1-курс / 1-курс / Kurs_mat_analiza_Архив WinRAR / Kurs_mat_analiza_-_Kudravcev_T1
.pdf
9 P E ( & ! )
& ! )
I I I<F (
" , A ,
A&I) I I I I < F #
I→ I & <
R <)
( j_s A(I) & < '
I →
)
J IK & ! )
< R < ! !
" JI |
K j_s I |
|
I T |
||
|
V |
|
I → |
V |
|
J I |
K |
|
|||
|
V |
|
|
|
|
J IK & R P) ' ! |
|||||
< |
|
|
|
|
|
% % 5 8
+ (A , 4
4 & 4, 4 )
! 4 @ 4
!
( C
*
& ' ( *$%&; A , 4 1 m 5 <9 & 5 & 2 B$6? 9 A < # < & 64 2@ %& (
& [ & 2
j_s A( ) IA& 4) |
&H <P) |
→ 4 |
|
&H <P)
* (A 4, '
*
A& 4)
!" &H <P) *
(A 4+ (A
4* ,
j_s A( ) I |
&H <R) |
→ 4 |
|
@ ' !
I I I < F j_s I I 4
I → ∞
j_s A( I) I |
&H <H) |
I → |
|
4 '
4 I I 4 I I < F' &H <H)
j_s A( 4) I |
&H <S) |
I → |
|
@
'
j_s A( 4) IA& 4) |
&H <[) |
I → |
|
@ &H <S) &H <[)A& 4) I |
|
5 (
%|$6? 9 A , : &%9 # 4
& 64 %<
j_s A( ) IA& 4) |
&H <>) |
→ 4 |
|
8 &H <>)
( 4 A' "
, (
A 4
@ F &H <>) (A , 4 4 @ ! (
A , j_s A( ) !
→ 4
T U 4
I I 4 I I < F
! j_s A( I) I j_s A( 4) |
IA& 4) |
|
I → |
I → |
|
(A |
||
|
|
j_s A( ) ! ! |
→ 4
3 (
* !
(
5 * H 4
(
!
(
"
"
+ m 6 4 : &%9 : < 4 & 6 4 ' %& %< %$8 %&$& 6 %& %&; f& 4)>& 4 & 6 # % f& 4) 6 & 4 % ' ( %& % %& & & <;6 : 4 & 64,
f& 4) I J 4K |
&H <=) |
"
" "
"
,m 64 : &%9 # <; 4 & 6 4
' %& %< <72 4 6 %& %& %$8 ( %&$& &< 9 & & 6 # < ' 8 9 ' ( %&$1
3& 64 : &%9 # <; 4 & 6 4
' %& %< %96 9 # 6 < & 9 6 %& %&;
& % >& ' %& #$%& # % c <9 <7( 2 4 # 6 < & 4 6 %& %& f& 4) # < 9 &%9 $%<
f& 4) |
|
+ |
|
|
; |
L M
& ) + '
C
S [
4
! ' !
! !
4 & 4 / )
! 4* *
* " 4
' *
& 4
) ' 41
" 4
"
@ *
& ' ( %96 9 B$6? 9 # 6 ' 4 : < (
4 & 6 ' %& % 5 # < 9
+ 4 /
( A -
S * f& 4) 4
4 f& 4) I J 4K 0 ! !
|
I I < F |
j_s |
|
I |
|
I |
|
I → |
I |
4 |
|
*I4"I WI4
I f& 4)
I f& 4) ;f& 4) I J 4K ' " I W I4 I I 4
I4 T < JA& I)K
, A& I) I A& 4) I W I4 + ' *
j_s A( I)IA& 4) ! |
||||
I → |
|
|
|
|
|
I I < F |
j_s |
|
I |
I |
|
I → |
I |
4 |
&H <>) ( A
4
; (
%6 & 9 <9 &%9 %& %<$(
# 5 ;( #
" " ! !*
! ;
' ( A& ) I < T
T
jq cf` Fπ & H F)
" I 4 < F
" < & " "
' (
) A ( ' ( "
" &4 <) &< <) &U< <) &F <) &UF <) &
F4)
3 P (
#
, *A& 4) + '
( & )
# "
(
)*+,-./.0/ 1(A ,
4
j_s A( ) IA& 4)
→ 4
f& 4)
+ ! (
! * !
( *
:*$%&; A , 4 w 1 |$6? 9 A ( : &%9 # 4 & 64# ' %&$w %<
j_s A& ) IA& 4)
→ 4w
3 ( A : &%9 # 4
& 64 w # ' %&$w %< >& 4 & 6 # (
%$' Aw>& 4 B$6? ' %& w,
j_s Aw( ) IAw& 4)
→ 4
; ( "A& R H R)
4 I 4 " "
j_s A& ) I < IA&4)
→ 4
"
" 4 I 4
" " ( "
* 5 ( "
+ ( A , 4
H
'
% + D ; 3 8
@ ( A ,
4! !
I 4 I I I < F
* " ( JA& I)K &
! ) ' !
" J IK
JA& I)K ,
j_s A( I) I (
I →
A 4
+ #
*
!
JA& I)K '
' ( A '
4
& ' ( !]<9 & 5 & 2 B$6? 9 A , < 6 ( 4 < # < 5 : 6 2 %6 4 # < & 64 9 <978 4%9 & 6 4 # 6 % 9 ' %& 2(
@ %& & & 2 <9 <72 4 # %< & <; %( &I 4 I I I < F# %< & <; %&; % &(
&%&$78 @ : 4 B$6? JA& I)K < 6 4 < # < 5 : 6 2 %6 4 # <1
- & ' . - ) / 0 ' ]<9 & 5 & 2 B$6? 9 A , < 6 4 # < & 64 9 <978 4%9 & 6 4 # 6 % (
9 ' %& 2@ %& & & 2 <9 <72 4 # %< & <; %&I 4 I I I < F # ( %< & <; %&; % & &%&$78 @ : 4 B$6? JA& I)K2 < %@ 98 4%91
; !" (
" *
(A 4
' & < H R)
* j_s A( I) "
I →
" J IK
* ( +A ,
! I 4 I I I < F
JA& I)K &
! )
7 ! ′I 4
′′I 4 ′I ′′I I I < F -
|
′ L I FI U < |
|
||
|
|
|||
L I |
I |
|
I I < F |
|
I′′ |
L I FI |
|||
|
|
|||
|
|
|||
|
|
& ! ) |
|||
4 L L I < F + ' |
|||||
|
* |
j_s A( ¢ ) |
|||
|
|
|
|
|
I |
j_s |
|
|
|
|
I → |
A( I² ) j_s A( L)JA& I)K |
|||||
I → |
|
L → |
|
|
′ |
|
|
|
|
||
JA& ′′ |
|
)K |
|||
I |
|
|
|
|
|
JA& )K ! J ′ |
K J ′′ |
K |
|||
|
|
L |
I |
I |
|
J LK
& ! )
! &R P) + '
j_s A( ¢ ) I |
j_s A( |
L |
) j_s A( |
I² |
) I j_s A( |
L |
) |
||
I |
L → |
I → |
|
L → |
|
||||
I → |
|
|
|
|
|
|
|||
|
I |
|
|
I² |
|
|
|
||
|
|
|
) |
|
|
||||
|
j_s A( ¢ ) I j_s A( |
|
|
|
|
||||
|
I → |
|
I → |
|
|
|
|
|
|
-! JA& I)KI 4 I I I < F !
J IK 5! !*
JA& I)K !
< H R j_s A( ) I
→ 4
8
R & $" *
% !
* " )
% , / 8
@ * (
* (
"
( 0 #
< H R
< m 6 : &%9 # < B$6? A ,
# 4 &< & & ' & 64)%< <9 <72 4 6 %& %& f& )& 6 %$8 %&$& & 6 9 6( %& %&; f& 4)& 64 &
A& f& 4)) f& ) |
&H F4) |
+ ( 0 # ! !
j_s A( ) (
→ 4
0 # ' ! # !
' H R
(
|
|
|
|
|
|
|
|
7 FP |
||||||||
Qε |
|
|
|
|
|
|
|
|
|
|
|
|
= 4 / |
|||
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
||
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|||
Fε |
|
|
|
|
|
|
|
|
|
|
|
|
|
|||
|
|
|
|
|
|
|
|
|
|
|
|
|
4 |
|
||
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|||
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|||
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
3 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
||
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
||
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
= |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
||
|
4 |
|
Fδ Qδ |
|
||||||||||||
|
|
* , |
|
|||||||||||||
|
|
4 |
|
|
|
4 |
4 |
|
|
|
||||||
|
|
|
|
7 FP |
|
|
|
j_s A( ) |
XYZ |
|||||||
|
|
|
|
|
|
|
I |
|||||||||
|
|
|
|
|
|
|
|
|
|
|
XYZ |
|
|
|
→ 4 |
|
|
|
|
|
|
|
|
|
|
|
|
f& ) f& 4),A& f& 4)) f& ) |
|||||
|
|
|
|
|
|
|
|
|
|
|
|
|||||
|
7 # ( ! &H F4) |
|||||||||||||||
= |
( * ! |
|||||||||||||||
m 6 : &%9 # < B$6? A , #
4 %< <9 <72 4 6 %& %& f& )& 6 %$8 %&($& & 6 9 6 %& %&; f& 4)& 64 & <9 <72 4 & 6
|
f& 4) |
&H F<) |
||
# < 9 &%9 6<7 |
|
|
||
|
A& ) f& ) |
|
&H FF) |
|
3 ' |
||||
* ! , |
|
|
||
|
j_s A( ) I |
XYZ |
|
|
|
|
|
||
XYZ |
→ 4 |
|
|
|
f& ) f& 4) f& 4),A& ) f& ) |
&H FP) |
|||
|
||||
" !
" =
( "
@(
^ %< : &%9 # < B$6? A & 64
%< <9 <72 5 ε W 4 %$8 %&$& & 6 δ W 4< & <9 % @ $< & 978 @$%< 9 Q U 4Q Vδ (
# < 9 &%9 %&QA& ) U Q Vε
< 3 #δ Iδ&ε) W 4 ! !δ ε
