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鏈鏤鏈鏤わ錆鏤鏈鏤器 鏈鏤鏈鏈鏈鏈鏈鏤器 鏈鏤鏈鏤器擦鏤鏈鏈鏤鏤器 鏈鏤鏈醐鏈鏤器
                                   鏤鏈鏈鏈鏈 鏈鏤鏈鏈鏈鏤器 鏈鏤鏤鏤鏤鏤器

                        惠        惆悸 悋        惘        惘 悋    悵悴 悋
                                                                                          :     悋
                                                                                惠         悋 悸 : 30
                                                                                        : 50     悋

                                                                        鏈鏤鏈鏤わ梱鏤器札 鏈鏤件鮫 )50 鏤鏤鏤(
                     1. 鏈べ 鏤鏤 鏤わ鏤わ鮫鏤鏈 鏈鏤件鏈鏈鏈 鏈鏤鏤わ梱鏤鏈鏈  鏈鏤鏤わ鏈鏈鏤鏈: 0 = . z族 (1 + i) z  2  i
                                                                                      
              鏤鏈鏤わ痕 鏈 1 z鏤 2 z鏤鏈わ梗鏤 鏤鏈鏤 鏈鏤鏤わ鏈鏈鏤鏈 鏈わ惨鏈 1 z鏤鏤 鏈鏤鏈べ 鏈鏤鏈鏤 鏈鏈鏈鏤 鏈鏤鏈わ鏤器鏤 鏤わ鮫鏈鏈.
                                                                         鏤
                                         2. 鏈鏤鏤わ佐鏈鏤鏤 鏈鏤鏤わ梱鏤鏈 鏤わ雑鏈器鮫鏈 鏈鏤鏤 鏤わ鏤鏤 鏤わ鏤鏈鏤わ懇 鏤鏤わ鏈鏈鏤鏈.
                B  A鏤  C鏈鏤鏤鏤鏤 鏈鏤鏈鏤 鏤鏤鏈鏈わ鏤鏈 鏤鏤鏤 鏈鏤鏈鏈鏈鏤器 1 z2  z鏤 3 z鏈わ惨鏈 . z3 = 3  2i
                                            鏈( 鏤モ鏤 鏤誌困鏤鏈 鏈鏤鏤鏤鏤鏈  I鏤わ雑鏈鏈種 鏈鏤鏤鏤鏤鏈 ] . [ BC
                                                                                   鏤癌
                                        1z3  z
                             鏤鏈鏈器鏤鏈鏈:             鏈( 鏈鏤鏈鏈 鏤鏤鏤 鏈鏤鏈醐 鏈鏤鏤わ鏤鏈鏤 鏈鏤鏤鏈鏈 鏈鏤鏤わ梱鏤鏈
                                        1z2  z
                     - 鏈鏤  C鏤鏤 鏈種鮫鏈鏈  B鏈鏈鏈わ鮫鏤陥 鏤鏤鏤鏤 ≠鏤鏤鏈 鏈鏤鏤器惨鏤 鏤鏤鏈鏈種梱鏤 鏈鏤鏤わ擦 モ鏈鏈.
                        鏤癌                         鏤癌                                 モ
                                                                  - 鏤鏤鏤 鏈鏤鏤わ鏤鏈 . ABC
                                         鏈( 鏤モ鏤 鏤誌困鏤鏈 鏈鏤鏤鏤鏤鏈  D鏤鏤鏤器梱鏈  A鏈鏈鏤鏤鏈器鏈 鏈鏤鏤 . I鏤癌
                                                                鏈鏤鏈鏤わ梱鏤器札 鏈鏤鏈鏈鏤鏤 )5,3 鏤鏤鏤(
                                              鏤鏈鏤鏤 )  ( un鏈鏤鏤わ鏈鏈鏤鏤器 鏈鏤鏤わ鏈鏤鏈 鏤鏤鏤  鏤鏤わ 鏤器鏤:
                                   2 = 0錚u
                                   錚霞
                                   1 + 錚un +1 = 2un
                             1    un = vn鏈鏤器札 鏈鏤 鏈鏤鏤わ鏈鏈鏤鏤器 )  ( vn鏤わ鏈鏈鏤鏤器 鏤鏤鏈鏈器惨鏈. 鏈( 鏤鏤鏤
                                                        鏤鏈鏈 鏤鏤鏈鏈鏈 鏤鏤  vn鏈鏤  un鏈鏈鏤誌鏈 . n
                                                   01= p      01= p
                                                  鏤 .  vp    u      p   鏈( 鏈鏈わ佐鏈 鏈鏤鏤わ鏤わ鮫鏤鏤器札:
                                                      0= p     0= p

                                                                鏈鏤鏈鏤わ梱鏤器札 鏈鏤鏈鏈鏤鏈 )50 鏤鏤鏤(
  鏈鏤鏈鏈 鏤鏈鏈 鏤わ痕鏤鏈鏈 鏈鏤鏈鏤鏤鏈 鏈鏈わ擦 鏈鏤件梱鏤鏈鏤 1 2 3 4 5 6 鏈鏈わ惨鏈 鏈鏈わ鏤わル 鏤鏤鏤鏈 鏤鏈鏤 鏈鏤件鮫鏈鏤 鏤鏤霞
 1 p6  p5  p4  p3  p2  p鏤鏤鏤 鏤わ鏤鏈鏈器鏈 鏤鏤鏤 鏈鏤鏈鏈鏈鏤器 鏤わ 鏈鏤件鏈鏈鏈 1 2 3 4 5 6 鏤鏤鏤 鏈鏤鏈鏈鏈鏤器.
                                                 1. 鏤 モ鏤 鏤鏈鏤鏤鏤 鏈鏤誌困鏈鏤わル 鏈鏤鏤わ梱鏤鏤 鏈鏤鏈鏤 鏈鏤鏈鏈鏈鏈鏈.
                                                                                        鏤癌
                                                   2. 鏤鏈鏤わ参 鏈鏤鏈鏈 鏈鏤鏤鏈鏈 鏤鏈鏤 鏤鏤鏤鏈鏈鏈 鏈鏤鏈わ鮫鏈鏈鏈:
" : A鏈鏤鏤鏈鏤 鏈鏤鏤鏈鏤鏈 鏤器困鏤べ 鏈鏤鏤わ 鏈鏤鏈鏤器"   " : B鏈鏤鏤鏈鏤 鏈鏤鏤鏈鏤鏈 鏤器困鏤べ 鏈鏤鏤わ 鏈鏤鏈鏈 鏤わ札 鏈鏤 鏤器佐鏈鏤鏤 3" 
                                                      " : C鏈鏤鏤鏈鏤 鏈鏤鏤鏈鏤鏈 鏤器困鏤べ 鏈鏤鏈鏤鏤 3 鏈鏤 4".
                                               鏈( 鏈鏈わ佐鏈 鏈鏈わ鏤わ鏤誌 鏈鏤鏈わ鮫鏈鏈鏈  B  A鏤 . C
                                                    鏈( 鏈鏈わ佐鏈 鏈鏤誌困鏈鏤わル 鏈鏤鏈醐梱鏤鏤 ) . PA ( B
                               3. 鏤 鏈鏤鏈わ鏈鏈鏈鏈鏤  A鏤  B鏤わ佐鏈鏤鏤鏈鏈鏤  鏤鏤  A鏤  C鏤わ佐鏈鏤鏤鏈鏈鏤 
                                   4. 鏤わ 鏤鏤 鏈鏈わ鏤わル 鏈鏤 鏤鏈わ瑳 鏤鏤鏤 鏈鏤鏈鏤鏤 6 鏤 モ鏈 鏤鏤鏤 鏈鏤件 
                                                 鏈



                                             1
鏈鏤鏈鏤わ梱鏤器札 鏈鏤鏈鏈鏈鏤 )5,60 鏤鏤鏤(
                       鏈鏤鏈鏈鏤鏈 鏈鏤鏤鏈鏈鏤器  f鏤わ鏈鏤鏈 鏤鏤鏤 鏈鏤鏤わ鏈ル  I鏈わ惨鏈 [+ ;2] =  I鏤鏤わ 鏤器鏤:
                               )2 + f ( x ) = 1 + x ln ( x
                 )  (C鏈鏤わ鏤器鏤鏈 鏈鏤鏈鏤器鏤鏤 鏤鏤 鏈鏤鏤わ佐鏈鏤鏤 鏈鏤鏤わ痕 モ鏈 鏈鏈鏤鏤わ鏤鏤 鏈鏤鏤わ鏤鏈鏤わ懇 鏤鏈鏤鏤わ鏈鏈鏤鏈 ) . (O;i, j
                                                         鏤
                               1. 鏈( 鏈鏈わ佐鏈 ) f ' ( x鏤 ) f " ( x鏤わ札 鏈鏈 鏤 鏤鏈鏈 鏤わ札 . I
                                          
鏈( 鏤 モ鏤 鏈鏈醐鏈鏈 ) f " ( x鏈鏤 鏈鏈器鏤鏈鏈 鏤鏈鏤鏈 鏤鏈鏈 鏈わ鏤器鏤 鏤鏈わ惨鏈  留鏤わ札 鏈鏤鏤わ鏈ル ]5,0;6,0[ 鏈鏈わ惨鏈
                                                        モ                     鏤癌
                                                                    0 = ) . f ' (留
                                                          2. 鏈鏈鏈鏈 鏈鏤 モ鏈鏈鏈 鏈鏤鏈鏈鏤鏈 . f
                                                                          鏤癌
                                                                   族留 + 2 留
                                = )  f (留鏈鏤 鏈鏈器鏤鏈鏈 鏈わ瑳鏈鏈 鏤 ) . f (留
                                                        モ                     3. 鏈鏤器札 鏈鏤モ
                                                                               モ
                                                                      2+留
                   4. 0  M鏤鏤鏤鏈 鏤わ札 )  (C鏤鏈鏈種鏈鏤鏈 0 x鏤 ) 0 (Tx鏈鏤鏤わ擦鏈鏈 鏤鏤鏤わ雑鏈わ雑鏤 )  (C鏤鏤 0 . M
                       (Tx鏤 モ鏈 鏈鏈鏤鏤わ鏈鏈  O鏈鏈鏈 鏤鏤鏤鏤 鏈鏈鏈 鏤鏈鏤 ) 0. f ( x0 ) = x0 f ' ( x
                                                                             鏤も     0
                                                                                       )   鏈( 鏈 モ鏤 鏈鏤モ
                                                                                           鏤 モ
               鏈( 鏈鏈器鏤鏈鏈 鏤鏈鏤鏈 鏤わ擦鏈鏈器惨鏤 )  (Ta鏤 )  (Tb鏤器擦 モ鏈鏤 鏈鏈鏤鏤わ鏈鏈  . O鏤鏤 鏈鏤鏤鏈鏈鏤器札  a鏤 . b
                                鏤癌
                                モ
                                                鏈
                                          5. 鏈鏈鏈器察 鏈鏤鏤わ擦鏈鏈器惨鏤 )  (Ta鏤 )  (Tb鏈鏤 鏈鏤鏤わ雑鏈わ雑鏤 ) . (C
                                                            モ




                                           2
鏈鏤鏈べ 鏈鏤鏤鏤わ鮫鏈鏈鏤 鏤鏈器梗鏤 鏈鏤鏈鏤鏤鏤器
                                          鏤            
                                                                                   鏈鏤鏈鏤わ梱鏤器札 鏈鏤件鮫 )50 鏤鏤鏤(
      .......................... 1       1. 鏈べ 鏈鏤鏤わ鏈鏈鏤鏈: 族)  z1 = 2 + i   = (3 + i鏤 1 = 2z
                                                                                        
    2. 鏈( 0,5 ........................................................................ z I = 1  i
                                                             1z3  z                    
     ................................................. 1             = i = cos + i sin       鏈(
                                                             1z2  z           2         2
                   錚 錚金
  - 鏤わ札 ) 1 z3  z1 = i ( z2  z鏤鏈器鏤鏈鏈 鏈鏤  C鏤鏤 鏈種鮫鏈鏈  B鏈鏈鏤鏈鏤鏈鏈鏤 0,75 ........ r 錚 A; 錚撃
                   錚     錚撃
                         錚撃                             モ
                   錚 2錚呉
                   錚
                                                                                   
                                                                          (
   - 鏤鏤わ雑鏤 =  AB, AC鏤  : AB = AC鏈鏤鏤わ鏤鏈  ABC鏤鏈鏈鏤 鏤鏤わ鏤鏈鏤器艮 鏈鏤鏈器鏤鏤器札 .......... 5,0
                                                                                   2
                                                                                        )
  鏈( 0,75 .......................................................... z D = z A + 2z1 = 3i
                                                                       鏈鏤鏈鏈鏈鏤鏤  ABCD鏤わ梱鏈鏤:
  )鏤鏤鏈鏈鏤 鏤わ鏤鏈鏈種鏈鏤 鏤鏤鏤器鯖 鏈鏈鏤鏤器 鏤鏈鏈鏤わ 鏤鏤鏤鏤鏈鏤 鏤わ鏈鏈鏤鏤器鏤 鏤わ鏤鏈鏤器佐鏈鏤( ...................... 52,0
                                                                        鏈鏤鏈鏤わ梱鏤器札 鏈鏤鏈鏈鏤鏤 )5,3 鏤鏤鏤(
   鏈( 鏈鏈鏈鏈鏈 鏈鏤 鏈鏤鏤わ鏈鏈鏤鏤器 )  ( vn鏤鏤鏈鏈器惨鏈 .................................................... 5,0
鏈鏤鏤器惨鏤 鏤鏈鏈鏈鏈鏤  vn鏤  un鏈鏈鏤誌鏈 0,5 + 0, 5 ................................................ n
                                                           01= p       01= p
    鏤 1 + 1 ................................................  v p     u      p    鏈( 鏈わ佐鏈鏈 鏈鏤鏤わ鏤わ鮫鏤鏤器札
                                                           0= p        0= p

                                                                                   鏈鏤鏈鏤わ梱鏤器札 鏈鏤鏈鏈鏤鏈 )50 鏤鏤鏤(
                    6
                                     1p  p  p  p  p  p    1
                   1=  p i    鏈わ惨鏈      = 6 =5 =4 =3 =2 =    1. 鏤鏈鏤鏤鏤 鏈鏤誌困鏈鏤わル:
                   1= i              1    2  3  4  5  6   12
                                                     k         1       2           3        4    5     6
  ........................................ 57,0                1       2           3        4    5     6
                                                     pk
                                                               12      12          12       12   12    12

                                                                                         4
                                                                   = 6 p ( A) = p2 + p4 + p
                                                                                           2. 鏈(
                                                                                         7
                                                                                         6
........................................... 5,03       = 6 p ( B ) = p3 + p4 + p5 + p
                                                                                         7
                                                                                         1
                                                                      = 4p (C ) = p3 + p
                                                                                         3
                                                                             5 )p ( A  B
  = ) 0,5 ........................................................ p A ( B             鏈( =
                                                                                )p ( A   6
                                                                         01                    42
 A鏤  B鏤鏤器梱 鏤わ佐鏈鏤鏤鏈鏤器札 ...................... 57,0           = ): p ( A  B     = ) p ( A) .p ( B鏤     3.
                                                                         12                    94
                                                                          4                     4
 A鏤  C鏤わ佐鏈鏤鏤鏈鏈鏤 ............................. 57,0         = )  p ( A) .p (C鏤 = ) : p ( A  C
                                                                          12                    12
                                                     4. 鏈鏈わ鏤わル 鏈鏤 鏤鏈わ瑳 鏤鏤鏤 6 鏤わ梱鏈 鏤鏤鏤 鏈鏤件:



                                               3
6
                                                                                   錚 錚金
                                                                                   錚5錚撃
  768,0 = 0,5 ......................................... p ( X  1) = 1  p ( X = 0 ) = 1  錚 錚撃
                                                                                   錚7 錚撃
                                                                                   錚 錚呉

                                                                                 鏈鏤鏈鏤わ梱鏤器札 鏈鏤鏈鏈鏈鏈鏤 )5,60 鏤鏤鏤(
                                                               4+x                                 x
................................ 5,0 2        = )f " ( x             + )2 +  f ' ( x ) = ln ( x     1. 鏈(
                                                            族)2 + ( x                             2+x
 鏈( ) f " ( x鏤わ鮫鏈鏈 鏈鏤わ鏤わリ 鏤件札 2 >  x鏤鏤わ雑鏤 '  f鏤わ鏈鏈鏤器懇鏈 鏈鏤わ鏤わ 鏤鏤鏤 鏈鏤鏤わ鏈ル 0,25 .......... I
                                                            モ
                                                鏤鏈鏤器雑鏈 270,0 = )5,0( '  f鏤 90,0 = ) 6,0( ' f
  ............... 5,0                                        鏤鏈わ佐鏈 鏤鏤鏈鏤器 鏈鏤鏤鏤器察 鏈鏤鏤わ鏤鏈器鏈
                              鏤器鮫鏈鏈 鏤鏈鏈 鏤鏈わ惨鏈  留鏤わ札 鏈鏤鏤わ鏈ル ]5,0;6,0[ 鏈鏈わ惨鏈 0 = ) f ' (留
                                                                                2. 鏈鏤 モ鏈鏈鏈 : f
                                                                                       鏤癌
+ = ) lim f ( x鏤 + = )2 0,5 ........................................... lim f ( x
                                                   +x                   2x

                                                                                        鏈鏈鏤 鏈鏤鏈鏤 モ鏈鏈鏈:
                                                                                            鏤癌

                                           x         2                   留                           +
                                        )f ' ( x                         0                +
 ....................... 57,10
                                                     +                                               +
                                          )f ( x
                                                                        ) f (留

                                                                                            族留 + 2 留
   = )  f (留鏤 98,0 < ) 0,5 ....................................... 0,026 < f (留                       3.
                                                                                              2+留
  4. 鏈( 鏈鏤鏤わ擦鏈鏈 鏤器擦鏈 鏈鏈鏤鏤わ鏈鏈 鏈鏈鏈 鏤鏤鏤鏤 鏈鏈鏈 鏤鏈鏤 ) 00,5 ............................. f ( x0 ) = x0 f ' ( x
                                                                                      モ
                                                                                                 2 0x
                                                     + )2 + 01 + x0 ln ( x0 + 2) = x0 ln ( x          鏈(
                                                                                               2 + 0x
  .............................. 5,0
                                           鏤鏤わ雑鏤 0 = 2  0 x0 族  x鏤鏤鏈鏈: 2 = 0 x鏈鏤 1 = 0x
                                     錚       1錚金
2 =  a鏤 1 =  b鏤鏤わ雑鏤 鏤わ鏈鏈鏤鏈鏈 鏈鏤鏤わ擦鏈鏈器惨鏤:  T2 : y = 錚ln 4 + 錚 x鏤 2 0,25 .... T1 : y = x
                                     錚        錚撃
                                              錚撃
                                     錚
                                     錚       2錚呉
                                                                                                    5. 鏈鏤鏈鏈器察




                                                     4
1 ........................................




                                             5

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Sujet math-33

  • 1. 鏈鏤鏈鏤わ錆鏤鏈鏤器 鏈鏤鏈鏈鏈鏈鏈鏤器 鏈鏤鏈鏤器擦鏤鏈鏈鏤鏤器 鏈鏤鏈醐鏈鏤器 鏤鏈鏈鏈鏈 鏈鏤鏈鏈鏈鏤器 鏈鏤鏤鏤鏤鏤器 惠 惆悸 悋 惘 惘 悋 悵悴 悋 : 悋 惠 悋 悸 : 30 : 50 悋 鏈鏤鏈鏤わ梱鏤器札 鏈鏤件鮫 )50 鏤鏤鏤( 1. 鏈べ 鏤鏤 鏤わ鏤わ鮫鏤鏈 鏈鏤件鏈鏈鏈 鏈鏤鏤わ梱鏤鏈鏈 鏈鏤鏤わ鏈鏈鏤鏈: 0 = . z族 (1 + i) z 2 i 鏤鏈鏤わ痕 鏈 1 z鏤 2 z鏤鏈わ梗鏤 鏤鏈鏤 鏈鏤鏤わ鏈鏈鏤鏈 鏈わ惨鏈 1 z鏤鏤 鏈鏤鏈べ 鏈鏤鏈鏤 鏈鏈鏈鏤 鏈鏤鏈わ鏤器鏤 鏤わ鮫鏈鏈. 鏤 2. 鏈鏤鏤わ佐鏈鏤鏤 鏈鏤鏤わ梱鏤鏈 鏤わ雑鏈器鮫鏈 鏈鏤鏤 鏤わ鏤鏤 鏤わ鏤鏈鏤わ懇 鏤鏤わ鏈鏈鏤鏈. B A鏤 C鏈鏤鏤鏤鏤 鏈鏤鏈鏤 鏤鏤鏈鏈わ鏤鏈 鏤鏤鏤 鏈鏤鏈鏈鏈鏤器 1 z2 z鏤 3 z鏈わ惨鏈 . z3 = 3 2i 鏈( 鏤モ鏤 鏤誌困鏤鏈 鏈鏤鏤鏤鏤鏈 I鏤わ雑鏈鏈種 鏈鏤鏤鏤鏤鏈 ] . [ BC 鏤癌 1z3 z 鏤鏈鏈器鏤鏈鏈: 鏈( 鏈鏤鏈鏈 鏤鏤鏤 鏈鏤鏈醐 鏈鏤鏤わ鏤鏈鏤 鏈鏤鏤鏈鏈 鏈鏤鏤わ梱鏤鏈 1z2 z - 鏈鏤 C鏤鏤 鏈種鮫鏈鏈 B鏈鏈鏈わ鮫鏤陥 鏤鏤鏤鏤 ≠鏤鏤鏈 鏈鏤鏤器惨鏤 鏤鏤鏈鏈種梱鏤 鏈鏤鏤わ擦 モ鏈鏈. 鏤癌 鏤癌 モ - 鏤鏤鏤 鏈鏤鏤わ鏤鏈 . ABC 鏈( 鏤モ鏤 鏤誌困鏤鏈 鏈鏤鏤鏤鏤鏈 D鏤鏤鏤器梱鏈 A鏈鏈鏤鏤鏈器鏈 鏈鏤鏤 . I鏤癌 鏈鏤鏈鏤わ梱鏤器札 鏈鏤鏈鏈鏤鏤 )5,3 鏤鏤鏤( 鏤鏈鏤鏤 ) ( un鏈鏤鏤わ鏈鏈鏤鏤器 鏈鏤鏤わ鏈鏤鏈 鏤鏤鏤 鏤鏤わ 鏤器鏤: 2 = 0錚u 錚霞 1 + 錚un +1 = 2un 1 un = vn鏈鏤器札 鏈鏤 鏈鏤鏤わ鏈鏈鏤鏤器 ) ( vn鏤わ鏈鏈鏤鏤器 鏤鏤鏈鏈器惨鏈. 鏈( 鏤鏤鏤 鏤鏈鏈 鏤鏤鏈鏈鏈 鏤鏤 vn鏈鏤 un鏈鏈鏤誌鏈 . n 01= p 01= p 鏤 . vp u p 鏈( 鏈鏈わ佐鏈 鏈鏤鏤わ鏤わ鮫鏤鏤器札: 0= p 0= p 鏈鏤鏈鏤わ梱鏤器札 鏈鏤鏈鏈鏤鏈 )50 鏤鏤鏤( 鏈鏤鏈鏈 鏤鏈鏈 鏤わ痕鏤鏈鏈 鏈鏤鏈鏤鏤鏈 鏈鏈わ擦 鏈鏤件梱鏤鏈鏤 1 2 3 4 5 6 鏈鏈わ惨鏈 鏈鏈わ鏤わル 鏤鏤鏤鏈 鏤鏈鏤 鏈鏤件鮫鏈鏤 鏤鏤霞 1 p6 p5 p4 p3 p2 p鏤鏤鏤 鏤わ鏤鏈鏈器鏈 鏤鏤鏤 鏈鏤鏈鏈鏈鏤器 鏤わ 鏈鏤件鏈鏈鏈 1 2 3 4 5 6 鏤鏤鏤 鏈鏤鏈鏈鏈鏤器. 1. 鏤 モ鏤 鏤鏈鏤鏤鏤 鏈鏤誌困鏈鏤わル 鏈鏤鏤わ梱鏤鏤 鏈鏤鏈鏤 鏈鏤鏈鏈鏈鏈鏈. 鏤癌 2. 鏤鏈鏤わ参 鏈鏤鏈鏈 鏈鏤鏤鏈鏈 鏤鏈鏤 鏤鏤鏤鏈鏈鏈 鏈鏤鏈わ鮫鏈鏈鏈: " : A鏈鏤鏤鏈鏤 鏈鏤鏤鏈鏤鏈 鏤器困鏤べ 鏈鏤鏤わ 鏈鏤鏈鏤器" " : B鏈鏤鏤鏈鏤 鏈鏤鏤鏈鏤鏈 鏤器困鏤べ 鏈鏤鏤わ 鏈鏤鏈鏈 鏤わ札 鏈鏤 鏤器佐鏈鏤鏤 3" " : C鏈鏤鏤鏈鏤 鏈鏤鏤鏈鏤鏈 鏤器困鏤べ 鏈鏤鏈鏤鏤 3 鏈鏤 4". 鏈( 鏈鏈わ佐鏈 鏈鏈わ鏤わ鏤誌 鏈鏤鏈わ鮫鏈鏈鏈 B A鏤 . C 鏈( 鏈鏈わ佐鏈 鏈鏤誌困鏈鏤わル 鏈鏤鏈醐梱鏤鏤 ) . PA ( B 3. 鏤 鏈鏤鏈わ鏈鏈鏈鏈鏤 A鏤 B鏤わ佐鏈鏤鏤鏈鏈鏤 鏤鏤 A鏤 C鏤わ佐鏈鏤鏤鏈鏈鏤 4. 鏤わ 鏤鏤 鏈鏈わ鏤わル 鏈鏤 鏤鏈わ瑳 鏤鏤鏤 鏈鏤鏈鏤鏤 6 鏤 モ鏈 鏤鏤鏤 鏈鏤件 鏈 1
  • 2. 鏈鏤鏈鏤わ梱鏤器札 鏈鏤鏈鏈鏈鏤 )5,60 鏤鏤鏤( 鏈鏤鏈鏈鏤鏈 鏈鏤鏤鏈鏈鏤器 f鏤わ鏈鏤鏈 鏤鏤鏤 鏈鏤鏤わ鏈ル I鏈わ惨鏈 [+ ;2] = I鏤鏤わ 鏤器鏤: )2 + f ( x ) = 1 + x ln ( x ) (C鏈鏤わ鏤器鏤鏈 鏈鏤鏈鏤器鏤鏤 鏤鏤 鏈鏤鏤わ佐鏈鏤鏤 鏈鏤鏤わ痕 モ鏈 鏈鏈鏤鏤わ鏤鏤 鏈鏤鏤わ鏤鏈鏤わ懇 鏤鏈鏤鏤わ鏈鏈鏤鏈 ) . (O;i, j 鏤 1. 鏈( 鏈鏈わ佐鏈 ) f ' ( x鏤 ) f " ( x鏤わ札 鏈鏈 鏤 鏤鏈鏈 鏤わ札 . I 鏈( 鏤 モ鏤 鏈鏈醐鏈鏈 ) f " ( x鏈鏤 鏈鏈器鏤鏈鏈 鏤鏈鏤鏈 鏤鏈鏈 鏈わ鏤器鏤 鏤鏈わ惨鏈 留鏤わ札 鏈鏤鏤わ鏈ル ]5,0;6,0[ 鏈鏈わ惨鏈 モ 鏤癌 0 = ) . f ' (留 2. 鏈鏈鏈鏈 鏈鏤 モ鏈鏈鏈 鏈鏤鏈鏈鏤鏈 . f 鏤癌 族留 + 2 留 = ) f (留鏈鏤 鏈鏈器鏤鏈鏈 鏈わ瑳鏈鏈 鏤 ) . f (留 モ 3. 鏈鏤器札 鏈鏤モ モ 2+留 4. 0 M鏤鏤鏤鏈 鏤わ札 ) (C鏤鏈鏈種鏈鏤鏈 0 x鏤 ) 0 (Tx鏈鏤鏤わ擦鏈鏈 鏤鏤鏤わ雑鏈わ雑鏤 ) (C鏤鏤 0 . M (Tx鏤 モ鏈 鏈鏈鏤鏤わ鏈鏈 O鏈鏈鏈 鏤鏤鏤鏤 鏈鏈鏈 鏤鏈鏤 ) 0. f ( x0 ) = x0 f ' ( x 鏤も 0 ) 鏈( 鏈 モ鏤 鏈鏤モ 鏤 モ 鏈( 鏈鏈器鏤鏈鏈 鏤鏈鏤鏈 鏤わ擦鏈鏈器惨鏤 ) (Ta鏤 ) (Tb鏤器擦 モ鏈鏤 鏈鏈鏤鏤わ鏈鏈 . O鏤鏤 鏈鏤鏤鏈鏈鏤器札 a鏤 . b 鏤癌 モ 鏈 5. 鏈鏈鏈器察 鏈鏤鏤わ擦鏈鏈器惨鏤 ) (Ta鏤 ) (Tb鏈鏤 鏈鏤鏤わ雑鏈わ雑鏤 ) . (C モ 2
  • 3. 鏈鏤鏈べ 鏈鏤鏤鏤わ鮫鏈鏈鏤 鏤鏈器梗鏤 鏈鏤鏈鏤鏤鏤器 鏤 鏈鏤鏈鏤わ梱鏤器札 鏈鏤件鮫 )50 鏤鏤鏤( .......................... 1 1. 鏈べ 鏈鏤鏤わ鏈鏈鏤鏈: 族) z1 = 2 + i = (3 + i鏤 1 = 2z 2. 鏈( 0,5 ........................................................................ z I = 1 i 1z3 z ................................................. 1 = i = cos + i sin 鏈( 1z2 z 2 2 錚 錚金 - 鏤わ札 ) 1 z3 z1 = i ( z2 z鏤鏈器鏤鏈鏈 鏈鏤 C鏤鏤 鏈種鮫鏈鏈 B鏈鏈鏤鏈鏤鏈鏈鏤 0,75 ........ r 錚 A; 錚撃 錚 錚撃 錚撃 モ 錚 2錚呉 錚 ( - 鏤鏤わ雑鏤 = AB, AC鏤 : AB = AC鏈鏤鏤わ鏤鏈 ABC鏤鏈鏈鏤 鏤鏤わ鏤鏈鏤器艮 鏈鏤鏈器鏤鏤器札 .......... 5,0 2 ) 鏈( 0,75 .......................................................... z D = z A + 2z1 = 3i 鏈鏤鏈鏈鏈鏤鏤 ABCD鏤わ梱鏈鏤: )鏤鏤鏈鏈鏤 鏤わ鏤鏈鏈種鏈鏤 鏤鏤鏤器鯖 鏈鏈鏤鏤器 鏤鏈鏈鏤わ 鏤鏤鏤鏤鏈鏤 鏤わ鏈鏈鏤鏤器鏤 鏤わ鏤鏈鏤器佐鏈鏤( ...................... 52,0 鏈鏤鏈鏤わ梱鏤器札 鏈鏤鏈鏈鏤鏤 )5,3 鏤鏤鏤( 鏈( 鏈鏈鏈鏈鏈 鏈鏤 鏈鏤鏤わ鏈鏈鏤鏤器 ) ( vn鏤鏤鏈鏈器惨鏈 .................................................... 5,0 鏈鏤鏤器惨鏤 鏤鏈鏈鏈鏈鏤 vn鏤 un鏈鏈鏤誌鏈 0,5 + 0, 5 ................................................ n 01= p 01= p 鏤 1 + 1 ................................................ v p u p 鏈( 鏈わ佐鏈鏈 鏈鏤鏤わ鏤わ鮫鏤鏤器札 0= p 0= p 鏈鏤鏈鏤わ梱鏤器札 鏈鏤鏈鏈鏤鏈 )50 鏤鏤鏤( 6 1p p p p p p 1 1= p i 鏈わ惨鏈 = 6 =5 =4 =3 =2 = 1. 鏤鏈鏤鏤鏤 鏈鏤誌困鏈鏤わル: 1= i 1 2 3 4 5 6 12 k 1 2 3 4 5 6 ........................................ 57,0 1 2 3 4 5 6 pk 12 12 12 12 12 12 4 = 6 p ( A) = p2 + p4 + p 2. 鏈( 7 6 ........................................... 5,03 = 6 p ( B ) = p3 + p4 + p5 + p 7 1 = 4p (C ) = p3 + p 3 5 )p ( A B = ) 0,5 ........................................................ p A ( B 鏈( = )p ( A 6 01 42 A鏤 B鏤鏤器梱 鏤わ佐鏈鏤鏤鏈鏤器札 ...................... 57,0 = ): p ( A B = ) p ( A) .p ( B鏤 3. 12 94 4 4 A鏤 C鏤わ佐鏈鏤鏤鏈鏈鏤 ............................. 57,0 = ) p ( A) .p (C鏤 = ) : p ( A C 12 12 4. 鏈鏈わ鏤わル 鏈鏤 鏤鏈わ瑳 鏤鏤鏤 6 鏤わ梱鏈 鏤鏤鏤 鏈鏤件: 3
  • 4. 6 錚 錚金 錚5錚撃 768,0 = 0,5 ......................................... p ( X 1) = 1 p ( X = 0 ) = 1 錚 錚撃 錚7 錚撃 錚 錚呉 鏈鏤鏈鏤わ梱鏤器札 鏈鏤鏈鏈鏈鏈鏤 )5,60 鏤鏤鏤( 4+x x ................................ 5,0 2 = )f " ( x + )2 + f ' ( x ) = ln ( x 1. 鏈( 族)2 + ( x 2+x 鏈( ) f " ( x鏤わ鮫鏈鏈 鏈鏤わ鏤わリ 鏤件札 2 > x鏤鏤わ雑鏤 ' f鏤わ鏈鏈鏤器懇鏈 鏈鏤わ鏤わ 鏤鏤鏤 鏈鏤鏤わ鏈ル 0,25 .......... I モ 鏤鏈鏤器雑鏈 270,0 = )5,0( ' f鏤 90,0 = ) 6,0( ' f ............... 5,0 鏤鏈わ佐鏈 鏤鏤鏈鏤器 鏈鏤鏤鏤器察 鏈鏤鏤わ鏤鏈器鏈 鏤器鮫鏈鏈 鏤鏈鏈 鏤鏈わ惨鏈 留鏤わ札 鏈鏤鏤わ鏈ル ]5,0;6,0[ 鏈鏈わ惨鏈 0 = ) f ' (留 2. 鏈鏤 モ鏈鏈鏈 : f 鏤癌 + = ) lim f ( x鏤 + = )2 0,5 ........................................... lim f ( x +x 2x 鏈鏈鏤 鏈鏤鏈鏤 モ鏈鏈鏈: 鏤癌 x 2 留 + )f ' ( x 0 + ....................... 57,10 + + )f ( x ) f (留 族留 + 2 留 = ) f (留鏤 98,0 < ) 0,5 ....................................... 0,026 < f (留 3. 2+留 4. 鏈( 鏈鏤鏤わ擦鏈鏈 鏤器擦鏈 鏈鏈鏤鏤わ鏈鏈 鏈鏈鏈 鏤鏤鏤鏤 鏈鏈鏈 鏤鏈鏤 ) 00,5 ............................. f ( x0 ) = x0 f ' ( x モ 2 0x + )2 + 01 + x0 ln ( x0 + 2) = x0 ln ( x 鏈( 2 + 0x .............................. 5,0 鏤鏤わ雑鏤 0 = 2 0 x0 族 x鏤鏤鏈鏈: 2 = 0 x鏈鏤 1 = 0x 錚 1錚金 2 = a鏤 1 = b鏤鏤わ雑鏤 鏤わ鏈鏈鏤鏈鏈 鏈鏤鏤わ擦鏈鏈器惨鏤: T2 : y = 錚ln 4 + 錚 x鏤 2 0,25 .... T1 : y = x 錚 錚撃 錚撃 錚 錚 2錚呉 5. 鏈鏤鏈鏈器察 4