**************************************
2 3 4-1-2-3-4-5
2
3
-1
-2
-3
0 1
1
x
y
2 3 4-1-2-3-4-5
2
3
-1
-2
-3
0 1
1
x
y
BAC2020
Facebookالجزائري العربي
y=lnx y=ln(-x)
y=-lnx
y=-ln(-x)
1
0;ln
x 0yy ln xyx e
2
xyn
1ln x ln yx y2ln x ln yx y
ln x 0x 1ln1 0lnx 1x elne 1
1ln(x.y) lnx ln y 2x
ln( ) ln x ln yy
3nlnx nlnx
11
ln( ) ln xx
21
ln x ln x2
3lnx² 2lnx
xnln(x) n ln xnnln(x) n ln xn
3ln(ax b)
ln(ax b) 0
e bx
a
ln(ax b)
1.a0
x x
2.a0
x x
x 0;1ln x 0 x 1; ln x 0
ln u(x)
ln u(x) u(x) 1u(x) 0
4a(ln x)² b(ln x) c 0
a(ln x)² b(ln x) c 0 X ln x
aX² bX c 0
5
1x 0lim ln x
2x 0lim x ln x 0
3xlimln x
4x
ln xlim 0
x5
x 0
ln(x 1)lim 1
x
x 1
ln xlim 1
x 1
n
x 0lim x ln x 0
nx
ln xlim 0
xn
6
1x ln xx1
(ln x) 'x
2 a
ln(ax b) 'ax b
abax b 0
3uD x ln u(x)
D u '(x)
ln(u(x)) 'u(x)
uu '(x)
ln u(x) 'u(x)
' '
ax b ax b a.d b.cln ln
cx d cx d (ax b)(cx d)
7x ln x
x ln x 0;
2 3 4 5 6 7 8
2
3
-1
-2
-3
0 1
1
x
y
e10x1
x
ln x1
e
0202 1
1
1ln x 1 0 2ln(x 1) 0 3ln x 1 0 42ln(x 3x 2) 2ln 2 ،51 (ln x)² 0
6ln(2x 3) ln(x 3) ln5 7ln(4x 5) ln(x 1) 5ln2 ln(x) ،8)5
(ln x)² ln x 1 02
9ln 2x 1 ln x 1 ln2 112xln e 1 x 11 2x xln e e 1 0 123ln x 3ln ²x 4 0
2
1ln x 12ln(x 1) 0 3x 2
ln 0x 1
4ln(x² 2x) ln(4x 5) 5ln x² 1 0
5(ln x)² ln x 2 0 7(ln x 1)(ln x 1) 0 81 ln x
01 ln x
932(ln x) 7(ln x)² 3lnx 0
Px 3 2P x 2x 3x 11x 6
1 P x 2x 1 x 2 3 x P x 0
23 22(ln x) 3(ln x) 11(ln x) 6 3x 2x x2e 3e 11e 6
P(x)3P(x) x 3x 2
1P( 1)P(x) 0
22(x 1)(ln x ln x 2) 0 2x x(x 1)e (x 1)(e 2)
1f (x) ln(x 1) 2f (x) ln(x² x 2) 3ln x
f (x) 1x
4x 2
f (x) x 1 2lnx 1
5 2 2f x ln x 1 ln x 1 6 2x xf x ln e e 1 7f (x) 1 (ln x)² 81
f (x) 1ln x
9 1
f x ln xx
11x ln x
f (x)x
11
xf (x)
ln x12
x 1f x ln x 1
x 1
21
20
23
24
0202 0
f 0; 2ln x
f x xx
1f 0; f ' x 2g x x 2 2ln x
2 0;g 'x 1
3g 3 0;
4f 0;
5 f x 0 1;2
6f
ff
O;i, j
f(C )A(3;1)
B(2;1 e)
y 1
f(C )C(1;3)
11f ''(1)f '(1)f '(2)
22(T)C(1;3)
33f (x) 0 3; f (x)
44mmf (x) m
55ff
66gg ; g(x) f (x) ln f (x)
g '(x)f (x)f '(x)..
gg
1ln 1;
26
1
e
25
27
0202 3
2 f : x ln x x 1 1;0
3 2f : x ln x 1 1;
4 2ln x ln 3x 4
5 f x x ln x xf ' x 1 x
6 1 ln 2 x 0 ;2
1 f 0; 2
f (x) 2 ln x ln x 3
x 0
lim f (x) 0
x 0
lim f (x)
x 0
lim f (x)
2 f1f (x) x² 2x ln(x 1)²
x 1x 1 x 2
33 5 3x 2 x 1x 1 x 2
4f01
xf (x) 3
1ln3
xln3
f '(x) ex²
1ln3
xln3
f '(x) ex²
1
ln3x
ln3f '(x) e
2x²
f 0;
(C) O;i, jA(e;2e)
e
2
2
f (x) 2x a ln x bln x c abc
1f '(x) abc
21
f 'e
f ' e f ' e
3 2
f (x) 2x 2 ln x 3ln x 2
e e
2
e
1
e
2e
A
2 3
2
3
4
5
6
7
0 1
1
x
y
A
e e 2
e
1
e
2e
28
29
0202 4
4f1t ln x f
5 x 0; f '(x) 2(ln x 1)(2ln x 1)
6f '(x)f
f 4; x
f (x) x² 2x 2ln(1 2x) ; 4 x 0
1 ef (x) ln ;x 0
2
(C) O;i, j.
1-x 0
f (x) f (0)lim
x
x 0
f (x) f (0) 1lim
x 2
f
O
2x 0xlimf (x) ln x ln 2 0
3f 4;
4f (x) 0 4; 3 f (0)f (x)
5(C)
6m
g 4;0
m mg (x) f (x) 1 m
m(C )
mgA(0;1)B( ;1)
12
0202 5
2 3
2
3
-1
-2
-3
0 1
1
x
y
f 0;2 2; 1
f (x) ln xx 2
f(C ) O;i, j.
1x 0
lim f(x)
x 2
lim f(x)
x 2
lim f(x)
xlimf(x)
2f 0;2 2;
3( )ln
x
lim f(x) ln x
f(C )( )
4( )f
(C )
6 g ; 1 1;0 g(x) f ( 2x)
g(x)g
Ig 0;1
g(x) (ln x)² ln x 1x
g(C )
g(1)xg(x)
IIf 0; 1 ln x
f (x)1 x ln x
f(C )
O, i , j
1x 0
limf(x)
xlim f (x) 0
2x من 0;:g(x)
(1 x ln x)²f '(x)
f
3e² e
y xe 1 e 1
(T)f
(C )
(T)f
(C )
4m(e 1)f(x) e²x em
100218
g(C )
110219
0202 6
f D ; 1 1; 2 x 1
f (x) x ln3 x 1
f(C ) O, i , j
1f
2 x 1
lim f (x)x 1
lim f (x)x
lim f (x)x
lim f (x)
f(C )
3xD2 x² 2
f '(x)3 x² 1
f
4f (x) 01,8 1,9
5( )2
y x3
f
(C )f
(C )( )
6( )f(C )
7mmx 1
(2 3 m )x 3ln 0x 1
If ;1
2
1 2ln(2x 1)f (x)
(2x 1)²
f(C ) O, i , j
11
x2
lim f (x)
xlim f (x)
2x ;1
2
3
8ln(2x 1)f '(x)
(2x 1)
f
3 ;1
2f (x) 0f (x)
4f(C )f(C )
Ig 0;g(x) x² 1 ln x
1g
22
g( )2
x 0;g(x) 0
130217
140217
150216
0202 7
II f 0;ln x
f (x) x 1x
(C) O, i , j
1x 0
lim f (x)x
lim f (x)
2x 0;g(x)
f '(x)x²
f
3(T)(C)1
4(C)( )y x 1
(C)( )
5(T)( )(C)
6mm
( )y mx m
mA(1;0)m
( )
mf (x) mx m
Ig 1; g(x) 1 (x 1)e 2ln(x 1)
1g
2g(x) 00,34 0,33
3 g(x)x 1;
IIf 1; e ln(x 1)
f (x)x 1 (x 1)²
f(C ) O, i , j
1x 1
lim f (x)
xlim f (x)
x 1; 3
g(x)f '(x)
(x 1)
f 1;
f(C )f ( ) 3,16
3k 1; 1 k(x) f ( x ) k(C )
k
k(C )f(C )k
mk(x) m
160216
0202 8
O, i , j
I x lnx
y x 3
1 0;
2g 0;g(x) x 3 lnx
xg(x)2,2 2,3
IIf 0;
1f (x) (1 )(ln x 2)
x f(C )
1x 0
lim f (x)x
lim f (x)
2 x 0; g(x)
f '(x)x²
f
3( 1)²
f ( )
f ( )
4f(C )f(C ) 0;e²
f 0;2ln x
f (x) 1x
f(C )
1x 0
lim f (x)x
lim f (x)
f 0;
2f(C )( )y 1
(T)f(C )1
f (x) 0 0 ;10,4 0,3e e
3(T)f(C )
4h02ln x
h(x) 1x
h(C )
xh(x) h( x) 0
h(C )f(C )
mln x² (m 1) x
170215
180214
2 3 4 5 6
2
3
-1
-2
0 1
1
x
y
α
(γ) (Δ)
0202 9
Ig 1; g(x) x² 2x 4 2ln(x 1)
1g
2 1; xg(x) 0
IIf 1; 1 2ln(x 1)
f (x) xx 1
f
(C )
1x 1lim f (x)x
limf (x)
2 x 1; g(x)
f '(x)(x 1)²
f 1;
f (x) 0 1; 0 0,5
3( )y xf
(C )
f(C )( )
4(T)3
2y x
e
f(C )
0x
0x(T)
f(C )
mf (x) x m
f ( I ;0x
f (x) x 5 6ln( )x 1
f(C )
1x 0lim f (x)x
limf (x)
2 x ;0 x² x 6
f '(x)x(x 1)
f
3( )y x 5 f
(C )
f(C )( )
4f (x) 03,5 3,4 1,1 1
190213
020210
0202 12
2 3 4 5 6 7 8-1-2-3-4-5-6-7-8
2
3
4
5
6
-1
-2
-3
-4
-5
-6
0 1
1
x
y
5f
(C )( )
63
A( 1;3 6ln )4
5 3
B( 2; 6ln )2 4
1 7 3y x 6ln
2 2 4 (AB)
(AB)f
(C )0
M
( Ig 1 x 1
g(x)x 1
g(C )
g
g(x) 0
x0 g(x) 1
IIf 1;x 1 x 1
f (x) lnx 1 x 1
f
(C )
1x 1
lim f (x)x
lim f (x)
2 x 1; 2
g '(x)(x 1)²
f '(x)f
f (x) 0 0x 3,62 ;3,63
f(C )
3Ix 1
lnx 1
1;
If1
I ;2
f (x) 1 ln(2x 1) f
(C )
010211
000212
g(C )
g(C )
0202 11
1xlim f (x)1
2xlim f (x)
2fI
3f
(C )(d)y x
4xIf (x) ln(x a) b
ab
f(C )(C )ln(C )
f(C )
IIgIg(x) f (x) x
112
xlim g(x)x
limg(x)
2gI
3g(1)g(x) 0 1,5;
2 3
g(C )g 0,5;5
4g(x)If
(C )(d)
5x 1;f (x) 1;
Ih 1; h(x) x² 2x ln(x 1)
1x 1
lim h(x)x
lim h(x)
2 x 1; 1 2(x 1)²
h '(x)x 1
h
3h(0)h(x)
IIf 1; ln(x 1)
f (x) x 1x 1
f
(C )
1x 1
lim f (x)
t
t
elim
t
u
ln ulim 0
u
xlim f (x)
xlim [f (x) (x 1)]
f(C )
f(C )
2 x 1; h(x)
f '(x)(x 1)²
f
3f(C )y 23,33,4
4f(C )
030229
0202 10
0202 13
Ig 0;
g(x) (x 1)(x e) e(xln x)
x 0
lim g(x)
g(x) 0;
IIf 0;eln x
f (x) ln(x 1)x 1
f(C ) O, i , j
1x 0
lim f (x)
xlim f (x)
x 0;g(x)
f '(x)x(x 1)²
f
2(T)f
(C )1
3A
0,7 0,8
4( )x ln(x 1) 0;
xlim f (x) ln(x 1)
( )f
(C )
(T)( )f
(C )
Ig 0;1g(x) 2 x ln x
1g 0;1
2g(x) 00,15 0,16
3xg(x) 0;1
IIf 1;1 2x ln x
f (x)x 1
f(C ) O, i , j
1x 1
lim f (x)
xlim f (x)
f(x)1 2x ln x
f (x)x 1 x 1
040219
050218
0202 14
2x
1g( )
xf '(x)(x 1)²
f1
1;
1;
3 f
(C )( )y 2
4f(C )1
f ( ) 1,8
5mf (x) m
f fD ;1 2; x 1
f (x) 2x 3 2lnx 2
f(C ) O, i , j
1 x 1
lim f (x)x 2
lim f (x)
xlim f (x)x
lim f (x)
2xfD2
f '(x) 2(x 1)(x 2)
f
3xfDf(3 x) D f (3 x) f (x) 0
f(C )
4f (x) 0 0,45;0,46
5( )y 2x 3 f
(C )f
(C )( )
6( )f(C )
Ig 0;1 2 ln x
g(x)2 x²
1x 0
lim g(x)x
lim g(x)
2g
3g(x) 01,71 1,72g(x)
IIf 0;1 1 ln x
f (x) x 22 x
f(C ) O, i , j
070217
060217
0202 15
1x 0
lim f (x)x
lim f (x)
f
2( )1
y x 22
f
(C ).
f(C )( )
3f ( ) 0,87f ( ) f ( ) 0 0,76 0,774,19 4,22
( )f
(C )
Ig 1; x 1
g(x) ln(x 1)x 1
1x 1
lim g(x)x
lim g(x)
g 1;
2g(x) 00,4 0,5
g(x) 1;
IIf 1; f (x) 1 (x 1)ln(x 1)
1x 1
lim f (x)x
lim f (x)
2f 1;
4f ( ) 4
1
f ( )210
3a 1; a
(T )(C)f
O, i , ja
x 1; h(x) f (x) f '(a)(x a) f (a)
x 1; h '(x) f '(x) f '(a)
gh '(x)xh 1;
(C)a
(T )
4a
(T )A(1;0)
(C)
I g 0;g(x) x xln x.
1x 0
lim g(x)x
lim g(x)
0902160
0802161
0202 16
g 0;
2g(x) 1 3,5 3,6
3g(x) 1 0;
IIf 0;ln x
f (x)x 1
f(C ) O, i, ji 2cmj 4cm
1f
(C )x 0y 0
2x 0;g(x) 1
f '(x)x(x 1)²
f 0; ;
(T)f
(C )1
x
f (x) f ( )lim
x
31
f ( )
f ( )210
f(C )
4xmx² x 2m(x 1) ln(x²)..(E)
(E)1
f (x) x m2
m(E)
5h*ln x
h(x)x 1
h(C )
hh
(C )f
(C )
I h 2; h(x) (x 2)² 2 2ln(x 2)
1(x 2
lim h(x)x
lim h(x)
2h
3x 2; h(x) 0
IIf 2; 2
f (x) x 1 ln(x 2)x 2
f(C ) O, i, j1cm
1x 2
lim f (x)x
lim f (x)
322015
0202 17
2 3 4
2
-1
-2
0 1
1
x
y
2 x 2; h(x)
f '(x)(x 2)²
f 2;
3( )y x 1 f
(C )
f(C )( )
4f
(C )A
f(C )
III g 2; 2
g(x) x 1 ln(x 2)x 2
1x 1
g(x) g( 1)lim
x 1
x 1
g(x) g( 1)lim
x 1
g
2
3f
(C )g
(C )g
O, i , j
I g 0;3g(x) x lnx x
1g
2g(x) 2 0;31,45 1,46
g(x) 2
IIf(C )f
0;3f (x) x 2 ln x
1f(C )f2
2
3f
IIIh0 ;2
h(x) (2 cosx)ln(cosx)
1( )x2
h(C )h(C )h
2h( )h(C )
I g 1; g(x) (x 1)² 2 ln(x 1)
1g 1;
310214
3002131
f(C )
0202 18
2g(x) 00,31 0,32ln( 1) 2 ( 1)²
3xg(x)
IIf 1; 2
f (x) (x 1)² 2 ln(x 1) f
(C )
11
lim f (x)x
lim f (x)
2 x 1; 2g(x)
f '(x)x 1
3f
4 2f ( ) ( 1)² 1 ( 1) f ( )
5f
(C ) 1;2
III( )h 1; h(x) ln(x 1)
A( 1;2)M( )x
1AMAM f (x)
2k 1; k(x) f (x)
kf 1;
B( )AM
AB ( 1) ( 1)² 1
Igxg(x) (x 1)e
1g
2xx1 (x 1)e 0
IIf 0;
xe 1f (x) ;x 0
x
f (0) 1
1f 0;xlim f (x)
2 x 0; x1 (x 1)e
f '(x)x²
f
IIInn 1n
f 0;x
n
e 1f (x) n ln x
x
n
C(O; i; j)
1n
f 0;2n
0limf (x)
nxlimf (x)
3302130
0202 19
3 n
C n 1
C
4B
5 10,3;0,4
1 1f ( ) 0
nn 1n 1
f ( ) 0
n 1
;1n n
f ( ) 0
IIx 0;1xe 1
e 1x
Ig 0;g(x) x² a bln(x)
1a bf
(C )A(1; 1)4
2a 2 b 2g
g(x) 0 0; g(x) 0;
IIf 0;2ln(x)
f (x) x 2x
f(C ) O, i, j
1x 0
lim f (x)x
lim f (x)
f '(x)g(x)
f '(x)x²
f '(x)f
2( )y x 2 f
(C )f
(C )( )
f(C )(T)( )
1,25 f (x) 01
x2
x
10,6 x 0,7
22,7 x 2,8( )(T)
f(C )
3m (m 2)x 2ln(x) 0
f 0;a bln(2x)
f (x)4x²
a b
f
C(O; i; j)
340210
350211
0202 02
1a b1
A( ;1)2
f(C )
2g 0;1 2ln(2x)
g(x)4x²
g(C )
xlimg(x)x 0
lim g(x)
g
0;g(x) 0
g(C )
g 1;g(x) 2x lnx
gx
g
x 1; g(x) 0
2 f 1;6ln x
f (x)2x ln x
f(C )
6ln x
xf (x)ln x
2x
xlim f (x)
ff
kf (x) k
1( )
f(C )1
3h 1;xh(x) f (e )h
(C )
h2
( )h
(C )1
1( )
2( )
f(C )
h(C )
360212
0202 01
f 0;f (x) x x² ln x ; x 0
f (0) 0
f(C ) O, i , j3cm
1
x 11 x 2xln x 0
0 x 1 1 x 2xln x 0
2f1
( )f(C )
( )f(C )
xlim f (x)
f
4(T)f(C )( )
f (x) 0 1;1,76 1,77
(d)( )( ;0)
(T)(d)( )f(C )
5mmx²ln x m 0 0;
f 0;1 1; *1
f (x) x 1 ;x 1ln x
f (0) 1
f(C ) O, i , j
1f1
h 0
f (h) f (0)lim
h
2xlim f (x)x 1
lim f (x)
x 1
lim f (x)
.
f
3f(C )( )
f(C )( )
380218
370219
0202 00
4f(C )1,49 1,5
f(C )1
y ( 3 )(x )
5( )f(C )
6h 1;h(x) 1 x xln x
h 1;h(x) 1;
x 11 h(x)
f (x) xx ln x x ln x
x 11
x f (x) x 1x ln x
7Af(C )
x x ee
1 1(e² ²) ln( 1) (e )(e 2A )
2 2
Ig 0;1
g(x) ln xx
1g
2g(x) 0 1,76;1,77g(x) 0;
IIf 0;
x 1f (x) ;x 0
x ln x
f (0) 0
f(C ) O, i , j
1f1x 0
f (x)lim
x
2x 0;g(x)
f '(x)(x ln x)²
3xlimf (x)
f
4 h 0;h(x) x ln x
x h(x) 0
f(C )y 1
f(C ))f ( ) 2,31
390217
0202 03
Ig 0;g(x) x 2 ln x
gg(x)
IIf*1 ln(x²)f (x) x e
2 x
f(C ) O, i , j
1xg(x²)
f '(x)2x²
f
2xf ( x) f (x)
x 0
lim f (x)x
limf (x)x 0
lim f (x)x
limf (x)
f
3( )1 e
y x2 2
f
(C ).f
(C )( )
4f(C )1
2
f(C )
2 2,10,5 0,4
5( )f(C )
6f(C )mx(e 2m) ln(x²)
Ig 0;g(x) 1 x² 2ln x
1g
2g(x) 0 0,52 ;0,53
3g(x) 0;
II f 0;3 2ln x
f (x) xx
f
C(O; i; j)
1x 0
lim f (x)x
lim f (x)
420217
410216
0202 04
2x 0;g(x)
f '(x)x²
f1
f ( ) 2
3 xlim f (x) x
f
C( )
f
C(T)( )
4 f
C0
x1
x
00,22 x 0,23
12,11 x 2,13
(T)( ) f
C
5mm3 2ln x mx 0
ff (0) 1x 0;f (x) 1 x² lnx
f
Cf(O; i; j)
1f1
x 0
f (x) 1lim
x
2xlimf (x)
f
3f (x) 0 0;
1,531 1,532
4gg(x) f ( x )
gCg(O; i; j)
g gC 2;2
400215
0202 05
1f 0;f (x) (1 2lnx)( 1 lnx)
f
Cf(O; i; j)
f
f
Ce
f
C f
C 0 ; e²
2 g 0;g(x) 1 ln x gC
g
f
C gC g
C 0 ; e²
I1u 0;xu(x) e 3x 4 e
u
x 0; xe e 3x 4
2v 0;3v(x) 3x 4x² 1 ln x
v '(1) 0v 'v
x 0; v(x) 0
x 0; 1 ln x
3x 4x²
3 x 0; x 1 ln x
e e 0x²
IIf 0;x ln xf (x) e ex
x
f(C ) O, i, j
1x 0
lim f (x)x
lim f (x)
2f 0;
3f (1)f
(C ) 0;2,5
I g 1; 3x
g(x) 2ln(x 1)x 1
430214
440213
450210
0202 06
1g
2g(x) 00,8 0,7
3xg(x)
4h 1; 3 h(x) g(x) ²
h '(x)g(x)g '(x)
h '(x)h
II f 1; 3
x²f (x) ;x 0
ln(x 1)
f (0) 0
f(C )
1f1Tf
(C )1
2 x 1;0 0;3
xg(x)f '(x)
ln(x 1) ²
f
f ( ) 2 ( 1) f ( )
f (3)x 1lim f (x)
f
3 x 1; 3 x ln(x 1) 0
f(C )T
4T'Tf
(C )3
5TT'f
(C )
6mf (x) x m
1 g 0;2g(x) x² ln(x ) 1
g
460211
0202 07
g(1)g(x)
2 f 0;1
f (x) (1 )(ln x)x²
f
Cf(O; i; j)
f 0;3
g(x)f '(x)
x
f
x ln x 0;
f
C x
1lim ln x
x²
f
C
g 0;g(x) x 1 2ln x g
(C )
1x 0lim g(x)
2xlimg(x)
gg(1)
g(x) 03,5 3,6
g(x)1
g( )x
3f 0;f (x) x² x x² ln x ;x 0
f (0) 0
x 0
f (x)lim
x
f
x 0;1
f '(x) xg( )x
470212
0202 08
ff1 1
2
f ( )
²
1f ( )
4f
(C )f 0;3
0202 09
1fx 0;1 1
f (x) ln xx x
f 0;
f
2(O; i; j)
1
E
I2(x) x² 4x 3 6ln x 2
1(1)(3)
2(x)
IIf26ln x 25
f (x) x 2x 2 x 2
f(O; i; j)
1x2(x)
f '(x)(x 2)²
f
f ( 1)f (0)f (4)f ( 4)1
10
(2;4)
fln2xf (x) x ln e 2 (C)
f(O; i; j)2cm
4895
4998
520221
0202 32
1f
xln2xf (x) 2x ln 1 2e
2(C)y 2xy x ln2 '
(C)
(C)
f*ln x²f (x) 1
x
(C)f(O; i; j)
1f(C)
(C)y 1
2f ( x) f (x)
3f (x) 0 1; 0,5
4(C)(T)A(0;1)(C)
(T)
5(T)(C)
6m f (x) mx 1
7g*ln x²g(x) 1
x ( )
g
g( )
510224
0202 31
( )u
(O; i; j) 0;u(x) x 1 4ln x.
( )(D)y x
( )4
( )(O; i )1
1u(1)u( )u '(4)x 0limu(x)
xlimu(x)x
u(x)lim
x
2u(x)u '(x)
f 0;x 1
4
ef (x) (x 1) 4ln x
x
(C)f(O; i; j)
1 x 0; u(x )f (x) e u(x)
x
lim f (x)
x 0limf (x)
2 x 0; u ( x )f '(x) u '(x) e 1
f '(x) 0 x 1;4 ; f
3xxe 2x 0
(C)( )
(C) 0;15
( )u
2 3 4 5 6 7 8 9 10 11 12 13 14 15
2
3
4
5
6
-1
-2
-3
0 1
1
x
y
500218
(D)
( )
0202 30
Ig 0;g(x) x² x 2 2ln x
1g(1) 0
2g
g(x) 0x 0;1
g(x) 0x 1;
IIf 0;2
f (x) x 1 ln xx
f(C )f(O; i; j)
1x 0
lim f (x)
x
lim f (x)
2x 0;g(x)
f '(x)x²
0;1 1;
f 0;
3 0;2
1 ln x 0x
f(C )(D)y x
f (x) xx 1;2f
(C )(D) 1;2
4(D)f
(C ) 0;5
Ig 0;1
g(x) 1 ln xx²
1g
2 g(1)g(x) 0;
IIf 0;1
f (x) (1 ln x)²x²
f(C )f(O; i; j)
1x 0
lim f (x)
x
lim f (x)
1x
g '(x)
g(x)
540214
530217
0202 33
2x 0;2g(x)
f '(x)x
3f
4x 0;1
(ln x)² 2ln x 0x²
5f (2)f (3)f (4)f (5)f
(C )(O; i; j)
6 h ;21
h(x) (1 ln(2 x))²(2 x)²
h(C )
h(C )
f(C )
g 1; x
g(x) 2ln(x 1)x 1
1g
g '(x)g
2g(x) 01 0,72; 0,71
g(x) 1;
fx 1
x²f (x) ;x 1;x 0
ln(x 1)
f (x) (1 x)e ;x 1
f (0) 0
f(C )f(O; i; j)
1f
2f11
f1
3x 1; 0 x.g(x)
f '(x)ln ²(x 1)
f '(x) ; 1
f
4(T)f
(C )1
(T)1f
(C )
f (α) 0;41f (3) 6;5f ( 2;5) 6;7
550216
0202 34
2 3 4
2
3
0 1
1
x
y
fx1
f (x)x(1 ln x)
f(C )
f(O; i; j)2cm
I1f fD 0;e e;
2x e
lim f (x)
x e
lim f (x)
x
lim f (x)
f(C )
x 0
lim f (x)
x(1 ln x) x xln x
3xf
Dln x
f '(x)x²(1 ln x)²
f 0;1
1;e e;
ff
D
IIg 0;
g(x) 1 x²(1 ln x) g
(C )g
(O; i; j)
1g(x) 0
g(x) 0α2,2 α 2,3
2xf
Dg(x)
f (x) xx(1 ln x)
(Δ)y xf
(C )1α
g(x)g
(C )1;α
f (x) x 0 x1;α
3(O; i; j)(Δ)f
(C )
2,42,32,22,1x
0,280,120,020,14g(x)
560215
g(C )
0202 35
1f 0;f (x) x 2 x 2
1xlimf (x)
2f1
3ff (x)
2g 0;g(x) ln(x 2 x 2)
(C)(O; i; j)
1xlimg(x)
xlim g(x) ln x
2x 0
g(x) g(0)lim
x
3g
4(C)( )x lnx
5( )(C)
6(C')k
0;k(x) ln(ex 2e x 2e) (C')
g 0;g(x) 1 x² 2x²ln x
1x 0
lim g(x)
xlim g(x)
2g
3g(x) 01,8 1,9
g(x) 0;
f 0;ln x
f (x)1 x²
fC(O; i , j)i 1j 4
1x 0;g(x)
f '(x)x(1 x²)²
f 0;
x 1; ln x
0 f (x)x²
xlim f (x)
1f ( )
2 ²
f ( )
2f 0; fC
570213
580212
0202 36
I ( )g
Cg 0, 2g(x) 1 ln x x
( )g x 0,
II f 0; 2ln
2 4x
f x xx
( )fC , ,O i j2cm
1 0
limx
f x limx
f x
( )D2 4y x f
C
fC( )D
2x 0; 2
2g xf x
x
f
( ) 0f x 0,4 0.52,3 2,4
3f
C
mD2y mx m m
m mD
m
22ln x (m 2)x (m 2)x 0
fxx xf (x) 2ln(e 2 e 2) C
(O; i , j)
1x x x xe 2 e 2 ( e 1)² 1 f
xxx
2 21 0
ee
2xlimf (x)x
limf (x) ln4
3xx x
x
2 e ( e 1)f '(x)
( e 1)² 1
f '(0) 0
620229
59Polynésie0212
2 3
2
3
-1
-2
0 1
1
x
y
0202 37
x( e 1)f 0; ;0
4xxx
2 2f (x) 2x 2ln(1 )
ee
(D)y 2x(C)
5x x x x xe 3 e 2 ( e 1)( e 2)
x( e 2)x x( e 1)( e 2)
x 0;ln4x x xe 2 e 2 e
x 0;ln4f (x) x
6(C)
