Лекции по всем курсам высшей математики МГУ (1108331), страница 24
Текст из файла (страница 24)
'4I/J W< *" )4 ! " !)4)4.%4 % K UY4^5I/J?'4I/JU)4^5?)4: ! )4 * W<'4I/JK>#"*$# $ '4I/J"1,+;0$#K;)4"#$ $+9;$#2IFE;2=22;B2K2=N=*;;>;?;7"#;1!#(+*0;'*$#!$$!2 W< *02P"OR" `/ !(2(IJ`/"! W*<ZI/JS%/5/-U/5?/- UX(*bZI/cJ?ZI/JbX $ % 4 " & ;"! 6+ ( ! W<S !0*" W*< Z4I/J Z4H I/J" % 0 0W<Z/I/J" S ]+*$$ "0SP/"5R2+ 0$#$$#$*$'4('*# '0/*$* #+&4(1'#007 1$#; 42A ;$# T/4V #$ #07 0$&a-H9!#*+#$+*+$*H*! + #*+#$+$0+ ( * # + + ( -H2 0("/5S/"/-S5"/XS5a-"/[S5a["/.SXa["222"/-H ^5SI-H `5Ja-H"/-H ^-S5a-H^5"2222:$$* ;$0# $ )5 S TZHI/5JV" ! Z4I/J = $ + *$# $ 67'" Z4I/J 2 ;$# )5 ! # $ $#'"; S"*] 7='4$$*0$# $)5;#( $ +,1$+**$#0 $ Z4BI/5J2:$$*$# $ #45"222"4B"222*0#4'$+ *$# $ ( *#1 #$*!0 1**$# $ 67'v5STm5" B I/JV"*!+m5" B I/JSZ4BI/J2!"*$# $ m5" BI/5JSS Z4BI/5J$ $+1752? ( * ; *# **$# $ 67'v-STm-" 5I/J"222"m-" BI/J"222V"$* +#*,$$;+ *$# $ m5" BI/J#$Z4I/J/#$ /52 *" m-" BI/J = **$#0 $ +Tm5" BI/JVm-" BI/-J7-*B2!*#++ 9 *7$$" * **$# $ vX SS TmX" BI/JV"v[STm[" BI/JV22"*!mH" BT/HJ7H*IFGB*$# $ mH" BI/J(**$# 0$ 1$ mH`5" BI/J*#$ H-2:$$* %! 1)*$# $ 607'TG4I/JV"!G4I/JSm4" 4I/J2@*$1"+$4SH"#$67G4I/J*4H(1**$# 0$ *$# $vH"*$ G4I/JSF4" 4I/Jv4 v4`5 222 vH2>$1 $" * 1( H 4 H $#+ *$#0 $ G4I/HJ +#+$+ **$# $ 1 + m4I/HJ" *9G4I/HJ7H*42@;" 7" *$# $ 67' G4I/J##+ 1 &4 #' $ $2 :$0$ *# $ _ / *;" $,$#4/S4/IJ'"*#$ B4_4/#+#$ %0#*#$#UZBI/J`Z4I/JUb2?+9!"$0* + #$*1 *#$ ;$# 67' "'$(S(IaXJ"*#$ /5/-0$$#U/-`/5 Ub(+1('67ZI/JUZI/-J`ZI/5JUbaX2( $ H $#+ (a- -`H b ( * #$#07 /5"222"/-H ^ 5$+"*#$ +, -H" # *+ #$+ #2 $_5"222"_-H ^ 5= #+7+"_R^5`_RS-`Hb(*#$R S 5" 222" -H ^ 52 @ *$1 1(+ $# *$#0 $'TGI_RJV$ $+"*9+'$+4'"*#$ 4B_4RUGBI_RJ`G4I_RJUbaX2* # $# 4/IJ #( 4/IJ S pqr 4R *0R-HS5;" ##+ ( $#+2 ?'$# 0"*$ /P/"5R_^=(;'4$;$#_5"222 " _ - H ^5 2c$"U/`_^ Ub-`Hb("#"UGHI/J`GHI_^JUbaX*#$ H2> *#$ B4_4/IJ4^UGBI/J`G4I/JUUGBI/J`GBI_^JU^U GBI_^J`G4I_^JU^^U G4I_^J`G4I/JUbaX^aX^aXS2<"*1&4*$# $ G4I/J$ 0$+#02 @& +#;5;$$# 0$$#*$!;$##*$$#-P/"5R#$ 67'"*# 0SP/"5R2;*0 "9$#+#+$+( +!;$0#67'2IFH:;;#*7)0?@)(;'*))2*) A=22K;;*=L?2=:;KO2K2=N!#"#$+, *"*0$ !#"$$#+( 41" ##1,1911$($# $($# !#23 $$ $($# ! 67'" #0$+, !$#!*2@$ 67+ZI/"7J*+! .S050-"!050-=#05SP&"OR"0-SPP"LR2?!$#0" .
$ ;$# TI/" 7JV ' *$$/n7"##+1,$#+&/O"P7L2]$ "*1(6$#70-67+mI/JSm7I/JSZI/"7J!*:P&"OR2O] A ZI/"7JL/29I7J *&6 70-2PP"LR!!7:$+" #$ 0- # $# ;$# ' *07;#$* 1(*;$#S#,$#'$n7"#9$($ + ##1#40!12@0-",#$!#$#!0;$#($$# #"0 " * $$ $ #,$#01*+1"2 $ % ( ZI/" 7J .2050-" 050-"052P&"OR"0-2PP"LR"W< O9I7JS A ZI/"7JL/&0-2IFI @$ *+! .
+#+$+ *" 67+ZI/"7J"*#+"+#+$+#*#'.23# "*1(_/I/-"7-J.$$#I/5`/-J-^I75`7-J-b(-$*###$#UZI/5"75J`ZI/-"7-JUb2A6$ *# 1 7/ 0-2 !+1(!7*'(0$$$n71(!/05SP&"OR+$CI/JSCI/"7"7/JSZI/"7J`ZI/"7/J07bCI/JUSUZI/"7J`ZI/"7/JUbC*$ $$+?I'")J;'SI/"7J)SI/"7/J"#U7`7/ U"*#4(2!+CI/J*0"*0OO&&U9I7J`9I7/JUS A CI/JL/ A UCI/JUL/bIO`&J2$*# $#(_/$1$"9I7J9I7/J*77/"2267+9I7J*##7S7/" 7/ #( *# " 9I7J *#0-2 ?+*$$1,*$((,2 $ % .W<95I7J9-I7J*0-2PP"LR &95I7J9-I7JO: %5W< GI7J" 9-I7JGI7JS A95I7J0-2ZI/"7JL/"@; # 9 " " 671GI7J;;$$# *$'!"*$ OGI7JS A Z5I/"7JL/"&!Z5I/"7JSZI/"7J*95I7J/9-I7JZ5I/"7JS/#*#$2 3# $$ *# 1 7/ 0-2 ?+*,+$GI7/JSGI7J`GI7/J67GI7J#9'0$4+9-I7J9-I7/J95I7J95I7/J$GI7/JS A9-I7JS A95I7JZI/"7JL/` A9-I7JIZI/"7J`ZI/"7/JJL/^ % A 95I7JZI/"7/JL/S9-I7/J95I7/JZI/"7/JL/` AS C5I7J^C-I7J2ZI/"7/JL/ & SIF>7#C5I7JC-I7J#**;"U7`7/ Ub(IJ"!(IJ_/_/1;$$"#529-I7JUC5I7JU A95I7JUZI/"7J`ZI/"7/JUL/U9-I7J`95I7JUIO`&J2?" $ S S fgh UZI/" 7JU" + # C-I7J *E795I7/J9-I7J95I7J9-I7/JUC-I7JU AZI/"7/JL/^ A95I7/JZI/"7/JL/ S A95I7J9-I7JL/ ^S A9-I7/JL/ SSSU$95I7/JU^SU$9-I7/JU2@$ 67 95I7J 9-I7J *# 0-" * $0 U$7/ U S U7 ` 7/ U b (5IJ #* #$#U$95I7/JUbU$9-I7/JUb2@;(/IJSpijI(5IJ"(-IJJ2!*#$ 7$$#U7`7/ Ub(/IJU$GI7/JUUC5I7JU^U C-I7JUbIO`&J^-SSIO`&^-SJ2E _ / *# " $1 $" 607+GI7J*##7S7/0-";#$00-2 3 "*##4 $#056$$$##$1, # #;0'2!"#(W< ZI/"7J.S050-"050-05SP&"OR0-SPP"LR"W*< mI/JSm7I/JSZI/"7J"7/0- m7I/Jm 7 I/JSZI/"7/J77/20/5!"# .
7/ PP" LR 7 7/ ZI/"7 Jl* %ZI/"7J /P&6OR "!7/* O! A ZI/" 7JL/2 : 7 7/ *&OO&&sip ZI/"7JL/S A ZI/"7/JL/277/ AIFCC2>;22=:;2A=22KO;;*=L?O2=:; $ % 4" ,!6+ . W< ZI/" 7J *.2050-" 050-"052P&"OR"0-2PP"LR.! Z 7 I/"7J.: W< mI7J" OmI7JS A ZI/"7JL/6& WW<0-"!OmI7JS A Z 7I/"7JL/& A6$*# 70-2@1(GS/$$0#7^G0-;*$ #$#Om " 7 ^G # `m " 7 #Z " /"7 ^G # `Z " /"7 #----------------------------------------- S A ----------------------------------------------------- L/2GG&@! + 67+ # *#' $ 9! #$# 0*#*/"*9!*:2@0++'6 *,'!;"*Om " 7 ^G # `m " 7 #----------------------------------------- S A Z 7I/"7^@GJL/"/b@b52G&$*#$Z 7I/"7J.$##;+5e5Z 7I/"7^@GJ Z 7I/"7J*G/205E7"$* +#;-e5"* #$#Om " 7 ^G # `m " 7 #sip ----------------------------------------SmI7JS A Z 7I/"7JL/GG& $ % 4,,- " ,!6+ 8 % *5 !" ! I7J I7JWW<0&I7J"I7JO: WI7J I7Jm7S % A ZI/"7JL/ & 72 A Z 7"/"7#L/1ZI"7J"7J"7J`ZI"7J"7J"7J2 I7JI7J @$ "#4"GS/7"7^G0-2:$$#0;LIGJ"! I7aGJ" 7 ^G # `m " 7 #LIGJS m----------------------------------------S --5- % AGG I7aGJI7JI7JZI/"7^GJ & L/` A ZI/"7JL/J2IF$* + $ (+ $ S I7 ^ GJ ` I7J"$SI7^GJ`I7J"$ZSZI/"7^GJ`ZI/"7J"!;*$ ##LIGJSG?5 A IZI/"7^GJ`ZI/"7JJL/^^$^G?5 A ZI/"7^GJL/^G?5 A ZI/"7^GJL/S'5^'-^'X2^$?$# *#++ $$;+ X" + ! '5*G/'5 A Z 7I/"7JL/2?"*++$+!#'-'X$0* +*#$ 67ZI/"7J"*$'-S` $------- ZI^@5$"7^GJ"'XS ------ ZI^@-$"7^GJ2GG>$1*G/'-`I7JZII7J"7J"'XI7JZII7J"7J2. X2 @# (*(($##;$* !* OOG/ &&sip A Z 7I/"7^@GJL/S A Z 7I/"7JL/"*+$ $##'$ $Z 7I/"7^@GJ Z 7I/"7J*G/"!05SP&"OR205& #$" ! * 05 67 9I/" GJ SS Z 7I/"7^@GJ$ *! $4-IzJS-9IzJSH25 9I0H"GJ$/HA$ *($+*($z/"*'$#;$# '" (# #$ (+TzV05SP&"OR2@9&S//b/-b222b/4SO(01("05"0-"222"04;$#$# P//"/5R"222"P/4`5"/4R(1!"#0;$/HS/H`/H`5#$#$#1, #2B7+-9IzJ*;$#'"#$z#pqr $/H""7"+O("(_/"($z/$$+H#$ ('z$$#$zb(2IF;* "$*_/#$ /05U9I/"GJ`9I/"/JUSUZ 7I/"7^@GJ`Z 7I/"7JUb"U-9I/"GJI:J`-9I/"/JI:JUbIO`&J2>$1$"$*G/#*$#Z 7I/"7^@GJ Z 7I/"7J"05*G/;-9I/"7JIzJ -9I/"/JI:J2'E!(*# *$,$#1#;$0('"22$,$#*IS sip sip -9I/"GJIzJS sip sip -9I/"GJIzJ2G/ $z/$z/ G/@9Osip -9I/"GJIzJS A Z 7I/"7^@GJL/"$z/&sip Z 7I/"7^@GJSZ 7I/"7J"G/OOG/ &&sip A Z 7I/"7^@GJL/S A Z 7I/"7JL/" #;$ #42 3 !' $" ! 0#;*+#5$#$* #+#' *#$ *! ' 672 ;!($$; #$2 $ % (W< ZI/"7J *.2050-" 052P&"OR"0-2PP"LR"% OLLO&PP&NS A L/ A ZI/"7JL7vS A L7 A ZI/"7JL/2 :$$#$*! 1671mI^"7J"!^mI^"7JS A ZI/"7JL/"^P&"OR"7PP"LR2&@;" 9 67+ *# .
* $#*$* I^"7J2?'$# "U$mUSUmI^^$^"7^$7J`mI^"7JS^^$^^&&S A ZI/"7^$7JL/` A ZI/"7JL/ IF9^^$^^ A IZI/"7^$7J`ZI/"7JJL/ ^ A ZI/"7^$7JL/ &^IO`&J pqrU$7ZI/"7JU^PU$^U"/05!PS pqr UZI/"7JU2I/"7JE@$ 67+ZI/"7J*#"pqr$7ZI/"7J/*/05$7/23# "$m/*I$7"$^JI/"/J"22mI/"^J*#.2?"m^I^"7JSZI^"7J"*9*X+67LL^PP&vI^JS A mI^"7JL7S A L7 A ZI/"7JL/LLPPLLvI^JS ----- mI^"7JL7S A m^I/"7JL7S A ZI^"7JL7SGI^J2L^ APL3 !' $" 67+ GI^J S A ZI^" 7JL7 ; *#"P*9*6E 1='(7^LGI^JS ----- A GI/JL/SNI^J"L^ &^^L&&P!NI^JS A GI/JL/S A L/ A ZI/"7JL723# "GI^JSNI^JSS vI^J2&!"#" vI/JSNI/JS/"*9*#$ ^0-$#$#vI^JSNI^J2$$"*^SOvSvIOJSNIOJSN2 IEF =*;;:;2<;?*;((,!*#'(7I[J##6!;$$#! 0'62<'6!;*$#+#0("*(##SgBowCgRLgI'P&LgBwgLg)gCIw4I5Y\ZJ eo^g I5YQZ" GDJ2 @# $#" *;22A#2 $ % 4("&"6+.W< ZI/J4%% %/".* W< /2/Ii"^J + i`/^^ZI/JS/2: W<9I7J"4%*%"W4HH `5H^ L" 9 " i #Z " i # #9I/Ii"^JS9IiJ^H25- ------------------------------------------------ ^V46 ---H `5H!Li /"i#L 4 % A 9 " / # " i `/ ^^Z " / # # 4 L/& i5V4S ---- ---------------------------------------------------------------------------------------244!Li/IiJ :$$671|HS|HIiJS A 9I/JIi`/^^ZI/JJHL/2i@667**i2@-*L| H---------- SH|H`5`^H9IiJZHIiJ"22Li^H5 L||H`5S ---- 9IiJZHIiJ^ --- ---------H- 2HH Li@667##*$#$#H`5"L H `5 | H `5^ H L H `5 " 9 " i #Z H " i # #5 L H |H---------------------------- S ----- ------------------------------------------------ ^ --- ------------2`5`5HHHH Li HLiLi@*$#+9#$#*HS5"222"4"*L|LiL| 5^ L " 9 " i #Z " i # #5 L- |---------- S ----- ------------------------------------- ^ --- ------------"LiLi- Li -|/S^9IiJZIiJ^ ---------5- "2222222222222222222222222222222222222222222L 4 `5 |^ 4 L 4 `5 " 9 " i #Z 4 " i # #5 L 4 |44 `5---------------------------- S ----- ------------------------------------------------ ^ --- ------------244 Li 4Li 4 `5Li 4 `5IEE@$#*$#;#**$22*0#!#;+"^ 4 L 4 `5 " 9 " i #Z 4 " i # #^ - L " 9 " i #Z - " i # #- ------------------------------------- ^222^ ----- ------------------------------------------------ ^|/S^9IiJZIiJ^ ---4 `5Li-!4!Li5 L4 |4- ------------- 2^ ---4! Li 4&!"+|/$*###$#/IiJ|/S A 9I/JL/S9I/IiJJ`9IiJ2i@$# 9 6 # *, #;2 @$6###;4H4 `5H^ L" 9 " i #Z " i # #- ------------------------------------------------ ^V4"9I/IiJJS9IiJ^H25 ---4 `5!H!Li /"i#L 4 % A 9 " / # " i `/ ^^Z " / # # 4 L/&4 i5 L |45V4S ---- ------------- S ----- ---------------------------------------------------------------------------------------24! Li 44!Li 4@##$ $+6!;252$!#*;$##$#ZI/JI5"6!;*#,$+#6'$$0#! '62-2@$ ZI/JSfij/2!67+/S/IiJ+#+$+40#+&*/`^fij/Si"!^=9$7$9*$'(## 2?+67VI/JS5`^wtf/*$*;#+!;^ H L H `5 " fij i # H ^5VI/IiJJS5`^wtfi^^ H25- ----------------------------------------- ---H `5H!Li"*$,$#"$#!$ $ *^b/"\\-2222 1 " (!$# $;+ *+++!;*#+1$ $$#+9!+"0 *# 2 <'" 2 82 (" @2 32 *$" ]1"2 2 2 @666" >2 C " 2 8'" >2 &4" &2 82 c0("@2?2821]:'"2:4"@22(4o#"22A0#"m223 7'"@22E$#2$$#+*#0*$ $ $ ((,' + !; $0!+2IEG ;2*2;BO*=N:Q2@+#'$ $67*(;$#+#+$+ ((, $$$! *++ #' $ 0$*$+#$#'$#*+*67*&42$$* $+!'**+ * = * * 8'" (!" #!2>(*+#'$ $=*&4*8'=9##"; #$+(** #$#'$6*+2>(9*0+($* # # $7+ "*9;(9##$*+'#'$ $ * &4 * 8' # (, $ $ $ *(;$#2E*($+$ # *'2.) " #" %!O5O-*O5 O-"O- O5UT/4V"/4 #" W )" !* O +!!!* ; T/4V )" ! O/4O!!/4^5O? ( $ " $$#+ ( ;$# )( + ( ' 6 ' ' *$0# $ 12&!"*!"*$#$ 0'()*$2:$$" 7" 671 ZI/J" *1 0O(;$#)2hI fW*<ZI/J)" )*sip ZI/4J2IT/4V"! 49$*4MNB` sipZI/JSI2)$(9##$*'*0*8'#($$"22*&42@#60#I$22D"7+X/J2IEH $ % " NB* sipZI/J%*) ! sip ZI/J l+ .)NB* sipZI/J2 sipZI/J))?+!(* " sipZI/J$ ((,*0)*&4"(;*$ sipZI/JS-0 sipZI/J2))? $# 9' *$+ # $1,"1,$$+ '$2 $ $ % .T/4V ) : 7H 2 /4H !TOH )V " ! % H OH^5 OH" 7H OH"7HOH^5.!TOHV5!($# O H2 $ $ % " ! O ) ! O H%!" O H O# #4 *++ *#+1 *0# *' (, *1 #' $ $2 ?+ 9!* # *# # $ ;$# # $671ZI/"7J($ ";$##()2 ;< ZI/" 7J % W< mI7J )$" `/* !OIJ)"!%/OIJ*7$UZI/"7J?mI7JUX)9$*4ZI/"7J mI7J2$M "!W< ZI/"7J%* f W< mI7J $" T/4V")"W<* Z4I7J2ZI/4"7J% mI7J*$I)JNB9$*4ZI/"7J mI7J2$IEI J?;2=2=NDO2Q;2*2QO*=* ;*'(9##$*+'#'$ $*&4*8'2 $ % 5(W< ZI/"7J% fmI7J)mI7J)$" ZI/"7J$)I)JNBmI7J"ZI/"7J-2(ZI/"7JmI7J2$$ :$$ #; 52 ] $$; *#!2I)JNB?*$"ZI/"7JmI7J+1(''*()*0$)mI7J$# $T/4V"#+$ $ ZI/"7J$$2@$$#"'$+_/"+1(!+O)'$+/OO7O$0"UZI/O"7OJ`mI7OJ2 $#$#!OO5$#'*$# $'(0/575$#$#1,/O57O52/5;*; $#$+O" *$0*$2@9'$+O)$$#/5O2@'$+$H5"OH5O"+!;/5OH52* #$#/-7-# /-S/OH OH57-S7OH $*#1*7$#$#2( * *$# $ /4 74" + $*###$#UZI/4"74J`mI74JU_*#$ 42@;"*$# $ /4+#+$+'*()2?+9!$#$6 $ 2A0"*$# $ $H4#$2E#$+O/)*-$;055 O H/"*H4_H//4^5 O H/ O / O/""#O/; ( H/ *$# $ T/4V" 2 2 6 2( $ /4" " /4 O H4" /4^5 O H42 E $ + ! O/ S O H4 $#/4O/"# *$ #1'O/ O H4O/ O H40; $#"//O/ O H4"22/4 O H4"#2E!/4^5 O H4 O/"22*$# 0$ T/4V2IE" *$ 1 *$# $ /4 #1"*$#$#1, 74 $$*##0#$# UZI/4" 74J ` mI74JU * #$ 4 2 < " #+ $ $ 67 ' *$# $Z4I7JSZI/4"7J67mI7J*4$"*0#$**;12("#;052I)JNB:$$ #; -2 @$ ZI/" 7J mI7J" *$1(_/'$+OSOIJ)"*#$7$*#$ /OIJUZI/"7J`mI7JUb2@$ * T/4V=1(++*$# $ *()2!#OIJ ; 4 ;$# /4 * $( 44_4/IJ"/4OIJ"* ;4mI7J*42 UZI/4"7J`mI7JUb"9"ZI/4"7J$@" # Z q ( ) #1$+ $01,!+M5J ; O ( ) *$" *$ #$'*$O-J+1( # 'O5O-(#1O5 O-"(#1O5 O-OXJ$,$# +(+*()*$#0 $ 2E *#' #!+ ; * $+" 9 !+#$ ( "$($#-";$($#"#1,$,$##OX O5 O-2E9$#$"*$ #$()*$#$!; $$# ( )/" 9##1 ) # $$"$,$##**()#$('$ $ *)/"(2@9#$$6# #4$0#+ + ( )/ ; ( #*2 E*" # $*+!*#+(NS)K"!)K$ (%^7^"#$#$#$#1,!N/;#+ ("$0$#1'#GSTI/"7JU/_&"7_&V2?+ * ;+ *# ((, + &04#'$ $67'*(;$#2 $ % 4" "?3."& "$&(!6+" !W< ZI/"7J" #$"%W<mI7J)"#"$"%*!"! `/+!O2OIJ)"! % !/5/- 7$ UZI/5"7J`ZI/-"7JUb2IE) U% $ZI/"7J mI7J"+#$+!_/$0$,$# OIJ " + #$ 7 $ $*###$# UZI/"7J`mI7JUba-2!+1( /5/-OIJ1(!7$UZI/5"7J`ZI/-"7JUUZI/5"7J`mI7JU^U mI7J`ZI/-"7JUba-^a-S2"!2 A6$ *# 1 7 $2! 67+ GI/J S G7I/J S ZI/" 7J ##+ (1&4+$ $*(23# "$,$0)#$mSmI7J"GI/J m"22$*0+$ $ )GI/JSG7I/JSZI/"7J mI7J"! mI7J = + 67+" *+ ;$# $2@;" + $ $ +#+$+ #' $2?'$# " $$ OIJ $ $#" *1( /5/-OIJ*1(7$#*+$+$#UZI/5"7J`ZI/-"7JUba-29#$#*6$#7*'**()* *'/-2!*UZI/5"7J`mI7JUa-b2@$ #$# #*+$+ * 1( /5 OIJ *1(7$2<")ZI/"7J mI7J2$ $# *+! $$#+ Q *# *+16# + &4 $$#+ #' $ 0$;$#$+67ZI/"7J*()"';$##24" " .
![](https://s.studizba.com/z.php?f=/templates/si/i/noavatar.png&w=100&h=100&t=1"){kind=avatar}
