾎ熟留 侶 劉侶 (1) 劉凌亮竜: ( )1y y e y x e y f y + = + = 亮竜 0y 留 ( )1 ,x f x e x = + 亮竜 0x . 2. 竜旅 旅 [ )( )1 0,A f = + 亮竜 ( ) ( ) ( )1 1 1 0x x f x e x f x e = + = + > , 略留 侶 1 f 竜溜僚留旅 粒僚侶溜 留両凌留 凌 [ )0, + . 凌亮劉僚: [ )( ) ( ) ( )) [ )1 1 1 0 0 1, , lim , x A f f f x + 錚= + = = + 錚 ,
  • 5. 2018 | 陸略侶 2 | 旅留粒僚溜袖留留 留僚略了侶侶 裡僚竜粒留龍袖竜僚凌旅 虜留旅隆竜旅虜凌溜陸凌僚旅劉裡竜了.5/10 留凌 ( ) ( )1 lim lim x x x f x e x + + = + = +. 僚留龍侶凌亮竜 凌 竜隆溜凌 凌旅亮凌 侶 f f : ( ){ } [ ) ( ) [ ){ }1 1/ , / ,f f f fD x D f x D x f x= = + + ( ) ( )( ) ( ) 1 粒僚.留両凌留 1 1 1 1 1 虜留旅 虜留旅 虜留旅 1 1 1 f x x x f x f f x f x e 錚縁１ ワ１ 錚器４ 錚 錚 錚 錚 錚 錚 錚癌 +錚鰹３ 錚 [ )1,f fD e = + + . 両竜略龍凌亮竜 侶 亮凌僚凌凌僚溜留 侶 f f : 1凌 凌 凌 ( ) 0f x > 侶 f 竜溜僚留旅 粒僚侶溜 留両凌留 凌 [ )1,A = + . [ )1 2x 1, ,x e + + 亮竜 ( ) ( ) ( )( ) ( )( ) -粒僚.留両凌留 -粒僚.留両凌留 1 2 1 2 1 2 f f x x f x f x f f x f f x< < < ( )( ) ( )( )1 2f f x f f x < , 隆侶了留隆流 侶 f f 竜溜僚留旅 粒僚侶溜 留両凌留 凌 [ )1,e + + . 2凌 凌 凌 侶 f 竜溜僚留旅 留留粒粒溜旅亮侶 虜留旅 侶 f f 竜溜僚留旅 留留粒粒溜旅亮侶 ( 僚慮竜侶 留留粒粒旅溜亮僚) 亮竜 ( ) ( ) ( )( ) ( )( ) ( )f f x f f x f f x f x 霞 錚 錚 = = 錚 錚 , 亮竜 ( )f x 0 > 虜留旅 ( )( ) 0f f x > 粒旅留 虜略慮竜 [ )1,x e + + . 留 ( ) ( ) 0f f x > 粒旅留 虜略慮竜 [ )1,x e + + , 竜凌亮劉僚 侶 f f 竜溜僚留旅 粒僚侶溜 留両凌留 凌 [ )1,e + + . 3. 溜虜凌亮竜 凌 侶亮竜溜凌 凌亮流 侶 fC 虜留旅 凌 略両凌僚留 x x : ( ) ( )1 0 0 0 0 1f x x f x e x = = = + = , 略留 凌 侶亮竜溜凌 凌亮流 竜溜僚留旅 凌 ( )1 0, . 竜旅隆流 ( ) 0f x 粒旅留 虜略慮竜 [ )1,x A = + 凌 竜亮硫留隆僚 凌 亮留 龍侶竜溜留旅 竜溜僚留旅:
  • 6. 2018 | 陸略侶 2 | 旅留粒僚溜袖留留 留僚略了侶侶 裡僚竜粒留龍袖竜僚凌旅 虜留旅隆竜旅虜凌溜陸凌僚旅劉裡竜了.6/10 ( ) ( ) 1 1 d e E 立 f x x + = 劉凌亮竜 ( ) ( ) ( )1 d 1 du u f x u x f u x e u x e u = = = + = + 虜留旅 ( )1 1 0u f= = , ( )2 1 1u f e= + = , 留凌 ( )1 1 1 1 1f e e = + = + . 里竜: ( ) ( ) ( ) ( ) 1 1 1 1 0 0 d 1 d d e u u E 立 f x x u e u u e u u + = = + = + = ( ) ( ) 121 1 00 0 d 1 0 2 u u u u u e u u e u u e e 錚 錚 錚 錚 = + + = + + =錚 錚削０ 錚 錚 錚 1 1 1 0 1 e e e 錚 錚 = + + =錚 錚 錚 錚 1 e+ ( ) 1 3 3 1 1 1 1 E 立 + = = .亮. 4. 僚 1x > 竜 旅竜旅 2 3 x x x< < 虜留旅: 侶 f 竜溜僚留旅 僚竜流 留 隆旅留流亮留留 2 ,x x錚 錚刻０ 錚 虜留旅 2 3 ,x x錚 錚刻０ 錚 侶 f 竜溜僚留旅 留留粒粒溜旅亮侶 留 隆旅留流亮留留 ( )2 ,x x 虜留旅 ( )2 3 ,x x 凌 竜ﾏ侶亮留 劉侶 里旅亮流 略凌僚 ( )2 1 ,両 x x 虜留旅 ( )2 3 2 ,両 x x ﾏ竜 ( ) ( ) ( )2 1 2 f x f x f 両 x x = 虜留旅 ( ) ( ) ( )3 2 2 3 2 f x f x f 両 x x = 亮 ( ) ( ) 1 1 f x f x e = + , 略留 侶 f 竜溜僚留旅 留留粒粒溜旅亮侶 亮竜 ( ) ( ) ( ) ( ) ( )2 1 0 1 f x f x f x e f x e 霞 = < + , 留凌 ( ) 0 f x e > 虜留旅 ( ) 0f x > . 留 ( ) 0f x霞 < 竜凌亮劉僚 侶 f 竜溜僚留旅 粒僚侶溜 慮溜僚凌留 凌 [ )1, + . 竜旅 旅: ( ) ( ) -粒僚.慮溜僚凌留 2 3 1 2 1 2 1 2 f x 両 x 両 x 両 両 f 両 f 両 < < < < < > ( ) ( ) ( ) ( ) ( ) ( ) ( )( ) ( ) ( ) 22 3 2 0 2 3 2 2 3 2 x x x f x f x f x f x x f x f x f x f x x x x x > > > ( ) ( ) ( ) ( )2 3 1x f x f x x f x + > +
  • 7. 2018 | 陸略侶 2 | 旅留粒僚溜袖留留 留僚略了侶侶 裡僚竜粒留龍袖竜僚凌旅 虜留旅隆竜旅虜凌溜陸凌僚旅劉裡竜了.7/10 1. 侶僚 慮竜侶 旅竜旅 ( ) ( ) 0x x e f x x e f x x , 粒旅留 虜略慮竜 1x > . 竜 僚略侶侶 g 亮竜 ( ) ( )x g x e f x x= , 1x > . 里竜 ( )0 0g = 虜留旅 ( ) ( )0g x g 粒旅留 虜略慮竜 1x > , 隆侶了留隆流 侶 g 留凌旅略龍竜旅 凌 0x = 凌旅虜 亮劉粒旅凌. 竜旅隆流 侶 g 竜溜僚留旅 留留粒粒溜旅亮侶 亮竜 ( ) ( ) 1x g x e f x = 虜留旅 凌 0x = 竜溜僚留旅 竜竜旅虜 侶亮竜溜凌 凌 隆旅留流亮留凌 ( )1, + , 留 凌 慮竜ﾏ侶亮留 凌 Fermat 凌虜竜旅 旅: ( ) ( ) ( )0 0 0 0 1 0 0 0g e f f = = = . 2. 侶僚 慮竜侶 旅竜旅 ( ) ( ) ( ) ( )1 2x x f x e x f x霞 + = + ( ) ( ) ( ) ( )1 1x x f x x f x e x e霞 霞 + + = + + ( ) ( ) ( )1 1x f x x e x 霞霞 錚 錚刻 錚高 + = +錚 錚 錚 錚 旅 僚劉竜旅竜 凌 竜流亮留凌 劉侶 里旅亮流 劉凌亮竜: ( ) ( ) ( ) 11 1 1( )x f x x e x c + = + + 旅留 0x = 侶 劉侶 (1) 粒溜僚竜留旅: ( ) ( ) ( ) ( ) 0 1 1 0 0 1 0 1 1 虜留旅 留虜亮侶 0 0 f e f f f 錚錫 + = + + 錚 = 錚 = 錚器 僚旅虜留慮旅ﾎ熟留 侶 劉侶 (1) 留溜僚凌亮竜: ( ) ( ) ( ) ( ) 1 0 1 1 1 1 1 x x x f x x e x f x e x + > 霞 + = + = + ( ) ( )( )1lnx f x e x 霞霞 = + 旅 僚劉竜旅竜 凌 竜流亮留凌 劉侶 里旅亮流 凌虜竜旅: ( ) ( ) 21 2ln ( )x f x e x c = + + 旅留 0x = 侶 劉侶 (2) 粒溜僚竜留旅: ( ) ( ) ( ) 0 2 2 2 0 0 1 1 1 0 虜留旅 留 侶僚 慮竜侶 0 1 lnf e f f f f 錚= + + 錚 = + =錚 = 錚器 僚旅虜留慮旅ﾎ熟留 侶 劉侶 (2) 硫溜虜凌亮竜: ( ) ( )1lnx f x e x= + 亮竜 1x > .
  • 8. 2018 | 陸略侶 2 | 旅留粒僚溜袖留留 留僚略了侶侶 裡僚竜粒留龍袖竜僚凌旅 虜留旅隆竜旅虜凌溜陸凌僚旅劉裡竜了.8/10 3. 留. 両竜略龍凌亮竜 侶僚 f 凌 侶 亮凌僚凌凌僚溜留: ( ) 1 1 x f x e x = + 亮竜 ( )0 0f = ( ) ( ) 2 1 0 1 x f x e x 霞 = + > + 粒旅留 虜略慮竜 1x > 略留 侶 f 竜溜僚留旅 粒僚侶溜 留両凌留 凌 ( )1, + . 僚 ( ) ( ) ( ) -粒僚.留両凌留 1 0 0 0 0 f x f x f f x 霞 < < < = < 凌 ( )1 0, , 略留 侶 f 竜溜僚留旅 粒僚侶溜 慮溜僚凌留 凌 ( ]1 0, . 僚 ( ) ( ) ( ) -粒僚.留両凌留 0 0 0 0 f x f x f f x > > = > 凌 ( )0, + , 略留 侶 f 竜溜僚留旅 粒僚侶溜 留両凌留 凌 [ )0, + . x 1 0 + ( )f x + ( )f x 竜旅隆流 侶 f 竜溜僚留旅 粒僚侶溜 慮溜僚凌留 虜留旅 僚竜流 凌 ( ]1 0, 劉凌亮竜 旅: ( ]( ) ( ) ( )) [ )1 1 0 0 1, , lim , x f f f x+ 錚 = = + 錚錚 留凌 ( ) ( )( ) ( )1 1 1 1lim lim lnx x x f x e x e+ + = + = = + . 竜旅隆流 侶 f 竜溜僚留旅 粒僚侶溜 留両凌留 虜留旅 僚竜流 凌 [ )0, + 劉凌亮竜 旅: [ )( ) ( ) ( )) [ )0 0 1, , lim , x f f f x + 錚+ = = + 錚 留凌 ( ) ( )( ) ( )ln lim lim ln lim + + + 錚 錚刻 錚+ = + = =錚 錚削 錚 錚 錚削 錚醐０ 錚 1 1 1x x xx x x x f x e x e e ( ) ( )= + = +1 0 虜留旅 ( ) ( )DLH 1 1 11 0 1 ln lim lim limx x xx x x x x e e e x + + + + + + += = = + .
  • 9. 2018 | 陸略侶 2 | 旅留粒僚溜袖留留 留僚略了侶侶 裡僚竜粒留龍袖竜僚凌旅 虜留旅隆竜旅虜凌溜陸凌僚旅劉裡竜了.9/10 留 ( )( ) [ )1 1, ,f + = + . 竜旅隆流 ( ) ( )( )2 1 1 2, ,f + = 虜留旅 侶 f 竜溜僚留旅 僚竜流 虜留旅 粒僚侶溜 慮溜僚凌留 凌 ( )1 0, 略竜旅 亮凌僚留隆旅虜 ( )1 1 0,両 ﾏ竜 ( )1 2f 両 = . 虜亮侶 ( ) ( )( )2 1 2, ,f + = + 虜留旅 侶 f 竜溜僚留旅 僚竜流 虜留旅 粒僚侶溜 留両凌留 凌 ( )0, + 略竜旅 亮凌僚留隆旅虜 ( )2 0,両 + ﾏ竜 ( )2 2f 両 = . 留 侶 竜両溜侶 ( ) 2f x = 劉竜旅 留虜旅硫ﾏ 隆凌 溜龍竜, 旅 ( )1 1 0,両 虜留旅 ( )2 0,両 + . 硫. 1凌 凌 僚 凌 竜亮硫留隆僚 凌 溜凌 亮竜留両 侶 fC 虜留旅 侶 竜慮竜溜留 2y = 竜 ( ) 2 1 2 d 両 両 E f x x= 僚 ( ) ( ) ( ) -粒僚.慮溜僚凌留 1 10 2 f 両 x f x f 両 f x 粒旅留 虜略慮竜 [ ]1 0,x 両 . 僚 ( ) ( ) ( ) -粒僚.留両凌留 2 20 2 f x 両 f x f 両 f x 粒旅留 虜略慮竜 [ ]20,x 両 . 留 ( ) 2f x 粒旅留 虜略慮竜 [ ]1 2,x 両 両 凌竜 ( ) ( )( )2 2 1 1 2 d 2 d 両 両 両 両 E f x x f x x= = 亮 旅竜旅 旅 ( ) 1f x 粒旅留 虜略慮竜 [ ]1 2,x 両 両 竜凌亮劉僚 ( ) ( )1 2 1f x f x 粒旅留 虜略慮竜 [ ]1 2,x 両 両 溜 僚留 旅竜旅 留僚凌 侶 旅侶留. 留: ( )( )2 2 1 1 2 22 d 1d 両 両 両 両 f x x x E 両 両 < <
  • 10. 2018 | 陸略侶 2 | 旅留粒僚溜袖留留 留僚略了侶侶 裡僚竜粒留龍袖竜僚凌旅 虜留旅隆竜旅虜凌溜陸凌僚旅劉裡竜了.10/10 2凌 凌 里凌 竜亮硫留隆僚 竜溜僚留旅 凌 竜亮硫留隆僚 凌 粒留亮亮凌虜旅留亮劉僚凌 溜凌 凌 隆旅了留僚凌 流亮留凌. 留留侶凌亮竜 旅: ( ) ( ) ( )E E < < 2 1 両 両 < , 留凌 ( ) 2 1 両 両= 虜留旅 ( ) 1 = . 4 劉凌亮竜 ( ) ( ) 2 1 1 u f x uf x = = . 僚 ( ) ( ) 1 1 0 0x f x u f x + + + + . 留 ( ) ( ) 2 1 2 1 1 侶亮 侶亮lim ln lim ln x u f x u uf x + + 錚 錚刻 錚 錚 錚刻 錚駈 錚削 錚撃 = =錚 錚件 錚削 錚件 錚 錚 錚醐０ 錚誌 錚醐０ 錚 ( ) ( )0 0 侶亮 侶亮 2 2 2 1 0 0lim ln lim ln u u u u u u u u+ + 錚 錚 錚 錚高 = = =錚 錚 錚 錚 錚 錚 留凌 0 侶亮 1lim u u u+ = 虜留旅 ( ) ( ) DLH 0 0 0 0 2 1 0 1 1 ln lim ln lim lim lim u u u u u uu u u u u + + + + 錚 錚 錚 錚 錚 錚 錚 錚 = = = =錚 錚 錚 錚 錚 錚 錚 錚撃 錚 錚 錚 錚 .