-
1 demahoM iluoatsuoM rf.aliov.etis.shtambara//:ptth
-I
1- .G Gj i o) ; ; ( f (1
.Cf ) ( D) ( Cf
) ( ) () ( ) (
4 4mil ; mil
mil ; milx x
x x
x f x f
x f x f
+
+
) 4 2 ( mil ; mil) ( ) ( ) (
x x
x fx x f
+ +x
-2 f 0 f ( 2
2
1 2
0 02 3 2
mil mil2 5 6 21 2
mil mil2soc 1 1 1
x x
x x
x x xx x
xx x x
+ +
2
mil 2 mil2 2x x2
x x xx x+ x + + +
\ f -( 3 ) () (
1 3 21 12
x xa x fx x fxx
; + = + =
\ f a 2nis2 2 ) ( f -
x fxx
.= 1 f
2 nis mil -( 4 x
+ = + +x x x -
0
nis nis mil1x
x+x
+ ( ) -2 A(
- .x0 f *
) ( ) ( ) ( ) ( ) ( 0
x xf0 0 0 mil0 ; ; = l x f x x D x l x f
.+ a;[ ] f * ; ; ; ; + = +A x f B x D x B A x f xf 0 0 mil) ( )
( ) ( ) (
.
-
2 demahoM iluoatsuoM rf.aliov.etis.shtambara//:ptth
- . x0 f
) ( f 0
x x) ( mil0 0 = x x f x f
- x0 l x0 f
0) () ( ) ( ) ( g D x x f x gf
l x g= =
x0 x0 f
- .b a;[ ] b a;[ ] a b a;] [ b a;] [
.b ( )
B( . g f
: + x0 x0 x0
-
3 demahoM iluoatsuoM rf.aliov.etis.shtambara//:ptth
f f l l0
+ + -
0 0 02
1 mil ; mil ; 1 milnis 1 soc 1 natx x x2
x x x xx x
= = = -
x0 I h g f ) ( x u l x f) ( ) ( , Ix *
0
0 milx x
= l x f x xmil0) ( = x u) ( *
0
milx x
l0 I f = l x f) ( *
0
milx x
x0 J l0 = l x f ; l x f J x0 ) (
) ( * 0
milx x
l l' I g f = l x g x x' mil0) ( = l x f) ( ) ( *
0 0
mil milx x x x
= l x h x xmil0) ( I g h f = = l x g x f) ( x u x f) ( ) ( , Ix
*
0
milx x
+ = x f x xmil0) ( + = x u) ( x u x f) ( ) ( , Ix *
0
milx x
= x f x xmil0) ( = x u x0 x0 +
; x x; 00 0[ ] ) ( + x x;0 0[ ] a;[ ] + a;[ ] I - - II 1 -
I x0 J I f) ( J g I f .x0 Df g x f0) ( g x0 f x0 x0 x0
J I f) ( J g I f .I Df g J g I f
nis3 22 ) ( f 2
x fxx
=
+ = Df;2 2;[ ] [ ]
:3 222
x uxx
+;2[ ] 2;[ ] D =u v f \ \ + v v;2 2 ;) ([ ] ) ([ ] \ x x vnis :
+;2[ ] 2;[ ] f
) () ( ) ( 1 2
30 1
x x x fx g
f= = =
D \= x f g x3 ) (
-
4 demahoM iluoatsuoM rf.aliov.etis.shtambara//:ptth
.1 f 1 Df g J I f) ( J g x0 I f -
) (0
milx x
l g = l x f) ( ) (
0
milx xl g x f g
D=
(=l x h0) ( )x I0} { f h x0 Dh g x0 h
I Dh g Df g ) ( ) ( ) ( ) (
0 0x x x xmil mil0
D D D= = = l g x h g x h g x f g
J I f) ( J g x0 I f ) (
0
milx x
D= l g x f g x xmil0) ( ) ( l g = l x f . x0 x0
0
soc milnisx4xx
-2 f J I -
nis ; ; ;) ( -1 2 2
\ = = = x x f I J = = =x x f I J; 2;1 ; 0;2 ) ( ] [ ] ] -2
.
b a;] [ b a;] [ f *
) () ( ) ( ] [
) () ( ) (; ;] [
pus fnib a x b a x
x f f M x f f m
=M m b a f; ;] [ ) (] [ = = = = I f \ I f) ( \ I *
f *
] [ ) ([ [ ) (: 3.2] [ f 0;2 23;0 1
x x x fx x x f
= + =
= f2;1 3;2] [ ) (] [ 0 3;2] [ f
-3 b a;] [ f *
= c f) ( b a;] [ c b f) ( a f) ( =M m b a f; ;] [ ) (] [ \ M m b
a;] [ f
) () ( ] [
) () (; ;] [
pus fnib a x b a x
x f M x f m
= = M m;] [ b f) ( a f) ( M m;] [ b a;] [ f
M m;] [
-
5 demahoM iluoatsuoM rf.aliov.etis.shtambara//:ptth
.= c f) ( b a;] [ c
b a;] [ c b f) ( a f) ( b a;] [ f .= c f) (
= x f0 ) ( b f a f0 ) ( ) ( b a;] [ f .b a;] [
; =x x nis2 2
-III -
I f) ( I f I f
= x f0 ) ( b f a f0 ) ( ) ( b a;] [ f
.b a;] [ ;11 = + +x x0 1 3
2
-
f1 I f Cf Cf1 f I f) (
.
) ( ) ( ) () ( ) ( ) (
1
;1 1
y f x y x f I x I f x
x x f f I x x x f f I f x
= = D D= =
1 2 ) ( \ f x fx
x + =
g1 I 1;1] [ 1;1] [ f g n -VI
-1 ` n*
-
6 demahoM iluoatsuoM rf.aliov.etis.shtambara//:ptth
\+ \+ x xn
`n* n n \+ \+ x xn .x n x n \+ x
\= = +y x y x y xnn ;2 ) ( \+ x
= =x x x x;1 2 - x x 3 -
` n*
nn ;2) ( ) (n n
n n
x x y x
y x y x
y x y x
= += =
\
\+ x xn * n mil*
x + = +x
\= a x xn -2 = = =x x x342 ; 8 ; 55 7 4 \
=a xn \ \a `n* -3
` \ +p n b a; ; ;2* 2) ( ) (
0 ; ;) ( ) (;
n n np p npn pnn
n n n npn p
b a a a aa abb
ba b a a a
= = =
= =
= = = = a a a a a a a an n np p p np nppn pnn p pp ) ( ) () ( `
\= + +a a a m n am nm n mn ;2* ) ( -1
-2 5 3
43
23 4201
81 652 46
3 ; 27 5 -3 -4
I x0 I f I f n I f ) (
0
milx x
= l x f x xnn mil0) ( = l x f) (
0
milx x
+ = x f x xn mil0) ( + = x f
-
7 demahoM iluoatsuoM rf.aliov.etis.shtambara//:ptth
+ x0 x0 x
. x x x3 2 2 5 -1 3 38 5 -2
23 mil ; 8 milx x
,+ ++ x x x3 3 6
0
mil ; mil1 1 1x x1
x x x +xx
+ + + +
-5 ( )
\ _ + a r; *
r q pp ; ;* * ) ( ap q ar q
a ` ]= .r \= +a a1 0 * -6
_ \ +r r b a' ; ; ;2 2*) ( ) (
' ' '' ) ( ) ('
'
; ;
; ; 1
rr r r r r r r rrr
r rrr r r
r r r
a a ba b a a a a
a aa a aa b ab
+
= = = = = =
r rn p' ; m q
' ' = =qn mp
a a a a a a a a amqr r qn mp qn mp n p r rmmq qm mq q+
= = = = =+ + -V
- -1
; x xnat 2 2 natcra \
nat natcra ; ; 2 2
\ = = y x y x y x -2
) () (
) () (
22 1 2 1 2 1
22 1 2 1 2 1
natcra nat
nat natcra ;2 2
natcra natcra ;
natcra natcra ;
x x x
x x x
x x x x x x
x x x x x x
=
= = =
\
\ \
\ x xnatcra - * - *
natcra mil ; natcra milx x2 2
= = + x x
-3
-
http://arabmaths.site.voila.fr Moustaouli Mohamed 8
- 1-
sinx x ;2 2 [ ]1;1 arcsin
[ ]1;1 ; ; arcsin sin2 2
x y x y x y = = 2-
[ ] ( )( )
( ) [ ]( ) [ ]
21 2 1 2 1 2
21 2 1 2 1 2
1;1 sin arcsin
; arcsin sin2 2
; 1;1 arcsin arcsin
; 1;1 arcsin arcsin
x x x
x x x
x x x x x x
x x x x x x
=
= = =
* - arcsinx x [ ]1;1
-3 - 1-
cosx x [ ]0; [ ]1;1 arccos [ ] [ ]1;1 ; 0; arccos cosx y x y x y
= =
2- [ ] ( )[ ] ( )( ) [ ]( ) [ ]
21 2 1 2 1 2
21 2 1 2 1 2
1;1 cos arccos
0; arccos cos
; 1;1 arccos arccos
; 1;1 arccos arccos
x x x
x x x
x x x x x x
x x x x x x
=
= = =
* - arccosx x [ ]1;1 * - [ ] ( )1;1 arccos arccosx x x =
3-
