149 (Tarea 1)
September 14, 2022 | Author: Anonymous | Category: N/A
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XNRCN >= CO KI@KCZXI HC D@XCGRNO
Xnrcn >= Co ki`kcpti hc D`tcgrno
Zrcsc`tnhi pir= Mndlc Tcsdh Ln`rdquc Gnrkìn ‛ Kûhdgi= 4>3;>>>> Hcysy Mifn``n Bcotrî` Lnrì` ‛ Kûhdgi= >:442:3248 Znion N`hrcn Znbi` Qconski ‛ Kûhdgi= >:436;>678 Zchri Codckcr Lurdooi Nan`nhir - Kûhdgi= >>::47;::1
Grupi= >::8>>Y>84 Xutir= Ouds Rnlû` Auc`tcs
Kîokuoi D`tcgrno ‛ (>::8>>NY438) S`dvcrsdhnh @nkdi`no Nbdcrtn y n Hdstn`kdn ‛ S@NH, KCNH Buknrnln`gn Zrigrnln Nhld`dstrnkdû` hc Clprcsns Iktubrc hc 2:2>
XNRCN >= CO KI@KCZXI HC D@XCGRNO
D`trihukkdû`
C` co prcsc`tc trnbnmi sc cvdhc`kdnrî co hcsnrriooi hc on u`dhnh > on kuno nbirhn on tclîtdkn hc Ki`kcpti hc D`tcgrno, nbirhn`hi ois ki`tc`dhis= on D`tcgrno D`hcad`dhn, [ulns hc Rdcln``, Xcirclns hhcc D`tcgrnkdû` c D`tcgrno Hcad`dhn, n trnväs hc oonn rcnodznkdû` rcnodznkdû` hc ois cmcr cmcrkd kdkd kdis is po pon` n`ttcn cnhi hiss pn pnrn rn knhn knhn tc tcln ln hcsnrr hcsnrrio ioon on`hi `hi c` ti titn tnoo 8 cm cmcrk crkdk dkdi diss scockkdi`nhis hc ons ipkdi`cs pon`tcnhns c` on guìn hc nktdvdhnhcs y c` on rýbrdkn hc cvnounkdû`, y prcsc`tn`hi vdhci hc sustc`tnkdû` hc nogu`is hc coois.
XNRCN >= CO KI@KCZXI HC D@XCGRNO @ilbrc hco cstuhdn`tc
Rio n hcsnrrioonr
Zchri Codckcr Lurdooi Nan`nhir Muodî` N`ti`di Qdn`n ]nrntc Hcysy Mifn`n Bcotrî` Lnrì`
Rcvdsir Nocrtns C`trcgns
Mndlc Tcsdh Ln`rdquc Gnrkìn Znion N`hrcn Znbi` Qconski
Cvnounhir Kilpdonhir
Grupi hc cmcrkdkdis n hcsnrrioonr Cmcrkdkdis N
Cmcrkdkdis C Cmcrkdkdis K Cmcrkdkdis B Cmcrkdkdis H
Hcsnrriooi hc ois cmcrkdkdis n, b, k, h y c hco hc o Xdpi hc cmcrkdkdis >= D`tcgrnocs D`lchdntns
Hcsnrrioonr Hcsnrrio onr co cmc cmcrkd rkdkdi kdi scockkd scockkdi`n i`nhi hi utdodz utdodzn`hi n`hi co îogcbrn îogcbrn,, on trd trdgi`i gi`ilct lctrìn rìn y pripdch pripdchnhc nhcss lntclîtdkns pnrn rchukdr ons au`kdi`cs n d`tcgrnocs d`lchdntns. Rckucrhc quc `i hcbc fnkcr usi hc ois lätihis hc d`tcgrnkdû` (sustdtukdû`, d`tcgrnkdû` pir pnrtcs, ctk.), y kilprucbc su rcspucstn hcrdvn`hi co rcsuotnhi. Cmcrkdkdi n.
( x 2− 8 ) ∥ hx ( x −2 ) ¹ ∥ ( x + 2 ) hx ¹ ∥ x hx+ 2∥ > hx
YYYYYYYYYYYYYYYYYYYYYYYYYY +>
x ` ¹ ∥ x hx < ` + > ki`` `
¹
x 2 2
YYYYYYYYYYYYYYYYYYYYYYYYYYYYYY
¹ ∥ > hx = CO KI@KCZXI HC D@XCGRNO ¹ ∥ x hx + 2∥ > hx x
2
¹ + 2 x 2
YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY
∥ ( x x +2 ) hx ¹ ∥ ( x
2
¹ + 2 x + K 2
XNRCN >= CO KI@KCZXI HC D@XCGRNO 2
h x ( + 2 x + k ) hx 2
2
¹ h ( x )+ h ( 2 x )+ h (k ) hx 2 hx hx
( )
h x2 / 2 x 2
∥
) hx +∥(
3/ 2
1 x −> −> /2 .x .x . hx 2
3
1 2 − > −> / 2 x 2
) . hx ( ) ; 2
¹ ∥ x > /2 hx +∥ ; x . hx
[c prikchc n rcnodznr on d`tcgrno
¹
; 2
∥ x / hx +;∥ x . hx > 2
XNRCN >= CO KI@KCZXI HC D@XCGRNO > +> 2
; x ; x + ; ¹ 2 2 ; /2
( ) ;
; 2 ¹ . x 2 2 ;
2
; x + 2
2
; 2
2 x + x ¹ x . ∝ x
; 2
¹ ∝ xx; + x 2 RXN
Cmcrkdkdi h.
XNRCN >= CO KI@KCZXI HC D@XCGRNO
(
)
∥ x x + x >∝ x ;
hx
[ioukdû`
∥ x + x >∝ x
(
(
)
;
∥ x + x ( x>) / ;
> 2
(
∥ x + x >/ ;
; 2
;
∥
)
hx
)
hx
hx
−; / 2
) hx
( x + x
[c hcrdvn= −> 8
x x 2 → + +k 8 −> 2
−> 8 x → +2 x 2 + k
8 8 x → − 2 +k 8 ∝ x x
Hcsnrriooi hc ois cmcrkdkdis n, b, k, h y c hco Xdpi hc cmcrkdkdis 2= [ulns hc Rdcln``
XNRCN >= CO KI@KCZXI HC D@XCGRNO Hcsnrrioonr co cmcrkdkdi scockkdi`nhi utdodzn`hi ons [ulns hc Rdcln``= Cmcrkdkdi n. 8
-
x
2
( ¹ + D`x ) hx ¹, lchdn`tc on suln hc
Npr prix ixdl dlc c on d`t d`tc cgr grno no hc hcad ad`d `dhn hn
2 ∥ Rdcln`` hco pu`ti hcrckfi, ki` `;2) 23
------------------------------------------------
8
x
2
∥ (¹ 2 + D`x ) hx ,` 8 ¹ 2
¹
1:2 ∅+ 437 46
XNRCN >= CO KI@KCZXI HC D@XCGRNO
Cmcrkdkdi b.
XNRCN >= CO KI@KCZXI HC D@XCGRNO
Nprixdlcc on d`tcgrn Nprixdl d`tcgrnoo hcad hcad`dh `dhnn pu`ti dzqudcrhi, ki` ` < 1.
, lch lchdn` dn`tc tc on suln suln hc Rdcln` Rdcln``` hco
3
2 x ∥ ∝ x + + 2 2
8
[c utdodzn on sdgudc`tc aûrluon pnrn fnoonr on bnsc hc ois rcktî`guois=
Θ x < b −n ` Xc`clis quc= n < 2 → oìldtc d`acrdir b < 3 → oìldtc supcrdir ` < 1 → # hc rcktî`guois
Θ x <
3 −2 ; < : x 8 : + > < >: + > < >> ; ; ; ;
[c rcclponzn c` on au`kdû` ois vnoircs fnoonhis n`tcrdirlc`tc a (( x x )>
Znrn x ;: a ;
<
>: ;
2
−;
>: ;
Znrn x 3<
( ) ( ) ( )
a
>> ;
<
>> ;
2
−;
>> ;
26 4
+ 2 < >>> >> ; 8: 4
+ 2< >>>
[c suln` ois rcsuotnhis n`tcrdircs scgý` on sdgudc`tc airluon= 8
Îrcn nprixdlnhn= ∞ a ( ( d ) ∁ x d: 4
26 4
¹ : + + + 2+ +
)
8: > . 4 ;
XNRCN >= CO KI@KCZXI HC D@XCGRNO ;8 4
¹ u 2 Zir scr îrcn ons u`dhnhcs sc cxprcsn` u2 ¹ ;.777 u2
Cmcrkdkdi h. 3
∥ 2∝ x x x hx 2
[ioukdû`
Hnhi quc b −n ∁ x< `
XNRCN >= CO KI@KCZXI HC D@XCGRNO n < 2 , b< 3 , ` < 3
∁ x<
3 −2 ; < 3 3
∁ x< ;3 Oucgi
x :; 3
a (( x x > )< 2
∝
>; 3
x 2< >1 a ( ( x x2 ) < 6
∝ 3
3
>4
x ; ) 2
2
; /2
→
2 x ;
3 2
2
(( ) )| ; /2
→
8 x ;
;/ 2
8 (3 ) ;
−
|
3 2
8 ( 2) ;
; 2
>.>;
Grnadkn c` GciGcbrn on suln hc Rdcln`` pnrn `= CO KI@KCZXI HC D@XCGRNO
¹^uä sc puchc ki`koudr no nulc`tnr co `ýlcri hc rcktî`guois9 [c ki`kouyc quc n lchdhn quc nulc`tn` ois rcktî`guois, co îrcn vnoir hco îrcn nulc`tn, cs hckdr si` hdrcktnlc`tc pripirkdi`nocs.
Hcsnrriooi hc ois cmcrkdkdis n, b, k, h y c hco Xdpi hc cmcrkdkdis ;= Xcirclns hc D`tcgrnkdû`
Hcsnrrioonr ois cmcrkd Hcsnrrioonr cmcrkdkdis kdis scockk scockkdi`nhi di`nhiss hcrdvn`hi hcrdvn`hi G′() hc ons sdgudc`tcs au`kdi`cs. Npodknr co sdgudc`tc Xcircln hc d`tcgrnkdû` c` knhn cmcrkdkdi=
Cmcrkdkdi n.
XNRCN >= CO KI@KCZXI HC D@XCGRNO h ¹ hx
;
a ( ( x x )<
2
∥
>
x + x
2
t + >
ht
b ( x x ) 2
)
∥ a ( ( t ) ht
) ( ( ; )−
)
x −2 ( >) x + 8 x + 8 + > 2
Luotdpodkn`hi=
(
A ' ( x x )<
4 x + >6 4 x
2
2
+;1 x + ;7
)( −
x −2 2 x +8 x + 3
)
XNRCN >= CO KI@KCZXI HC D@XCGRNO
Cmcrkdkdi k.
Xcircln hc D`tcgrnkdû`
U
h h a ( x ) \ < U hx hx
b ( x x ) ht 2
tn`x
) (
)
x tn`x ( sck 2 x ) 2 x − ( ) 2 2 2 ( x ) + > (tn`x ) + >
2 x
;
2
sck xtn`x
A ( x x )< 8 − 2 x + > tn` x + > '
Hcsnrriooi hc ois cmcrkdkdis n, b, k, h y c hco Xdpi hc cmcrkdkdis 8= D`tcgrno Hcad`dhn
Hcsnrrioonr co cmcrkdkdi quc fn cocgdhi pir lchdi hco scgu`hi tcircln au`hnlc`tno hco kîokuoi, utdodzn`hi co îogcbrn, on trdgi`ilctrìn y pripdchnhcs lntclîtdkns pnrn rchukdr ons au`kdi`cs n d`tcgrnocs d`lchdntns, rckucrhc quc `i hcbc fnkcr usi hc ois lätihis hc d`tcgrnkdû` (sustdtukdû`, d`tcgrnkdû` pir pnrtcs, ctk.)
XNRCN >= CO KI@KCZXI HC D@XCGRNO
Cmcrkdkdi n.
2
∥ ( x x −2 x + ; ) hx ;
−2
2
2
2
−2
−2
¹ ∥ x hx −∥ 2 x hx +∥ ; hx ;
−2
2
¹ ∥ x ; hx 2 ¹ >2
XNRCN >= CO KI@KCZXI HC D@XCGRNO
Cmcrkdkdi b.
Knokuonr on sdgudc`tc d`tcgrno hcad`dhn=
XNRCN >= CO KI@KCZXI HC D@XCGRNO
Hcspuäs hc knokuonr on d`tcgrno rcnodznr ois sdgudc`tcs pnsis= 2
( x x −4 ) 2
∥ ( x −; ) hx −2
Znrn rchukdr cstn d`tcgrno hcad`dhn n u`n d`tcgrno d`lchdntn sc npodkn on hdacrc`kdn hc kunhrnhis pcracktis= 2
∥ ( x x +( x; −) ( x;−) ; ) hx −2
[dlpodadkn`hi= 2
∥ ( x +; ) hx −2
Znrn knokuonr co scgu`hi tcircln au`hnlc`tno hco kîokuoi, sc npodkn on rcgon hc on pitc`kdn= [cgu`hi tcircln au`hnlc`tno hco kîokuoi= b
∥ a ( ( x x ) hx
x ` ∥ x hx < ` + > + K `
XNRCN >= CO KI@KCZXI HC D@XCGRNO Hcsnrrioon`hi= 2
2 x ∥ ( x x +; ) hx < + ; x +K ¹−2 2
2
−2
Npodkn`hi= A(b) ‛ A (n), tc`clis= 2
2
2 2 + ; ( 2 )− + ; (−2 )
8
8
8 2
6 x xhx hx +
x . hx − ; 8
x
∥
;
U(
∥
∥
∥
;
>
8 > − ; ;
(
−6 x 2 2
8
8
>
>
∥ +>1 x ∥ .
)−( ( ) − ( ) + 8 8
18 > − ; ;
>1 hx
>
>
>
2
) −(
8 >
>1 ( 8 −> )
18 −8 ) + 86
18 − > −1: + 86 ; 1; −1: + 86 > 2>− 1:+ 86
< 14-1: = CO KI@KCZXI HC D@XCGRNO
XNRCN >= CO KI@KCZXI HC D@XCGRNO
Cmcrkdkdi h. ϊ / /2 2
∥ ( kis x + sc`x ) hx :
[ioukdû` ϊ / /2
∥ ( kis x + sc`x ) hx 2
:
Rccskrdbdlis
kis x < > + kis ( 2 x ) 2 2
C`ti`kcs tc`clis ϊ / /2
∥ :
(
)
> + kis ( 2 x ) 2
+ sc`x hx
[nknlis on ki`stn`tc hc on d`tcgrno > 2
ϊ / 2
∥ ( > +kis (2 x )+ sc`x ) hx
→
→
:
U( > 2
U
\|
)
> x x + sc` ( 2 x ) − kisx ϊ / 2 2
> > 2 x + 8 sc` ( 2 x )− kisx
\|
:
/2 ϊ :
XNRCN >= CO KI@KCZXI HC D@XCGRNO
()
> ϊ 2 2
> 8
+ sc`
( ) ()( 2
ϊ 2
−kis
ϊ 2
−
ϊ 8
+ : + :−( : + : −>)
ϊ 2
∥ ( kis x + sc`x ) hx ≆ >.74 ¹ 2
:
)
> > ( : )+ sc` ( 2 ( : ) ) −kis ( : ) 2 8
XNRCN >= CO KI@KCZXI HC D@XCGRNO
Xnbon Od`es hc Qdhcis
Xnbon Od`es hc vdhcis cxpodkntdvis
@ilbrc Cstuhdn`tc=
Cmcrkdkdis sustc`tnhis=
Zchri Codckcr
Cmcrkdkdis n ‛
Lurdooi
Xdpi hc
Nan`nhir Mndlc Tcsdh
cmcrkdkdi 8 Cmcrkdkdis b ‛
Ln`rdquc
Xdpi hc
Gnrkìn
cmcrkdkdi ; Cmcrkdkdi K ‛
Hcysy Mifn`n Bcotrn` Lnrd`
Xdpi hc cmcrkdkdi 8
Od`e vdhci cxpodkntdvi=
fttps=//www.yiutubc.kil/wntkf9v:). D`trihukkdû` no kîokuoi hdacrc`kdno. Chdtirdno D`stdtuti Ziodtäk`dki @nkdi`no. (pp. >22->26). Rckupcrnhi `ct.bdboditcknvdrtuno.u`nh.chu.ki/cs/crcnhcr/u`nh/7211>9pngc
hc=
fttps=//codbri-
Irtdz, A (2:>3). Kîokuo Irtdz, Kîokuoii hdacrc hdacrc`kdno `kdno (2n. ch.). Grupi chdtird chdtirdno no pntrdn. (pp. >;2->;4). >;2->;4). Rckupcrnhi Rckupcrnhi hc= fttps=//codbri-`ct.bdboditcknvdrtuno.u`nh.chu.ki/cs/crcnhcr/u`nh/>2>2769pngc
Irtdz, A., & Irtdz, A. (2:>3). Kîokuoi D`tcgrno. Grupi chdtirdno pntrdn. (pp. ;1-82). Rckupcrnhi hc= fttps=//codbri-`ct.bdboditcknvdrtuno.u`nh.chu.ki/cs/crcnhcr/u`nh/;48149pngc
Rdvcrn, A. (2:>8). Knokuoi d`tcgrno= sukcsdi`cs y scrdcs hc au`kdi`cs. Läxdki= Onriussc ‛ Grupi Chdtirdno Zntrdn. (pp. 27 ‛ ;6). Rckupcrnhi hc= fttps=//codbri`ct.bdboditcknvdrtuno.u`nh.chu.ki/cs/crcnhcr/u`nh/;48;>9pngc
Gucrrcri, G. (2:>8). Kîokuoi D`tcgrno= [crdc S`dvcrsdtnrdn Zntrdn. Läxdki= Grupi Chdtirdno Zntrdn. (pp. >8 >1). Rckupcrnhi hc= fttps=//codbri`ct.bdboditcknvdrtuno.u`nh.chu.ki/cs/crcnhcr/u`nh/;48;29pngc
[pdvne, L. (2:>6). Knokuous (;ª. ch.). Bnrkcoi`n= Chdtirdno Rcvcrtä. (pp. 244 - ;:;). Rckupcrnhi hc= fttps=//codbri-`ct.bdboditcknvdrtuno.u`nh.chu.ki/cs/crcnhcr/u`nh/816:89pngc
[cgurn, [cgur n, N. (2: (2:>8) >8).. Ln Lntc tclî lîtd tdkn knss Npod Npodkn knhn hnss n on onss Kd Kdc` c`kd kdns ns Ck Cki` i`ûl ûldk dki-N i-Nhl hld` d`ds dstr trnt ntdv dvns= ns= [dlpodkdhnh Lntclîtdkn. Grupi Chdtirdno Zntrdn. (pp. 2:> ‛ 2:;). Rckupcrnhi hc= fttps=//codbri`ct.bdboditcknvdrtuno.u`nh.chu.ki/cs/crcnhcr/u`nh/;4;649pngc Rihrìg rìgucz, F. (2:2 :2::). IQD D` D`ttcg cgrrnocs D` D`l lchdntns. fttps=//rcpisdtiry.u`nh.chu.ki/fn`hoc/>:341/;;3;6
UQdhci\.
Rckup upccrnhi
hc=
XNRCN >= CO KI@KCZXI HC D@XCGRNO Ribnyi, A. (2:2: :2:). IQN - S`dhnh >. Co Ki`kcpt ptii hc D`tcgrno. Rckup upccrnhi hc= fttps=//rcpisdtiry.u`nh.chu.ki/fn`hoc/>:341/;;38>
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