Hmsusu` Lckj? @lusskvd ^k``d (;84;45….) (;84;45 ….)
Hlsk` Vk`bdapu? (….)
Wudtu ndcli nktl` nkrtucd`b tkrcktdi hm dtds nk`td`bd` skhkrjd`d 2,6 a hk`bd` n1;66 aa, h1462; aa, j144;6 aa. Ndcli ak`huiu`b nknk` ikrod yd`b tkrhmrm hdrm nknd` jmhup akrdtd ;> i@/a hd` nknd` adtm akrdtd 7> i@/a. Vkrmisdcdj dpdidj ndcli adapu ak`djd` alak` ck`tur yd`b tkrodhm, omid ? d. Vk`ucd`bd` 5 H7>, hd` eg½ 1 >6 Apd, ey 1 766 Apd (@lrkb. Bd`oc) Iktk`tud` ? nk`td`b ndcli 2,6 aktkr 1 sdtu d`bid tkrdijmr hmbd`tm sksudm d`bid dijmr `lalr rkbmstrdsm adjdsmswd!
⁈ ⁈ ⁈
Nknd` Jmhup 1 ;>
2,; a
Nknd` Adtm 1 7>
Nknd` Xltdc 1 ;> ;> + 7> 1 :8 Aadx
1 . q . C¾
Aadx 1 ;=6,5>; i@a
1 . :8 . (2,;)¾ 1 ;=6,5>; i@a n1;66
Hmdbrda ^kbd`bd`
Hmdbrda Xkbd`bd`
17;7,=>; 1 . 47
eg” mom` 1 = 1 =
Z17;7,=>;aa
@H
j144;6
542,482
h1462;
1
542,482 12>>4,62; 1 .
@X 1
Hmi ? eg” 1 >6 Apd
eg” mom` 1 6,8; x >6 1 = Apd
462;-x 1 2>4,62;
ey 1 766 Apd
es mom` 1 486 Apd
Ds 5H7> 1 8:>;,; aa Bdyd Xkid`
Bdyd Xdrmi
@H 1 . eg.n.x
@X
1 . eg.;66.x
1 es . Ds 1 8:>;,; es
1 >;6 eg.x
Hk`bd` ikskmand`bd` bdyd-bdyd ₣J 1 6 --‿ --‿ @H ‗ @X ‗ @X 1 6
^dsml es tkrjdhdp eg” tkrsknut hdpdt oubd hmpkrlckj hk`bd` ak`bbu`did` junu`bd` tkbd`bd` cm`kdr hd` juiua Jllik.
@H 1 @X >;6 eg”.x 1 8:>;,; es
, 1 ∞ 1 ∞ . 1
∞ ∞ 1 1 . ` 1 . .=
∞ ∞ . , 1
42 >6 >; 76 7; 86
` 46 = = : 2 5
Idrk`d eg” 1 >6 Apd, adid ` 1 =
>;6 x¾ 1 878>=,; ( 462; ‗ 462; ‗ x x )
>;6 x¾ 1 855:524>,; ‗ 855:524>,; ‗ 878>=,; 878>=,; x >;6 x¾ + 878>=,; x ‗ x ‗ 855:524>,;1 855:524>,;1 6 Z¾ + 427,2> x ‗ x ‗ 4:5285,:; 4:5285,:; 1 6
∞ , ´ ´ , ∞ . . ∞, 1 .
1 427,∞ ,2>2>´ ´::4,∟ ;2,. 427,+, 2> ::4,;2 1
>
1 > ´ >
Vk`ykcksdmd` pkrsdadd` iudhrdt ?
∞´∟ ∞ 1 ∞´∟
1 :5,:5 ´ 886,2:;
≊7;7,=>; ≊;>2,58; 7;7,=>; hd`
Aw 1 ;=6,5>; i@a 1 ( @H dtdu @X ) x ( Ck`bd` ) _ ( Ck`bd` ) 1 h -
1 462; - .
1 =;2,6>; aa
1 6,=;26>; a
@H 1 @X 1
1542,482 ,, 1
Xkbd`bd`-tkbd`bd` Xkbd`bd`-tkbd`bd` hmhdpdtid` akcdcum pkrsdadd` p krsdadd` ?
eg 1 es 1
, · 1 . , , , . · 1 , , , 14>2,:=>:56: 1
1 5,=28:=645 3 eg” mom` (=AVd) mom` (=AVd)
1
3 es mom` (486AVd)
idrk`d eg1 5,=28:=645 3 =, iurd`b hdrm tkbd`bd` yd`b hmmom`id`, adid ndcli iudt ak`djd` alak` ck`tur. Idrk`d es1
4>2,:=>:56:
3 486, ndcli iudt
ak`djd` alak` ck`tur. Odhm, iksmapucd``yd dhdcdj ndcli iudt ak`djd` nknd`-nknd` yd`b dhd.
^k`gd`did` sudtu ndcli nktl` nkrtucd`b pkrskbm pdhd huiu`bd` skhkrjd`d hk`bd` nk`td`bd` 2,6 a, ak`huiu`b nknd` ikrod akrdtd yd`b tkrhmrm hdrm nknd` jmhup akrdtd 76 i@/a” i@/a” hd` nknd` adtm akrdtd (tmhdi tkradsui nkrdt sk`hmrm ndcli) >7 i@/a”, i@/a”, . Nkrmid` siktsd rk`gd`d`yd!
1>6, 1766
Iktk`tud` ? Nk`td`bd` ndcli 2,6 2,6 a ↞ sdtu d`bid tkrdijmr hmbd`tm sksudm sdtu d`bid dijmr `lalr rkbmstrdsm adjdsmswd! Hmiktdjum ?
CC (nknd` jmhup akrdtd) HC (nknd` adtm akrdtd) Nk`td`b ndcli (C) (autu nktl`) ey (tkbd`bd` cucuj ndod)
1 76 i@/a 1 >7 i@/a 1 2,; a 1 >6 AVd 1 766 AVd
Vkandjdsd` ?
Ak`k`tuid` es es 1 426 Apd
1 6,8; 1 6,8;8; >>66 1 =
Xucd`bd` Autu ey 866 dtdu cknmj hd` odrm`b idwdt cds (plcls dtdu dt du uc ucmr mr 426 AVd W@M 67->: 67->:82->6 82->66> 6> jca >87
Ak`k`tuid`
Ak`k`tuid` `mcdm ` 42 >6 >;
` 46 = =
Xkbd`bd` skrdt tkid` tkrcudr dimndt pk`bdruj prdtkbd`b, 1 6 ,8; e'g nknd` adtm hd` nknd` jmhup tktdp
76 7; 86
: 2 5
XDNKC D-2 @mcdm ^dsml Alhucus Kcdstmsmtds
Ak`gdrm 8 nksdrd` pkrk`gd`dd` (a, o, i, hd` )
4. >. 7.
1 + 1 + 16,7>>2 1 4 . 1 1 4 .6,7>>216,:=>8 1 . . . 1 . =. 6,7>>2. 6,:=>8 14,>=;= 1 . . 1 . ,. 16,66:;8
AVd
8. τ
Ak`k`tuid` uiurd` ndcli skak`tdrd hk`bd` pkrimrdd` nkrdt ndcli 2 i@/a 4. Aw (Nknd` Jmhup)
1 1
. . . 7676 . 2,;¾ . 2 . ¾ .>72 . 2,;¾
1 >46,=8 i@a >. Aw (Nknd` Adtm)
1 1
1 >46,=8 i@a 7. Aw (Nknd` Xltdc)
1 Aw (nknd` jmhup) + Aw (nknd` adtm) 1 >46,=8 + >46,=8 1 8>4,::i@a
Ak`k`tuid` alak` ck`tur mom`?
.. 1
Wkcd`out`yd hmcdiuid` gdrd glndglnd `mcdm n hd` h skndbdm nkrmiut? hmglnd n
hmhdpdt h
8>4, : : 46 .. 1 4,>=;5 .. 17>;5>;4=7 h1
766
468>,=
7:6
=>5,2
8;6
:;4,5
;66
:62,=
Hk`bd` akapkrimrdid` ak`bbu`did` hud cdpms ndtd`b tucd`bd` ndod nkrhmdaktkr sdad, tm`bbm tltdc yd`b hmpkrcuid` 1 :62,=+ skcmaut nktl` + hmdaktkr sk`bid`b + hmdaktkr ndtd`b tucd`bd` +sktk`bdj odrdi nkrsmj d`tdr cdpms tucd`bd`. Hmad`d skcmaut nktl` 1 86 aa, hmdaktkr ndtd`b sk`bid`b uaua`yd hmpdidm H46 dtdu H4>, ndtd`b tucd`bd` plili H>; (d`bbdpd`), sktk`bdj odrdi nkrsmj cdpmsd` tucd`bd` 4>; aa. hk`bd` hkamimd`, u`tui ndcli hk`bd` hud cdpms ndtd`b tucd`bd` ndod akakrcuid` tdandjd` tm`bbm :;-466 aa tkrjdhdp tm`bbm kekitme h (hmsm`m 466 aa).
℀1:62, ℀ 1:62,=4661=62,=
Xktdpid` uiurd` ndcli ;66 aa x =;6 aa
Vkakrmisdd` nkrdt ndcli sk`hmrm hd` rkvmsm cd`bidj dpdnmcd hmpkrcuid`
1 1 1 6,;6 6,=;. >7 1 46,=>; / / 4 1 ℀ : 1>46,=8 4: >746,=>;2,; 1 8888=,=,82; =62,=
[`tui n 1 ;66 aa, hk`bd` ak`bucd`b gdrd glnd-glnd hmhdpdtid` h 1 :62,=aa skjm`bbd j1 :62,= + 466 1 ga x =;6 ga hdpdt hmpdidm.
aa. Adid uiurd` ndcli ;66
Ak`k`tuid` cuds ndtd`b tucd`bd` ndod yd`b hmpkrcuid`. Dpdnmcd hmpkrimrdid` did` ak`bbu`did` ndod tucd`bd` H46, adid u`tui ak`hdpdtid` h hdpdt hmiurd`bm =6 aa tkrjdhdp j.
1 =;6 =6 1 :56 88=, 8 2; 46 1 . 1 4266,:=>8:56 1 78788;8;,,62828
Ak`gdrm Ds 0 788;,628 aa>
5878 5878 6
Ds0 788;,628 aa>pdhd tdnkc D-8 mdcdj 75=8,5 aa> adid ak`bbu`did` 5 ndtd`b tucd`bd` H>: hdcda > cdpms, DW1 75=8,5 aa>
Cktdi bdrms `ktrdc
@mcdm h
1 =;=;66 ℀ ∋∋ ∋ 1=;6 8646>:4>, ; 1:;=,; 4 > 1 . @mcdm x
;66 175=8,5=:;=,; ;66 >;6 77>;4,8>:;2=;2:,716 477,66;544874:,747>16
Vk`ykcksdmd` pkrsdadd` iudhrdt ?
´ 477,66;5> . 4 8 .4.. 4.444487874:,4:,747> 747> 1 477,66;5 ´
∞´∟ ∞ 1 ∞´∟
1 ∞, ´ ∟ ,. +,
477, 6 6;5 ´ 5:=, 4 25 477, 6 6;5 5:=, 4 25 1 > 1 > ´ > 1 55,; ´ 786,;= ≊>28,6= ≊862,6= 4 4 7 1:;=, ; 7 >28,6== 1:;=,;=4,75125:,48 88=, 8 2;46 1 1 1 25:,48 1;:;,482 1 1 ,, 1 4;4;:,:,72= AVd AVd
hd`
Ck`bd` Ilpkc Alak`
Ak`gdrm @H hd` @X
Ak`gdrm es hd` eg
, 1 . 1 , 1 :,;8;8 AVd
;66 :,;8 AVd >28,6=
:;=,; 5 H>:
1 426= 14:,:= 1 4;:,72= 142,5 =
^k`gd`did` ndcli nktl` nkrtucd`b rd`bidp nkrpk`dapd`b pkrskbm pdhd huiu`bd` skhkrjd`d hk`bd` nk`td`bd` =,4; a. Hmak`sm ndcli 766aa x 566aahd` 566aahd` h”1 =6aa yd`b ak`huiu`b nknd` ikrod akrdtd yd`b tkrhmrm hdrm nknd` jmhup akrdtd >6 I@/a” I@/a” hd` nknd` adtm akrdtd (tmhdi tkradsui nkrdt sk`hmrm ndcli) 4> I@/a” I@/a” , eg” eg” 1 76Apd , ey 1 866Apd. Nkrmid` bdandr siktsd`yd! n eg” Ds”
n
Ds”
@H4
ah h
Ds
eg” mom`
h”
1
h-
+
Ds4
Ds> @X4
Hmiktdjum? n x j 1 766 x 566 aa nknd` jmhup 1 >6 I@/a nknd` adtm 1 4> I@/a 1 =,4;a
@H>
Eg” Ey h” h
@X>
1 76 Apd 1 866 Apd 1 =6aa 1 566 ‗ 86 86 ‗ 46 46 ‗ 86 86 ‗ 4>,; 4>,; 1 8:2,; aa
d. Ak`k`tuid` esmzm` (tkbd`bd` tdrmi pdhd tucdbd`) esmzm` (tkbd`bd` tdrmi pdhd tucd`bd`) 1 426 Apd
Xucd`bd` Autu ey 866 dtdu cknmj hd` odrm`b idwdt cds (plcls dtdu ucmr) 426 AVd
1 6,8; 1 6,8; 7676 1 .
n. Ak`k`tuid`
Xkbd`bd` skrdt tkid` tkrcudr dimndt pk`bdruj prdtkbd`b, nknd` adtm hd` 1 6 ,8; e' g nknd` jmhup tktdp
g. Ak`k`tuid` `mcdm ` Nkrhdsdrid` tdnkc D-2 adid hmhdpdt `mcdm
`1:
XDNKC D-2 WMEDX-WMEDX HD@ IL@WXD@XD NKXL@
e'g
@
86 AVd
5
7; AVd
2
76 Apd
:
h. Ak`k`tuid`Xkbd`bd`-tkbd`bd` Mzm` Xkbd`bd` ‗ Xkbd`bd` ‗ tkbd`bd` tkbd`bd` mom`, eg”1 47,; AVd, hd` es 1 426 AVd (autu ndod 86) `mcdm ` 1 :.
+ . .
a1
1
, ,+ . ,. ,
1 6,7::;
o 1 4 - a 1 4 - . 6,7::; 1 6,:26; i1
τ 1 .
e”g . a . o 1
1 .
47,; . 6,7::; . 6,:26; 1 >,>:77 AVd
1 6,64;
k. Dsuasm Wkak`tdrd Nkrdt Ndcli
n . j . no 1 6,7 . 6,5 . >7 1 8,48 I@/a” e. [iurd` Ndcli Wkak`tdrd ?
. >6 . =,
Aw nknd` jmhup 1 . q . ℗¾ 1
4;¾ 4;
1 >6=,7I@a Aw nknd` adtm
1
. q . ℗¾
1 . (4>+8,48) . =,4;¾ Aw tltdc
1 45:,=4 I@a 1 >6=,7 + 45:,=466 1 72:,>4 I@a
Aw4 1 i . n . h¾ Ds4 1 τ . n .h
1 >,>:77 . 766 . 8:2,;¾ . 1 45>,2=> I@a 1 6,64; . 766 . 8:2,; 1 >4=7,2; aa¾,
46∞
pkrmisd hk`bd` ? Ds4 1
, . . . ., ., 1
1 >>;5,;7aa¾
Aw> 1 Aw - Aw4 1 72:,>4 ‗ 72:,>4 ‗ 45>,2=> 45>,2=> 1 >4;,84:I@a
w , . ∞ ,∞ 1;84,=>8 i@ . , 1
1
Ds> 1 Ds
1
1
1 74:2,2=
1 Ds4 + Ds> 1 >>;5,;7 + 74:2,2= 1 ;888,7> Xucd`bd` Xdrmi
Xucd`bd` Xdrmi Xdrmi ( Ds”) 1 ;888,7>
, hmbu`did` >H86 hd` 7H75
Ds” >H86 + Ds” 7H75 1 >;47,7 + 76;7,5 1 ;;55,= Odrdi d`tdr tucd`bd`
1
∞.∞. ∞.
.
1 56 (akak`ujm)
a . h 1 6,7::; . 8:2,;
1 4:=,7=8 aa
, , ∞ ∞ , H . ;84, = >8 ∞ ∞ .∞ ∞ , 1
>.`. Ds”
1
1 2,6:; Apd
1 >.:.2,6:; 1 447,75 AVd 3426 AVd (es mom`)
1
1 ;6==,>5Xucd`bd`Xkid`
1
Xucd`bd`Xkid` ( Ds”) 1 ;6==,>5
, hmbu`did` >H86 hd` 7H75.
Ds” >H86 + Ds” 7H75 1 >;47,7 + 76;7,5 1 ;;55,= Odrdi d`tdr tucd`bd`
1
∞.∞. ∞.
.
1 56 (akak`ujm)
WIKXWD VK^K@GD@DD@ VK@[CD@BD@ NKXL@
>H86
566 a >H75a 566
766 a
[`tui `l rkb.bd`omc
Jmtu`b alak` ck`tur yd`b hdpdt hmhuiu`b lckj ndcli yd`b nkrhmak`sm 766 aa Z 5;6 aa hk`bd` tucd`bd` tkid` > ndtd`b 46aa hd` tucd`bd` tdrmi 5 ndtd`b 7> aa. Autu ndjd` eg” 1 76 AVd hd` ndod autu 76. Hmiktdjum?
nxj
1 766 x 5;6 aa
Eg”
1 76 Apd
h”
1 =6aa n 766 aa
h”1;; aa
x
>H46 h1;;;,; aa
j15;6 aa
5H7>
Ak`k`tuid` esmzm` (tkbd`bd` tdrmi pdhd tucdbd`)
esmzm` (tkbd`bd` tdrmi pdhd tucd`bd`) 1 486 Apd
Xucd`bd` Autu 766 /7;6 486 AVd (Cmjdt W@M nktl` >66> jdcdad` >87)
1 6,8; 1 6,8;8; 7766 1 .
Ak`k`tuid`
Xkbd`bd` skrdt tkid` tkrcudr dimndt pk`bdruj prdtkbd`b, nknd` adtm hd` nknd` jmhup tktdp
1 6 ,8; e'g
Ak`k`tuid` `mcdm `
42 >6 >; 76 7; 86
` 46 = = : 2 5
XDNKC D-2 @mcdm ^dsml Alhucus Kcdstmsmtds
Ak`k`tuid` Ds
5878 5878 6
Xucd`bd`Xkid` (Ds”) 1 4;2,6 4;2,6 Xucd`bd`Xdrmi (Ds) 1 8:>;,;
Xkbd`bd` skrdt tkid` tkrcudr dimndt pk`bdruj prdtkb adtm hd`>H46 nknd` jmhup tktdp 1 6 ,8; e'g , nknd` ak`bbu`did`
,ak`bbu`did` ,ak`bbu`did` 5H7>
Ak`k`tuid` `mcdm h hd` h”
Wkcmaut nktl` 1 86 aa Hmdaktkr sk`bid`b 1 46 aa Hmdaktkr tucd`bd` tkid` 1 4> aa (sdtu cdpms) cd pms) Hmdaktkr tucd`bd` tdrmi 1 7> aa (hud cdpms) Odrdi d`tdr cdpms tucd`bd` tdrmi 1 >; aa
h 1 j - skcmaut nktl` - Ú sk`bid`b - Ú tucd`bd` tdrmi utdad - odrdi d`tdr h” 1 skcmaut nktl` nktl` + Ú tucd`bd` tucd`bd` tkid` + Ú tucd`bd` tkid` cdpms tucd`bd` tdrmi aa 1 15;6-8 5;86+46+;1;; 6-86-4 6-46-7 6-7>-4 >-4> > ; 1 ;;; ;;; ; aa Ak`k`tuid` odrdi bdrms `ktrdc
>4 ‾ 766 >. : 4 4 4;2 4;4;2 =8, ; 1: 8:>;,;;;;,; 4;6 >7;;4>=;>;1>4888;>>7:568 4;6 >7;;4>=;>;>4888;>>∗7:56816 4;6 4;6 86=;=>4;2868216 ∞,´,∞∞, (x-h”) (x-h”) 1 `(Ds) (h-x) (h-x)
(x-;;) 1 :(8:>;,;) (;;;,;-x)
x> +>27,65 x ‗ x ‗ 487:>5,=: 487:>5,=: 16
x1
x1>55,;8 aa
Nd`hm`bid` >`eg”4 tkrjdhdp es mzm`
>`eg”4 1 >(:)(47,;)
,, ∞,
1 47=,84: AVd 3 486 Apd
Hk`bd` hkamimd` pk`dapd`b trd`selradsm hdpdt hmtkrmad. Ak`k`tuid` alak` ck`tur hdcda hk`bd` gdrd ilpkc alak`
eg4”
1 47,;
,, ∞
1 46,2 Apd @H4
1 1
@H>
44⁈> ⁈>
nx(eg”4)
(766) (>55,;8) (46,2) (46-7) 1 8>2,2 i@
1 ` (Ds”) (es.mom`) 1 : (4;2) (486) (46-7) 1 42;,: i@
@X
1 Ds (es mom`) 1 (8:>;,;) (486) (46-7) 1 52;,;2 i@
Aw
1 @H4 (h -
4⁈7 4 ⁈7
x) + @H> (h ‗ (h ‗ h”)
1 8>2,2 (5;6 -
Y>55,;8Q) (46-7) + 42;,: (;;;,; ‗ (;;;,; ‗ ;;) ;;) (46-7)
1 >86,66; + :2,=
1 7>2,=6; i@a
Wudtu ndcli nkrtucd`b pkrskbm tkrcktdi pdhd sudtu pkrcktdid` skhkrjd`d hk`bd` nk`td`bd` 2,6 a, ak`huiu`b nknd` ikrod akrdtd yd`b tkrhmrm hdrm nknd` jmhup akrdtd >6 i@/a hd` nknd` adtm akrdtd >8,6 i@/a (suhdj tkradsui pkrimrdd` nkrdt sk`hmrm ndcli), ak`bbu`did` tucd`bd` ndod autu 866, eg” 1 >6 Apd hk`bd` ckndr ndcli 866 aa. Vmcmj nmcd`bd` nucdt u`tui j, sk`bid`b hdrm ndtd`b tucd`bd` H46. Vkrmisdcdj dpdidj ndcli tkrsknut guiup iudt ak`djd` nknd` hk`bd` gdrd akand`hm`bid` Au hk`bd` Ab. Nudt siktsd rd`gd`bd``yd. Hmi? c
RCC R HC ey
1 2,; a 1 >6 i@/a 1 >8,; i@/a” 1 866 Apd
Vk`ykcksdmd` ?
Nknd` [ctmamt (Ru)
R[ 1 4,> RHC + 4,5 R CC 1 4,> (>8,;) + 4,5 (>6) 1 >=,8 + 7> 1 54,8 i@/a > Alak` [ctmamt (Au) A[ 1 4/:.Ru.c>
1 4/:(54,8)(2,;) > 1 874,2> i@a Ak`bjmtu`b τ rdsml
g .4.566 1 1 6,:;e566 : ;566 1 6866,:;>66, 566866 16,6>452; ‾
adis
1 6,2; n 1 6,6457
eg” n h
4
1 >6 Apd 1 866 aa 1 :66 aa 1 6,:;
1
am`
, , 1
1 6,667;
1 6,4; n n 1 6,4; x 6,6>452;
1 6,667>;3 adis Adid yb hmpdidm
1 6,66=> (Xdnkc D-5)
. , 1
1
1 6,4:8
i 1 eg” .
( 4 - 6,;=
)
1 >6 x 6,4:8(4 - 6,;= . 6,4:8) 1 7,5: ( 6,:= ) 1 7,>: AVd
8. Ak`gdrm h pkrcu
∋ ∋ ∋ . . , , ., .,.
A^ 1 x n x h¾ x i A^ 1 A[
n1±h
A^ 1 x ± x
hpkrcu
x i
1
1
1 6,2872 a 1 287,2 aa n 1 ± h 1 ± (287,2) 1 724,:; aa adid, n 1 8;6aa hd` h 1 2;6aa
;. Ak`bjmtu`b ikandcm ? j
1 2;6+86+46+45 1 :45 aa ¹ :>6 aa
5. Ak`bjmtu`b Cuds Xucd`bd` ? Ds
1 nh 1 (6,66=>)(866)(2;6) 1 >256 aa> (Ds pkrcu)
2. Akamcmj Xucd`bd` ? Ds ;H>: 1 762:,2 aa> 0 Ds pkrcu 1 >256 aa>
:. Gki Ckndr Ndcli ?
Odrdirdi tucd`bd` d`bd` tkrpm tkrpmsdjdj 1 8;6 >.86 8>.46 ;.>: 1;>,;aa
n am` 1 (>.86) + (>.46) (>.46) + (;.>:) + (8.>:) 1 7;>aa 3 8;6aa 8;6aa (LI!)
0 H tkrpdsd`b (LI!)
=. D`dcmsd Vk`dapd`b @X
ey 1 Ds. ey 1 762:,2
@H
1
46∞ 46 x 866
1 4>74,8: i@
@X
eg” .d.8;6 6,:;. eg” .d.8;6 1 4>74,8: i@
8 : 1 6,:; .4>74, 456,,=2 >6 . 8;6.46∞ 1 456 1 :>68646±>: 12;5 1 4> 2;5 ,> 46∞ 1 4>74,8:
A^
1 :74,::7i@a
1 ú . A` 1 6,: . :74,::7 1 55;,;658 i@a
A^ (55;,;658 (55;,;658 i@a) 0 A [ (874,2> i@a)
(LI!)
WIKXWD ^D@GD@BD@
WKCMA[X NKXL@ 86 X[CD@BD@ WK@BID@B H46
;H>:
j 1 :>6 aa
n 1 8;6 aa
WLDC Wudtu ndcli nktl` hk`bd` nkrtucd`b hk`bd` Ds1 7H>;, Eg”1 76 AVd, tucd`bd` ndod autu 866. Xk`tuid` iudt alak` (A`) hd` il`trlc il`hmsm tucd`bd``yd dpdnmcd n1 766 aa. h1 756aa hd` ndod tucd`bd``yd 866 Hmikt ? Ds
1 7H>;
Eg”
1 76 AVd
Ey
1 866 AVd
n
1 766 aa
h
1 756 aa
Vk`ykcksdmd` ? Vk`ykcksdmd` ? Cd`bidj ‗ Cd`bidj ‗ cd`bidj cd`bidj skndbdm nkrmiut
ak`bjmtu`b rdsml pk`ucd`bd` ?
482>,5 16.6472 1 .. 1 766756
6, : ;. . 4 566 6, : ;. 7 6. 6 , : ; 566 4766; 1 1 566 1 1 566 866566866 866666 16.67>; 16.2;16.6>88 1 4.8 1 8664.8 16.667; ≨≨ 6.667;≨6.67>;≨6.6>88 ↞ . . 1 .. . 125.=== 1756 . 17>4.; 46∞ ∋. 1 6.: − 4:=.7: 1 4;4.;
Nd`hm`bid` tkrjdhdp
hd`
46.
Ak`bmtu`b tm`bbm ndcli tkbd`bd` (d) ?
44.
Ak`bmtu`b Vd`od`b Vd`od`b ck`bd` alak` hdcda (z) ?
4>.
Jmtu`b alak` mhkdc hd` alak` tdjd`d` (alak` hdcda)?
d1
_1
A`
1 @X._
A^
1
1 Ds.Ey._
1 482>.5(866)(7>4.;)
1 4:=.7: i@a
[`tui akanuitmid` tucd`bd` ndod tkcdj cucuj dtdu nkcua hmnuitmid` skndbdm nkrmiut ? d 1 6,:; . g 25,=== 1 6,:; . g g 1 =6,;= aa
0 ∞ 1 ( 1
) 6,667
∞, ,
(6,667)
1 6,66:=> aa/aa 1
1
1 6,66> aa/aa
0
Hk`bd` pkanuitmd` hmdtds, hdpdt hmiktdjum ndjwd ndod tucd`bd` tkcdj cucuj idrk`d .
[`tui sudtu ndcli nkrtucd`b pkrskbm hk`bd` h k`bd` ckndr n 1 766 aa ak`huiu`b alak` nknd` bu`d yd`b tkrhmrm hdrm nknd` jmhup A CC1 =;,;
[email protected]` nknds adtm A HC1 ;8,; i@a, eg” 1 >: Apd, ey 1 7;6 Apd, tk`tuid` t k`tuid` uiurd` pk`dapd`b hd` pk`ucd`bd``yd, pkrmisd pucd tkbd`bd`tkbd`bd``yd hd` bdandr siktsd. Hmiktdjum? n 1 766 aa
eg” 1 >: Apd
ey 1 7;6 Apd
ACC1 =;,; i@a
AHC1 ;8,; i@a Odwdn? 4. Vkrimrdid` hmak`sm ndcli. n 1 ± h, adid h 1 >n h 1 > x 766 1 566 aa. h 1 j ‗ j ‗ 466, 466, adid j 1 h + 466 j 1 566 + 466 1 266 aa. >. Ak`bjmtu`b alak` rk`gd`d. Au 1 4,5 A CC + 4,> AHC Au 1 4,5 (=;,;) + 4,> (;8,;) 1 >4:,> i@a. 7. Xkrcknmj hdjucu hkpkrjmtu`bid` dpdidj akau`bim`id` o mid ak`bbu`did` tucd`bd` tu`bbdc.
‾.ξ4.566 6,:;.>:.6,:;.566 6, : ;. e g 1 1 566 566 1 7;65667;6 16,675; 16,2 ;16, 2 ;. 6 , 6 75;1 1. ‾ 16,6>28. 7;6>: 16,78>; 6,6>28
I adis adis 1 eg”. (4-6,;=.
)
1 >: . 6,78>; (4 ‗ 6,;= 6,;= . 6,78>;) 1 2,5;>4 AVd A^ adis 1 n h> i 1 6,: . 766 . 566 > . 2,5;> . 46 -5 1 554,48 554,48 i@a. i@a.
A^ adis 0 A[, adid hmpkrcuid` tucd`bd` tu`bbdc.(tdrmi sdod) 8. Vkrimrdd` rdtml pk`ucd`bd`
1 6,2; . 1 6,2; . 6,675; 1 6,6>28
1 4,8 1 7;64,8 16,668 1 6,4; . 1 6,4; . 6,675; 1 6,66;; 3316,66836,66;;36,6>28
(LI)
;. Gdrm h pkrcu A^ 1 1 Au
1 ∋.6,;. 1 6,:6,6,;52,545;>4 16,;==≊566 1 1 .. . . 1 6,66;; .766 . 766 .566 . 56611 ==6¾ 1 1 766.==6566 16,66;; 316,66;;36,6>28 1 6, :; ... 1 6,====6:;6.>:. >:.7;. 7;6 6766 18:,;7 1 >1566 8:,>;7 1;2;,27;
5. Jmtu`b cuds tucd`bd` yd`b hmpkrcuid`.
Idrk`d
adid tucd`bd` ndod tdrmi suhdj akcucuj.
2. Vmcmj tucd`bd`.
Danmc ;H45 1 466;,7 aa 0 Ds pkrcu. ( LI) :. Gki ckndr ndcli. n am` 1 (>.86) + (>.46) (>.46) + (=.45) 1 >88 aa 3 766 766 aa LI . Odrdi tucd`bd` tkrpdsd`b 1 hmdaktkr tucd`bd` LI =. D`dcmsms pk`dapd`b. @X 1 Ds. ey 1 ==6 x 7;6 7;6 1 785;66 i@ @H 1 @X 6,:; eg”dn 1 785;66 785;66
1 785;66
46. Wiktsd ^d`gd`bd` n 1 766 aa
Wkcmaut 86
Wk`bid`b H46 j 1 266 aa
Ndcli hk`bd` n 1 766 aa, j 1 566 aa, h ”1 5; aa, Ds 1 5H7> (> cdpms), D s” 1 >H7>, pd`od`b nk`td`b tuapud` skhkrjd`d 46,; a. Wudtu nknd` akrdtd (hm cudr nkrdt sk`hmrm) nkikrod hmdtds`yd tkrhmrm hdrm nknd` adtm hd` nknd` jmhup, eg” eg” 176 Apd, ey 1 866 Apd. D. Xk`tuid` nksdr`yd alak` yd`b tkrodhm pdhd ndcli tkrsknut N. Vkrnd`hm`bd` Ar hdrm ndcli tkrsknut hk`bd` alak` adismaua ndcli tkrsknut. Hmiktdjum ?
n
1 766 aa
C 1 46,; a
j
1 566 aa
Eg” Eg” 1 76 Apd
”
h
1 5; aa
Ds 1 5H7> (> cdpms) 1 8:>;,;
ey 1 866 Apd
16,:;
Ds” Ds” 1 >H7> 1 456:,5 Vk`ykcksdmd` ?
Nksdr nknd` ikrod yd`b hdpdt hmhuiu`b lckj ndcli
Ak`k`tuid` cktdi bdrms `ktrdc Hmd`bbdp tucd`bd` ndod tkid` hd` tdrmi suhdj cucuj Ds>1 Ds” Ds 1 Ds4 + Ds> Ds41 Ds ‗ Ds ‗ Ds” 1 8:>;,; - 456:,5 1 7>45,=
4 . 7>45, = . 866 4>:5256 1 >‾ 1 1 1 45:,,>68 6,:; .. . 6,:; .. . 6,:; . 76 . 766 25;6 1 45:
1 1 ,, 14=2,::2 1 ∞ . 6,667 1 ,,∞ .6,66716,66>64
Ak`bl`trlc tkbd`bd` yd`b tkrodhm pdhd sddt alak` uctmamt
1 1 ∞ .6,6671 ∞, , .6.66716,6685
16,66> 1 1 1 0
Xucd`bd` ndod tkid` adupu` tdrmi tkcdj ak`gdpdm cucuj tkrcknmj hdjucu sknkcua nktl` tkid` ak`gdpdm rkbd`bd` 6,667
Xkrnuitm skaud tucd`bd` suhdj cucuj.
Ak`k`tuid` `mcdm hdrm adsm`b-adsm`b ilpkc alak` A`4 1 Ds4.ey (h-4/>d) 17>45,=.866 (;66 ‗ (;66 ‗ 4/> 4/> . 45:,>68).46 -5 1 ;7;,45 i@a A`> 1 Ds”.ey.(hDs”.ey.(h -h”) 1 456:,5.866.(;66-5;).46 456:,5.866.(;66-5;).46 -5 1 >2=,:= i@a A` 1 A`4 + A`> 1 ;7;,45 i@a + >2=,:= i@a 1 :4;,6; i@a
Ak`bjmtu`b A ^ A^ 1 6,:. A` A^ 1 6,:. :4;,6; 1 5;>,68 i@a
Ak`k`tuid` nkrdt sk`hmrm struitur n1 766 aa
hd`
j1 566 aa
Nkrdt sk`hmrm struitur 1 n . j . no 1 6,5 . 6,7 .>7 1 8,48 i@/a” Alak` dimndt nkrdt sk`hmrm Aadtm sk`hmrm 1 4/: . w. C > 1 4/: . (4,>x8,48) . 46,;> 1 5:,82 i@a
Ak`bjmtu`b Alak` A ^ hmcudr hmcudr nkrdt sk`hmrm A^ ‗ ‗ A Aadtmsk`hmrm 1 5;>,68 ‗ 5;>,68 ‗ 5:,82 5:,82 1 ;:7,;2 i@a
Ak`bjmtu`b nknd` ikrod tkreditlr tltdc yd`b hmhuiu`b hmhuiu`b lckj struitur struitur (hmcudr nkrdt sk`hmrm)
1 4: . . 1 : 1 : 46,;:7,;;2 1 8>,7;7; / /
Vkrnd`hm`bd` Ar hdrm ndcli tkrsknut hk`bd` alak` adismaua ndcli tkrsknut. tkrsknut.
Ak`k`tuid` Ds adis Ds adis 1 6,2;. Dsn Dsn 1
.n.h
‾.ξ4.566 6,:;.76.6,:;.566 6, : ;. e g 1 1 566 566 1 866566866 16,67>;
1 1 .. . . 1 6,67>;.766.;66 1 1 6,2; . . 11 6,2;.8:2;1 :2; 1 , , >
>
Ak`k`tuid` cktdi bdrms `ktrdc hd` pkakrmisdd` hmdbrda tk bd`bd` hd` rkbd`bd` D`bbdp skaud tkbd`bd` suhdj cucuj
( ∞ . 1 ..). 1 .... 1 ,.∞, .. 1 44445,5,: 1 1 ,. 1472,87 1 ∞ .6,6676711 ,,∞ .6.66716,664;: 1 1 ∞ .6,6676711 ∞, , .6.66716,662= 16,66> 1 1 1, 3 1, Idrk`d
adid tkradsui il`hmsm MM MM
Ak`k`tuid` cktdi bdrms `ktrdc pdhd il`hmsm MM
(6,:; . eg”.n.
) g> + (566.Ds”(566.Ds”- Ds . ey) g ‗ g ‗ 566.h”.Ds” 566.h”.Ds” 1 6
(6,:;.76.766.6,:;) (6,:;.76.766.6,:;) g > + (566.456:,5 - 7:8>,24.866) g ‗ 566.5;.456:,5 566.5;.456:,5 1 6 5;6>,;g> ‗ ;24=>8g ‗ ;24=>8g ‗ 5>27;866 5>27;866 1 6 G> ‗ ::g ::g 1 =582,:: (g-88)> 1 =582,:: - 88 > G1
2244,:: ∟ 2244,
+ 88
G 1 474,:42 aa
∞” .566 1 768,47; 3 866 1 . 1 6,:; . 474,:42 1 ,
Ak`k`tuid` es” hd`
Es” 1
Ak`k`tuid` bdyd tkid` @H4 1 6,:; eg” . n . d
@H4 1 6,:; . 76 76 . 766 . 44>,688 44>,688 . 46 -7 1 :;2,4755 i@
@H> 1 Ds”.Es” 1 456:,5 . 768,47; 768,47; . 46 -7 1 8:=,>7 i@
Vkrmisd @X
1 @H4 + @H> 1 :;2,4755 i@ + 8:=,>7 i@ 1 4785,72 i@
@X
1 Ds . Ey 1 47;4 i@
Ak`k`tuid` A^ A`4
1 @H4 (h-4/>d) 1 :;2,4755 (;66 -;5,6>>).46 -7 1 7:6,;; i@a
A`>
1 @H> (h-h”) (h-h”) 1 8:=,>7 (;66-5;).46-7 1 >4>,:4; i@a
A`
1 A`4 + A`> 1 ;=7,75; i@a
A^ 1 1 6,:. ;=7,75; i@a 1 825,5=> i@a A^ Dsadis 1 825,5=> i@a 3 A^ dwdc dwdc 1 5;>,68 i@a
Vkakrmisdd` hditmcmtds DW4
1 Ds ‗ Ds ‗ Ds”.es”/ey Ds”.es”/ey 1 >54=,574 aa>
V ditudc ditudc 1 >54=,574 aa>/766.;66 1 6,642858 V am` 1 6,667; 3 6,6427:5: (LI)
Ndcli X hm dtds nk`td`b skhkrjd`d 5,4; a, odrdi d`tdr ‗ ndcli ndcli (p.i.p) >,;6 a. Dpdnmcd eg ”1 >6 AVdey1 866 AVd, Jmtu`b idpdsmtds alak` A ^ .> .>
466 Xucd`bd` Wk`bid`b H46
86
h 1 566
Ds 1 2H 75
nw 1 766 Hmiktdjum ?
C
1 5,4; a
ey
1 866 AVd
h
1 566 aa
p.i.p
1 >,;6 a
j e
1 466 aa
h”
1 86 aa
eg”
1 >6 AVd
DW
1 2H75 1 24>;,4 aa >
Hmtd`yd
? Idpdsmtds alak` A<
Odwdnd`
?
1 766 aa
1 4⁈8 Ò 54;6 1 , 45℀ 1766 1766 45Ò466 45Ò466 1 1 Ò 1 24>;,4 Ò 866 1 , 1(6, : ;Ò ) Ò ℀ 16,:;Ò>6Ò4;72,; Ò4661, 3 >:;6,68 >547,2;;11 , Odrdi d`tdr ndcli 1 >;66 aa
‾
Wkcmsmj bdyd 1
X aur`m
>75, > = 1 6, ℀ 1 :;Ò 6,:;Ò>6Ò766 4661, 1 4, 8 1 8664,8 1, 24>;,4 1,06,667; 1 Ò 1 766Ò566 , ‾
^dsml pk`ucd`bd`
466
d 1 44=,55
766
14;72,;Ò4661 1766Ò466,6851,4 : (466 ⁈ . 4 6 6 , 6 8 5 ) > 1 4;72;676647, 1 , 4;72;676647, : 1 1 566 >;,78 1 ,6, ;46Òh adx16,67=4Òj nn nnw j 4 adx16,67=4Ò4664;72,;7666,;46Ò566 4 466 10,
Bdandr Wikstd
466
566
55:
Wmstka cd`tdm nktl` nkrtucd`b hdrm pcdt tkndc 466 aa hmhuiu`b lckj ndcli nk`td`b ak`krus akank`tui ndcli X, pd`od`b nk`td`b :,4;a, odrdi d`tdr ndcli X (p.i.p) 4:66 aa. Hmak`sm ndhd` ndcli hmtk`tuid` nkrhdsdrid` pdhd alak` `kbdtme hd` pkrsydrdtd` bdyd bkskr pdhd huiu`bd`,
1 8;6aa, j 1 566aa, pmcmj tucd`bd` ndod yd`b hmpkrcuid` pdhd
tk`bdj nk`td`b u`tui ak`huiu`b alak` rk`gd`d plsmtme tltdc Au 1 2:6 i@a (tkradsui nkrdt sk`hmrm), Eg”1>6 Apd, ey 1 866 Apd. Hmiktdjum ?
℀ 11:,464664;6 1 :4:4;6;6 1 2:6
Alak` rk`gd`d tltdc
. .18;8;6164:66 ℀ 1 566
(hmiktdjum)
Ak`ktdpid` tm`bbm kekitme ndcli
h 1 j ‗ j ‗ 26aa 26aa 1 566 ‗ 566 ‗ 26 26 1 ;76 aa
4⁈8 Ò :4;6 11 , 1 45℀ 18;6 45Ò466 1 1 4:66 4
Ak`ktdpid` ckndr eck`s kekitme ndcli
Odrdi d`tdr ndcli 1
Bu`did` ckndr eck`s kekitme,
Ak`k`tuid`
1 ∋ 6,:;..℀. > ℀ 16,: 6,:;>6 ;>64:66 4:66466466 ;76 4> 46646∞
1 44442;,2;,6868 0↞
11>62: 6 1 868666
2:6 ∝ 4 6 1 ∋ 1 6,:∝4:66∝;76 1 4,=>:
1 ∝ 46,;= = 4,=>: 1>6 1>646,;= = 4,=>:1>644, : 44,: >64, = >:16
´∟ , 1 > 8 >6 >6 ´ >6 >6 8∝44, : ∝4, = >: 1 >∝44, : ; : 1 >6´42, >7, 5 ; : 1 >642, 16,467 >7, 5 1 ‾ 6,4671 866>6 1 6,66;4; 1∝∝16, 6 6;4;∝4:66 ∝;7618=47, 4 : >: 18=>5, 6 1 8;8;66 15668646 4> >: 1 ;7;755 4,8 4,8 1 1 866 16,667; 1 ∝ 1 8;6∝8=>5;76 16,6> 0 16,674= (℀) 6,;℀46∝ 4 16,674=∝ 466 {4:668;66,;46∝466;764} 17, 4 =∝ =∝ 4:664>4;, 7 ; ; 1=54:, = 5 ~ =54= 0 ↞ =5=54=4= 08=>5 Cuds tucd`bd` ndod tdrmi
Bu`did` tucd`bd`
466
Vkrmisd
Vkrmisd
hd`
Xucd`bd` Wk`bid`b H46
86
h 1 ;76
Ds 1 :H>:
nw 1 8;6
