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F



         1.                                            3 F              13 F (60               )
         2. F            1                                                           F               กF (20    )
                F        2                                                      F    กF        ก      ก F F F (20                   )
                F        3                                          ก             ก      ก       ก F F F (20      )
         3.                                   F    F                                F F ก F 20         F ก     ก                F         F
              20                  F

     F   1                                F                    กF


1.                     lim      -x
                      x→ -1 x - 1
                                  ( ) 2                        ก x<0                                                                     (5       )

2.
                     x→1
                              ( )
                      lim x -x1                                                                                                          (5       )

3.       ก               F f(x 2) =                     x+1                         F f(x)            F           x=0       F           (10       )
                                                       ( x + 1 )2
                                                             3
4.                            F   กF              f(x) = 3 xx -- 28 F                     F (1, 5)            F                         (10       )




 F       2                F               กF            ก               ก F F F


1.       ก                F f(x) = xx- -11                                 F        กF     f         x=2                                 (5       )
2.                             F                                               18                                       ก           F
                             ก                                                                                        (5                          )
3.                      ก           F          F                F y = x3 3x2 + 6        (2, 2)                        (5                          )
4.       ก                 F f(x) = u(x) ⋅ v(x)                    u(x) = (x3 + k)2, v(x) = x2 + k, k ∈ R+ F f′( 1) = 72                      F
                    f(k)                                                                                              (5                          )
5.                    F                F     F                          F     กF f(x) = x3 + 2x2 + x + 2             (10                          )
F   3ก           ก           ก                    ก F

1.                                            F         F    F    F y = x2, F   y=0  y=3                   (10    )
2.           F                                                  F F F F x 4x 8y 12 = 0
                                                                              2
                                                                                         F                y=3
     ก                F       F       F             F       ก F       F    y=0                             (10    )
                            2
3.   ก           F f′(x) = x 2 4 F f(1) = 0
                              -                                              F
                                  x
     1) กF f(x) F                F [ 4, 0) ∪ (1, 5]                                F                         (5   )
     2) f(x) F               F     F            F                        F F                                 (5   )
     3)      ก       F         y = f(x)                                                                    (10    )
4.   ก       F g(x) = [u(x)]4 + 1, u′(x) = c , c                         F             F u(0) = 1   u(1) = 3
                                                                 x
     1)      F        g′(1)                                                                                 (5    )
     2) u(x)                              F                          F       F F                            (5    )
     3)      ก            F                       y = u(x)                                                 (10    )

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ลิมิต

  • 1. F 1. 3 F 13 F (60 ) 2. F 1 F กF (20 ) F 2 F กF ก ก F F F (20 ) F 3 ก ก ก ก F F F (20 ) 3. F F F F ก F 20 F ก ก F F 20 F F 1 F กF 1. lim -x x→ -1 x - 1 ( ) 2 ก x<0 (5 ) 2. x→1 ( ) lim x -x1 (5 ) 3. ก F f(x 2) = x+1 F f(x) F x=0 F (10 ) ( x + 1 )2 3 4. F กF f(x) = 3 xx -- 28 F F (1, 5) F (10 ) F 2 F กF ก ก F F F 1. ก F f(x) = xx- -11 F กF f x=2 (5 ) 2. F 18 ก F ก (5 ) 3. ก F F F y = x3 3x2 + 6 (2, 2) (5 ) 4. ก F f(x) = u(x) ⋅ v(x) u(x) = (x3 + k)2, v(x) = x2 + k, k ∈ R+ F f′( 1) = 72 F f(k) (5 ) 5. F F F F กF f(x) = x3 + 2x2 + x + 2 (10 )
  • 2. F 3ก ก ก ก F 1. F F F F y = x2, F y=0 y=3 (10 ) 2. F F F F F x 4x 8y 12 = 0 2 F y=3 ก F F F F ก F F y=0 (10 ) 2 3. ก F f′(x) = x 2 4 F f(1) = 0 - F x 1) กF f(x) F F [ 4, 0) ∪ (1, 5] F (5 ) 2) f(x) F F F F F F (5 ) 3) ก F y = f(x) (10 ) 4. ก F g(x) = [u(x)]4 + 1, u′(x) = c , c F F u(0) = 1 u(1) = 3 x 1) F g′(1) (5 ) 2) u(x) F F F F (5 ) 3) ก F y = u(x) (10 )