1
1 3
x x
0;
ln( 3) x x
0;
3 x x
0;
0;
f
2
2
2
ln( 3) ' 3 ln( 3) 3 '
'( )
3
3 ' 3 ln( 3)
3
3 1 ln( 3)
3
x x x x
f x
x
x x x
x
x x x
'( ) f x 1 ln( x3)
1 ln( x 3) 0
ln(x 3) 1 ln(x 3) ln( )e
3 x e
3 x e
0;
0;
1 ln( x 3) 0
ln(x 3) 1 ln(x 3) ln( )e
3 x e
3 x e
0;
x
0;
0;
x 1 ln( x 3) 0' ) 0 f x
0;
f(0) ln 3 f 3 lim ( ) 0
x f x
3
x
lim ln 0
u
u
u
2 (a
0;
f1 n x n
( ) ( ) ( 1)
f n f x f n
( 1) ( ) ( )
f n f x f n
(b nN
n n; 1
f
n n; 1
x( 1) ( ) ( )
f n f x f n
1 1 1
( 1) ( ) ( )
n n n
n f n dx n f x dx n f n dx
1 1
( 1) ( 1)
( 1). 1
( 1)
n n
n f n dx f n n dx
f n n n
f n
( 1) f n
1 1
( ) ( )
( ). 1
( )
n n
n f n dx f n n dx
f n n n
f n
( ) f n
ln 3 3
0 x f’(x)
f
0
1
n ( )
n f x dx un
n
( 1) n ( )
f n u f n
lim ( ) 0 (c
x f x
lim ( 1) 0
n f n
lim ( ) 0
n f n
lim n 0
n u
un0
3 ln( 3) (a
x x
0;
0;
F
( ) ln 3 2 2 ln 3 ln 3
1 ln( 3)
2 ln 3 2
3 3
F x x x x
x x
x x
0n ( ) (b In
f x dx ( ) 2 ( )F x f x
( ) 1 '( ) f x 2F x 2
f F
0;
n N
0
0
2 2
( ) ( )
2 ( ) (0)
2 2
ln( 3) ln(3)
2 2
n n n
I f x dx F x
F n F
n
4 n
0 1 1 N
1 2
0 ( ) 1 ( ) 1 ( )
n n
n n
S u u u
f x dx f x dx f x dx
Chasles
0n ( )
n n
S
f x dx Ilim n
n S
23 ln( 3)
ln( 3) n
n n