Литвин І.І., Конопчук О.М., Желізняк Г.О. Вища математика
Подождите немного. Документ загружается.
1
’
-
.., ! ".#., $ %.".
&! '
– 2004
2
32.973.273
12
681.3(75)
:
.., ( -! , , (! (
'!) &
« ».
.., ( -! , , (! (
. .*.
12 .., .., !" ..
.
&! '. – : + ! ,
– 2004. – 368 .
ISBN
/' ( «57 » '
()! ( 7 ( 9 ( (-
, ( ( ! ( #
’ 1998 .
/' !< ( ( ! (-
! , , ( . 9
(< ' (!.
681.3(075)
32.973.273
ISBN
©
.., ! ".#., $ %."., 2004.
©
+ ! , 2004.
3
...............................................................................................8
1. !!...........................................................................9
1.1. & !.................................................9
1.2. / !....................................................9
1.3. !...................................................10
1.4. 5 !..................................................11
1.5. >( !........................................12
1.6. /( ! (< 9...........................13
1.7. 5...................................................................................20
1.8. " ..................................................................22
2. "#$!% #!!..................................................................23
2.1. @') ( '. # '......................23
2.2. 5 ( ( ' !..............................25
2.3.
5...................................................................................28
2.4. " ..................................................................30
3. &!% ...........................................................................31
3.1. @'! !................................31
3.2. %! !.....................33
3.3. A! !........................36
3.4. / !...............................40
3.5. 5...................................................................................41
3.6. " ..................................................................45
4. '*!+%,. -!+ /*!+%,..............................................................46
4.1. *. 5 .................................................46
4.2. % !..........................................................48
4.3. & ............................................................51
4.4. &! ! ........................55
4.5.
%
fo
x
...................................................56
4.6. B( ........................................................................58
4
4.7. 5...................................................................................61
4.8. " ..................................................................64
5. :%!. *!! &:%!, %$!! /*!+%,..........65
5.1. C(!, ( ( (.
"! (...................................................................65
5.2. %! (................................................66
5.3. / ()....................................................69
5.4. /( ..............................................71
5.5. /( 7 (.........................................................77
5.6. / ........................................................84
5.7. D . (
() 9 (.................................................85
5.8. (
() (
(................................................................................87
5.9. &'9 9 ! (..............88
5.10. " ! ........................................92
5.11. C (( '( .....94
5.12. / ................................................................96
5.13. 5...............................................................................100
5.14. " ...............................................................110
6. /!+%..................................................................................111
6.1. / ( ..............................................111
6.2. %! (........................................111
6.3. C ( ( ' '!.........113
6.4. 5.................................................................................116
6.5. "
.................................................................118
7. ";!!< %!=................................................................119
7.1. / ! .........................................119
7.2. 5 ! ...................................120
7.3. E(< ..................................................122
7.4. ( ( ( ).............124
7.5. !......................................................126
7.6. ( , 7 ( !........126
5
7.7. ........................................131
7.8. 5....................................................................................135
7.9. " .................................................................139
8. ;!!< %!=....................................................................140
8.1. / ! ............................................140
8.2. %! ! ..........................141
8.3. "
! ..........................143
8.4. E(< '! ! ..................145
8.5. "'! ! ( (....147
8.6. "'! ! !.....................149
8.7. &' ( '! ! ..........151
8.8. /! ! ...................154
8.9. & ...........................................................162
8.10. 5...............................................................................166
8.11. " ...............................................................172
9. /!+%>!% %!!!............................................................174
9.1. " ...................................................................174
9.2. () ......175
9.3. ( 9 (.................177
9.4.
(( ( ( (
<.....................................................179
9.5. 5.................................................................................181
9.6. " .................................................................184
10. ?..............................................................................................185
10.1. B (. " ...........................185
10.2. * (.............................................................192
10.3.H (...................................................................192
10.4. I( (. I( #.............195
10.5. %! .........................................................200
10.6. A! (. I( *’<......................................202
10.7. /! ! ..........................................207
10.8. 5...............................................................................216
10.9. " ...............................................................221
6
11. -%&#%!% /*!+%,...................................................................222
11.1. " .................................................................222
11.2. 5 '! .....................................225
11.3. /( ( '! ( !
..............................................................................227
11.4. 5................................................................................229
11.5. " ...............................................................231
12. ! %, <%!%.....................................................232
12.1. " '..........................................232
12.2. 5( (. J (......................................234
12.3. ( ( ...................................236
12.4. * ...............................................240
12.5. * E...............................................................241
12.6. ( !,
.......................................................................242
12.7. C !...........................................................245
12.8. 5...............................................................................248
12.9. " ...............................................................252
13. ! %!%<!, =#........................................................253
13.1. #. " ..................................................253
13.2. ( ..............................................................255
13.3. 5!, ' '!.............259
13.4. "' . I .......................................265
13.5. H n n (........................270
13.6. I’ c n n (...273
13.7. 5
...............................................................................280
13.8. " ...............................................................283
14. .......................................................................................285
14.1. 5. 5( .......................................................285
14.2. ( ..............................................................286
14.3. I( '.................................................292
14.4. ( ( (.............294
14.5. 5...............................................................................297
7
14.6. " ...............................................................300
15. % ! &!%......................................................................301
15.1. I .................................................................301
15.2. C ...................................................305
15.3. ...............................................................306
15.4. / .................................................................308
15.5. 5( ( ! ( .............................................309
15.6. 5
...............................................................................311
15.7. " ...............................................................314
16. % *== &*................................................................315
16.1. ...................................................................................316
16.2. D..................................................................................317
16.3. %'...........................................................................322
16.4. /'...........................................................................329
16.5. C ( ( ( ........333
16.6. 5...............................................................................334
16.7. " ..................................................................337
&= ;% @..............................................................................338
...............................................................................................339
A%*..........................................................................................367
8
? C
«57 », ! 9 '’<, !<
7 ! ( 9 ( (. / '!-
( !-(!) ), ' ), (-
<. E9 )! (! ' 7 ( (
1990 , , ) ,
9
, 7 ! (.
C 59 ' ( «57
» ' ()! ( 7 ( 9 (-
(, ( ( ! ( #-
’ 1998 .
&! ' (<
11 (, ( -
!- , ( ’ (!, (
! ! ! , , -
' ( (. " (
' (.
" ,
( (( , ! -
( (, ! ,
', (9 ( ( ( '-
) .
#) ' ( ( ( ( 9
(
!.
'9 ( 9 <
! ! ; ’ (! ( -
! ; ( ( ! ( ((,
((, 7 ) ( ,
(; ! < '.
I !
( ): -
) ( ; -
( (( , ( ((
; ) ! , 7 9< '9 !
( ' .
/' !< ( ( ! (!
-
, , ( . 9
(< ' (!.
@ )) 7 ( (
.-. H %.A. (& . . *), ( .-. ) /..
(& « »).
9
?CA 1. DA""E
1.1. "&;+%<!% !!.
"&;+%<! ) !, '-
< < ! ( , < !.
/( !, (9 ( 9 ! (
<, < !. ( !
) : I, V, X, C, D, M .(., !) ! (, ’,
(, ’(, , ! .(.. C '(- 9 ! (
: ( , 7 !, ') !, 7 (-
)< !, (() , ( – , OO – ((,
(9 ( !< 9 !) ( 9
( !< '9 !), '< ) (( !, ( IV –
!, XL – , , (9 ( 9,
'< (( !, ( XI – ((, VI – 9, 7.
1.2. ;+%<!% !!.
;+%<! ) !, !
!< 9 ) ), (<)), <
!.
C!F
! < ! , <,
' ( '(- ( ( ( ( 9 (.
H ! ) '( ! ! . "!(, 7 )
! !< , ) (
! ( !. ") ( ! < !
(
, ( '(- ! < ( : 0, 1,
2, 3, 4, 5, 6, 7, 8, 9.
5 ! ) )
!
O
O
O
,...,
21
, ) #;F !. I) -
! ) (’<) !) '). -
! (’<) ') !) (
! !)! ; ! !) ')
!) ( !, ! 7 (
. R , 0, 1
! !) !
().
B ! ) ) (
, ( ) (' !. R7 '
n
,
n-1
, },
1
,
0
,
-1
, ...
-m
!) , (
n
n-1
}
0
,
-1
-2
...a
-m
!< !
n
p
n
+
n-1
p
n-1
+
1
p
1
+
0
p
0
+
-1
p
-1
+...+
-m
p
-m
.
10
@! ( ( ! '(- ! -
) , 7 ( . "( (
( ! ' ' (( <
.
W' ! ! 9 !, (-
! !
! , ! .
I '9 D"# !.
1.3. %< !!.
+ ! < ( 0, 1, !) !
() ((. ") < < ! (.
&! ( ' ( ! ( !:
1
10
= 1
2
7
10
= 111
2
2
10
= 10
2
8
10
= 1000
2
3
10
= 11
2
9
10
= 1001
2
4
10
= 100
2
10
10
= 1010
2
5
10
= 101
2
0,5
10
= 0,1
2
6
10
= 110
2
0,25
10
= 0,01
2
.
/ (( ( !, ( !, ( -
) ') ((:
0 + 0 = 0
0 + 1 = 1
1 + 0 = 1
1 + 1 = 10 .
A' ( ! ( :
0u 0 = 0
0u 1 = 0
1 u 0 = 0
1 u 1 = 1.
) ((: 11011101,01 ') (: _111001,11
+
1110010,11
1011,11
101010000,00 ; 101110,00 ;
) : 10110,1 ) (: _ 1110011 10111
u 10,1 10111 101
+
101101 _10111
101101 10111
111000,01; 0 .
1.