-2 -1 2 0 1 · 2019-10-31 · 0202 1 f x² 5x 21 f(x) x² 1 D 1;1 f ^` 3x² 4x 52 f(x) (x 2)² D2 f...
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Transcript of -2 -1 2 0 1 · 2019-10-31 · 0202 1 f x² 5x 21 f(x) x² 1 D 1;1 f ^` 3x² 4x 52 f(x) (x 2)² D2 f...
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2-1-2
2
-1
-2
0 1
1
x
y
2-1-2
2
-1
-2
0 1
1
x
y
BAC2020
Facebookالجزائري العربي
0202
1
f
1 x² 5x 2
f (x)x² 1
fD 1;1 2
3x² 4x 5f (x)
(x 2)²
fD 2
3 4x 8
f (x)x² 4x 3
fD 1;3 4 f (x) x² 4x 5 fD
5 x² 1
f (x)x 1
fD 1; 6
xf (x) 1
x² 1
fD ; 1 1;
Ig3 x² 5x 5
f (x)x 3
)C( f
1abcx 3 c
f (x) ax bx 3
2f
3)C( f
4)C( f
f232x 11x² 25x 27
f (x)(x 2)²
)C( f
1f
3 xlim f (x) (2x 3)
2)C( f( ) : y 2x 3
I
13x 1
x² 3x 2lim
x 1
2
2
xlim (x x 1)
3x 0
x 1 1lim
x
4
xlim (2x x² 4x 3)
II
13
2x 2
x 4x² 5x 2 1lim
x x 2 3
2
x 0
sin xlim 2
x 1 1
3
x 1
x x 1 1lim
x² x 2 2
4
xlim ( x² 3 x 2) 2
21
20
03
20
0202
0
f D ;0 2; 2f (x) x 2x 2x 1
1xlim f (x)x
lim f (x)
2 xlim f (x) x
f(C )
3 xlim f (x) ( 3x) 2
f D 1; 2x sin x
f (x)x 1
2x 1 2x 1
f (x)x 1 x 1
xD
xlim f (x)
x 0
sin xlim 1
x
x 0
f (x)lim 3
x
x 1
lim f (x)
f
1x 02x 3x x 2
xlim(3x x 3x)
20 x 1 2x x 4 <2x2
xlim( x x 4 2x)
f2f (x) x 5 f
C
1x 2 2
2
x 5 3 x 2
x 2 x 5 3
22
x 2
x 5 3lim
x 2
f
32
x
x 5 3lim 1
x 2
2
x
x 5 3lim 1
x 2
4y xf
C
a xlim f (x) ax) 0
f
C
20
20
20
25
0202
3
2 3-1-2
-1
-2
-3
-4
-5
-6
0 1
1
x
y
f3f (x) x 3x 1
1f ،
2
f (x) 0f (x)
f (x) 2 1;20,1
f (x) 2020 1;1
If
1f (x) 1
2f (x) 3
g(C )g 1; 3g(x) ax bx c
1
g(0)g(1)g '(1)abc
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33x 3x 4 0 2;2,25
g(x)
f 1;1 1; 1
f (x) x 1x 1
1f
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3f (x) 0 1;2f (x)
4 x 1;0 f (x) 0,5;2
20
12
11
10
0202
0
fa
1f (x) x² 3x a 1 2f (x) x² x 1 a 13f (x) 4 x² a 2
fC gC
f g 2;3
1
f 1 g 1
f 2
g 2
2x 0;2 h x f 2x 1
h 2;3
h 03
h2
TDL
f 1:f (x) 3 x 1 )C( f
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f (h 1) f (1)lim
h
2f
3)C( f
13
10
T
D
L
15
0202
5
2-1-2
2
3
4
-1
0 1
1
x
y
g(C )
g
g(C )AB10
I1
g( 1)g(0)g(1)g '( 1)g '(0)g '(1)
2
101g(C )
33 3
;2 2
g(x) 0g'(x) 1 g'(x) 4
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f (x) x² 2x : x 2
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1f2
219
f
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f
x² 3f (x) : x 1
x 1
f (x) x² 3 : x 1
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1f1
21
3f
10
10
10
0202
0
fD 1 x² 3
f (x)x 1
1ff '(x)f (x)D
2ghkg(x) f (x²)1
h(x) f ( )x
k(x) f ( 2x 1)
ghk
3REV R(x) f (x) ² 3
E(x) f (x)1
V(x)f (x)
R '(x)E'(x)V'(x)f (x)f '(x)
REV
f ;2 2;
320x
0
2
4
1
f(x)
(C)
1f1
fx
f (x) 2 0;2
2g31
g(x) ;x 2f (x)
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f1 f
(C )
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22020
f (x)
02
10
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01
3-
0202
0
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C
2f
3f (x) 0f (x)
4g g(x) f (x) ²
g
x1g'(x) 2f (x).f '(x)
g
O,i, j4cm
f 1;1f (x) x 1 x² f
(C )
1f
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f (x)lim
x 1 x 1
f (x)lim
x 1 3f
4(T)f
(C )
(T)f
(C )
5(T)f
(C )
f(C )f
1
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f
2xlim(f (x) x 1
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00
03
0202
0
x
y
4 f (x) 0f '(x) 0
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h
05
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0202
0
2 3 4 5 6-1-2-3-4-5-6
2
3
4
5
6
-1
-2
-3
-4
-5
-6
0 1
1
x
y
f 2 x² x
f (x)x 2
)C( f
1)C( fA(1; 3)2
323 7
)C( fy x 1
)C( f4y x 0
)C( f
If3f (x) 2x 3x² 1
1f
2f
3f (x) 0 1;2110
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2
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21
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x 1
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f
4x(D)f ( x) f (x)
00
00
00
0202
12
2 3 4 5 6 7-1-2-3-4-5-6-7-8
2
3
4
5
6
7
8
9
-1
-2
-3
-4
-5
-6
0 1
1
x
y
( c )
2
1
g
x0 g(x) 1
g(x)x
0 f 1;1 1; 1
f (x) (x)g
x 1
lim f (x)
x 1
lim f (x)
xlimf (x)
f '(x)f
f
f*
2
1f (x) x 1
x (C)(O; i; j)
1g*
3 2g(x) x x 1
g
g(x) 0 1; 0.5
2xlim f (x)x 0
lim f (x)
(C)
x3
2f '(x) 1
x f
3(C)( )y x 1
(d)(C)1
4f ( )( )(d)(C)
00
32
0202
11
Ig3g(x) 2x 4x² 7x 4
1xlim g(x)x
lim g(x)
g
2g(x) 00,7 0,8
xg(x)
IIf3x 2x 1
f (x)2x² 2x 1
f(C ) O, i , j
1xlim f (x)x
lim f (x)
2x1 1 3x
f (x) (x 1)2 2(2x² 2x 1)
f(C )( )
f(C )( )
3xx.g(x)
f '(x)(2x² 2x 1)²
f 'f
f '(x)xff ( ) 0,1
4f (1)f (x) 0
5( )f
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6h3x 4x² 2x 1
h(x)2x² 2x 1
h
(C )
xh(x) f (x) 2
h(C )
f(C )
h(C )
If I ; 1 1;0 4
f (x) xx 1
300220
310210
0202
10
2-1
2
3
-1
-2
0 1
1
x
y
f(C )
(O ;i ; j )
1fI
f
2g 0;4
g(x) xx 1
g(C )
g
g(C )( )
g
IIk 1 4
k(x) xx 1
1h 0
k(h) k(0)lim
h
h 0
k(h) k(0)lim
h
21
( )2
( )0
x 0
31
( )2
( )k
(C )
C)g
I 1; 3g(x) x 3x² 3x 1
1
gg(0)g(0,5)
0;0,5g( ) 0
g(x)I
2f 1;
3x 3x² 3x 2f (x)
(x 1)²
( )
x I3
g(x)f '(x)
(x 1)
x
f (x) f ( )lim
x
x 1
lim f x
xlim[f x (x 1)]
f
30,26 f ( )10-2
( )
330220
2-1-2-3-4-5-6-7
2
3
4
5
6
7
-1
-2
-3
-4
-5
0 1
1
x
y
0202
13
Ig3g(x) x 6x 12
1g
2g(x) 0 1,48; 1,47
xg(x)
IIf3x 6
f (x)x² 2
f(C ) O, i , j
1xlim f (x)x
lim f (x)
xx.g(x)
f '(x)(x² 2)²
f
2( )y xf
(C ).
f
(C )( )
33
f ( )2
f ( )
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f (x) xx 1
f(C )f
1f
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f(C )(D)
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1,3 x 1,4
( )f(C )f(C )
( )f(C )
4 g 1; g(x) f (x)g(C )g
g(C )f(C )
m2g(x) m
300210
350220
0202
10
f1
f (x) x 1x² 1
f
(C )
(O ;i ; j )
1f
2x2
1f '(x) 1
(x 1) x² 1
3f
4(T)f
(C )0
5f
(C )(T)f
(C )
6(D)y=x+1f
(C )
(D')
7(D)(D')f
(C )
8 g1
g(x) x 1x² 1
g
f(C )
g(C )
300212
0202
15
I gCg
3g(x) x ax b
1
g( 1)g(1)g (0)g''(0)
g
2g(x) 0
2,2; 2,1 g(x)
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1xf (x) 4g(x)
f
2f ( ) 3 ( 3) f ( )
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(C )
1k
2k
3k0
f
212x
00f'(x)
2
2
f(x)
f(x)c
f (x) ax bx 1
abc
1f '(x)ac
2f
2-1-2
2
3
4
5
-1
0 1
1
x
y
30
30
0202
10
a bc
x 1
lim f (x)x 1
lim f (x)
1
2
3
4f
3a b c 1 )C( f
(O ;i ; j )
x( )( ))C( f( )y x 1
)C( f( )
( 1;0) )C( f
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mf (x) m 2
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abC
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7)C( fmf(x)=3x+m
30
0202
10
f ; 1 1; f (x) x x² 1
(C)(O;i; j)
1ff
2 xlim f (x) 2x 0
3f 1
4f 1; ; 1
5(C)2y 51 2
6(C)
f 1;3 2
2
x 2x 15f x
x 2x 3
Cf ; ;O i j
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2C5
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m 2
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x mx 3
m
mfmC
mC
4;1
f1
;22
2
2
4x 5xf x
2x 5x 2
fC
1abcx1
;22
b b
f x a2x 1 x 2
3ffC
02
011002
001000
0202
10
4fC0
5fC
6
1f 1 1
f (x) 2x 3(x 1)²
C(O ;i ; j )
1x 1 3
2(x 2)(x² x 1)f '(x)
(x 1)
2f
3C
4C 0x 0,37; 0,25
5C0
6C
732x (7 m)x² 2(4 m)x 2 m 0....(e) m x
x(e)f (x) m
Cm(e)
f 1 x²(x 2)
f (x)(x 1)²
f(C )(O ;i ; j )
1،، x 1
f (x) x(x 1) (x 1)²
2f
3f(C )
f(C )
f(C )
4 f(C )1
5f(C )
031000
001000
0202
10
f2
x 2f (x) x
x 1
f
(C )
(O ;i ; j )
1xlim f (x)x
lim f (x)
2f2
2 2
x(x 1)(x x 4)f '(x)
(x 1)
3f
4(D) : y x f
(C )f
(C )(D)
5f
(C )1f ( 1.25)
6(D)f
(C )
7gg
(C )g
(C )f
(C )
1
1v g(x)
g(C )
f 2ax² bx c
f (x)x 2
f(C )
Iabcf(C )y x 3
3
IIa 1b 5 c 7
1f
2f(C )1
(D )2
(D )3
1(D )
2(D )
31
(D )2
(D )f(C )
4mf (x) 3x m 0
5 f 2;2 g(x) f ( x )
g0
g(C )gf(C )g(C )
05
00
0202
02
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(C )
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2g(x) 0 2,1;2,2g(x)
3xg( x) g(x)
IIf 1; 1 3
2
2x 3f (x)
x 1
f
(C )
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(x 1)
2 f
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(C )
f(C )( )
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6f
(C )
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(C )
f 1;1 2
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00
00
0202
01
fC( )( )
fC
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fC
4 mDy mx 1 m
m mD
m2
x| x 1| mx 1
x 1
f 2f x x 1 x fC ; ,O i j
1lim ( )x
f x
lim ( ) 0x
f x
2x
2
2
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x 1
x( ) 0f x
3f
xlim f x 2x 0
4 fC f
C
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g(C )
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52
51
0202
00
323 10 8
f ( )2 4
f ( )
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f
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7( )f
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(x a)f (x)
x b
ab
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(C )
f(C )( )
4g1
g(x) fx
gf
50
**************************************
********************
BAC2020
Facebookالجزائري العربي
52
(1 Ixlimg(x)x
limg(x)
3g(x) 2x 4x² 7x 4 3
x xlimg(x) lim(2x )
3
x xlimg(x) lim(2x )
g
gg'(x) 6x² 8x 7
g'(x) 06x² 8x 7 x²g
5g(x) 0
g
0,7 ; 0,8g(0,7) g(0,8) 0
g(0,7) 0,37 g(0,8) 0,06
0,7 ;0,8αg(α) 0
g(x)x
g2
g( ; ) ;0 g(x) 0 x ;
g( ; ) 0; g(x) 0 x ;
II1xlimf (x)x
limf (x)
3
x x x
x xlimf (x) lim lim
2x² 2
3
x x x
x xlimf (x) lim lim
2x² 2
5x1 1 3x
f (x) (x 1)2 2x² 2x 1
1 1 3x 1 (x 1)(2x² 2x 1) 1 3xf (x) (x 1)
2 (2x² 2x 1) 2 (2x² 2x 1)
3 31 (x 1)(2x² 2x 1) 1 3x 1 2(x 2x 1) x 2x 1f (x)
2 (2x² 2x 1) 2 (2x² 2x 1) 2x² 2x 1
f(C )( )
x
g'(x)
g(x)
115211
53
1 1 3xf (x) (x 1)
2 2x² 2x 1
x
1 3xlim 0
2x² 2x 1
f
(C )( )1
y (x 1)2
f(C )( )
f(C )( )
1 3xf (x) y
2x² 2x 1
(1 3x)
1x ;
3
f(C )( )
1x ;
3
f(C )( )
1x
3
f(C )( )
1 2;
3 3
1xx.g(x)
f '(x)(2x² 2x 1)²
f2 4 3(3x² 2)(2x² 2x 1) (4x 2)(x 2x 1) (2x 4x 7x² 4x)
f '(x)(2x² 2x 1)² (2x² 2x 1)²
3 2x(2x 4x 7x 4) x.g(x)
f '(x)(2x² 2x 1)² (2x² 2x 1)²
f '(x)f
f '(x)f '(x)x.g(x)
x.g(x)
0x
0x
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f (x)
1
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f ( )
54
1f (1)f (x) 0
f (1) 0
f (x) 03x 2x 1 0 3x 2x 1 (x 1)(x² x 1) 0 f (1) 0
(x 1) 0 (x² x 1) 0 x 11 5
x2
1 5x
2
f (x) 0f
(C )
2( )f
(C )f
(C )
3xh(x) f (x) 2 3 3x 4x² 2x 1 (x 2x 1) 2(2x² 2x 1)
h(x) f (x) 22x² 2x 1 2x² 2x 1
h(C )
f(C )
h(C )
h(x) f (x) 2 f
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2 3 4 5-1-2-3-4
2
-1
-2
-3
0 1
1
x
y
f(C )
h(C )
( )
55
I1fI
x x
4lim f (x) lim ( x )
x 1
x 1 x 1
4lim f (x) lim ( )
x 1
x 1 x 1
4lim f (x) lim ( )
x 1
5f
x x
4lim g(x) lim (x )
x 1
g(C )( )
( )y xx x x
4 4lim g(x) lim (x x) lim ( ) 0
x 1 x 1
g
g[0; [
4 (x 1)² 4 (x 3)(x 1)g '(x) 1
(x 1)² (x 1)² (x 1)²
g'(x) 0(x 1)(x 3) 0 x=1x 3
x 1
10x
g'(x)
4
3
g(x)
II1x 0
k(h) k(0)lim
h
x 0
k(h) k(0)lim
h
x 0 x 0
h² 3h h 3lim lim 3
h(h 1) h 1
x 0 x 0
4h 4
k(h) k(0) h 1lim limh h
01x
g'(x)
4
g(x)
155226
56
x 0 x 0
h² 5h h 5lim lim 5
h(h 1) h 1
x 0 x 0
4h 4
k(h) k(0) h 1lim limh h
k035
kk
0(0;4)k
21( )2( )
1( )0x 00x 0y k '(0)(x 0) k(0) y 3x 4
2( )0x 00x 0y k '(0)(x 0) k(0) y 5x 4
11( )2( )k(C )
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x 0k(x) g(x)k(C )g(C )
2 3 4 5 6 7 8-1-2-3-4-5-6-7-8
2
3
4
5
6
7
-1
-2
-3
-4
-5
-6
0 1
1
x
y
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3
4
5
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1
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15
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x
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