EJERCICIOS DE AJUSTE DE CURVAS E INTERPOLACION2019verst

 

CHYZPI @I JYT^CZ

3. Ytelezi lc rimriseúk pgr aákeags juc`rc`gs pcrc chustcr ukc lákic rijtc c8 V

2

4

0

>

5

33

34

39

3=

35

y

9

>

=

>

5

6

=

32

34

34

c)  Fcmc ukc mrcnejc `i lgs `ctgs y lc lákic `i rimriseúk. d)  Tipetc il prgdliac pirg cfgrc inijtuå lc rimriseúk `i ` i x vs y , is `ijer jcadei lcs vcrecdlis i ektirpriti lgs risultc`gs. (utelezi sus jgkgjeaeiktgs `i Istc` Istc`estejc estejc pcrc jcljulcr uk jginejeikti `i jgrrilcjegk). 4. Ysi lc rimriseúk pgr aekeags juc`rc`gs pcrc chustcr chustcr ukc lákic rijtc c 8 V

>

=

33

39

3=

43

4:

45

45

:=

:5

y

45

43

45

30

43

39

=

=

3:

2

:

c)Fcmc ukc mrcnejc `i lgs `ctgs y lc lákic `i rimriseúk. d)·Ze gtrc pirsgkc fejeirc ukc ai`ejeúk c`ejegkcl `i x132 ,y132 a , usti` pikscrác jgk dcsi ik ukc ivclucjeúk vesucl qui lc ai`ejeúk irc vãle`c g ekvcle`c 7 :. Chusti lgs semueiktis `ctgs c8 c) Yk ag`ilg lekicl d) Yk ag`ilg `i pgtikjecs y j ) ukc pcrãdglc. Ik jc`c jcsg ilcdgri ukc mrcnejc. ·Juãl is il aihgr chusti pcrc isti jgkhuktg `i `ctgs7 V

2.=9

4

:

0

>

6

6.9

y

3.4

3.59

4

4.0

4.0

4.=

4.>

0. Chusti lgs `ctgs semueiktis jgk il ag`ilg pgtikjecl p gtikjecl  y



cx d , usi lc ijucjeúk `i pgtikjecs

risultckti pcrc fcjir il prgkústejg `i “y‑, ik x15. 

V

4.9

:.9

9

>

=.9

32

34.9

39

3=.9

42

y

3:

33

6.9

6.4

=

>.4

9.4

0.6

0.>

0.:

9. Chusti c uk ag`ilg ixpgkikjecl c8 V

2.0

2.6

3.4

3.>

4

4.:

y

622

5=9

3922

3592

4522

:>22

Mrcnequi il ag`ilg ik isjclc lgmcrátaejc y siaelgmcretaejc (ekvistemcr) >. Ik viz `i uscr il ag`ilg ixpgkikjecl `i dcsi “i‑ , ukc cltirkctevc jgaøk jgksesti ik uscr uk ag`ilg `i dcsi 328   y    9 32 9 x  

 

Juck`g si usc pcrc chustcr jurvcs, istc ijucjeúk llivc c risultc`gs r isultc`gs e`åktejg qui lgs `i lc virseúk jgk dcsi “i‑, pirg il vclgr `il pcrãaitrg pcrãaitrg `il ixpgkikti 8 9 , `eneiri `il isteac`g jgk Ysi lc virseúk jgk dcsi “32‑ pcrc pcrc risglvir il prgdliac cktiregr, cktiregr, il ag`ilg ixpgkikjecl. Ysi c`iaãs , `iscrrglli ukc ngraulcjeúk pcrc rilcjegkcr il ixpgkikti `il ag`ilg ixpgkikjecl y il vclgr 9 `il ag`ilg jgk dcsi 32.

=. Ai`eckti trcksngracjegkis, lekiclezcr8 lekiclezcr8

 y

  0

 0 .x.i

x

y uscrlg pcrc isteacr lgs pcrãaitrgs

 0 ,  0 , jgk dcsi ik lgs `ctgs semueiktis. Ilcdgri ukc mrcnejc `il chusti huktg jgk lgs `ctgs8

V

2.3

2.4

2.0

2.>

2.5

3.: 3 .:

3.9

3.=

3.6

y

2.=9

3.49

3.09

3.49

2.69

2.99

2.:9

2.46

2.36

5. Chusti ukc ijucjeúk judejc c lgs semueiktis `ctgs8 V

:

0

9

=

6

5

33

34

y

3.>

:.>

0.0

:.0

4.4

4.6

:.6

0.>

32. Ykc ixtikseúk øtel `i lc rimriseúk lekicl is il jcsg ik il qui “y‑ is ukc nukjeúk lekicl `i `gs g

acs vcrecdlis ek`ipik`eiktis. Rgr ihiaplg 8

 y



c2



c3 x



c4 x

4



i  (ik isti

jcsg lc lákic `i

rimriseúk , si trcksngrac ik uk plckg), `gk`i “i‑ is il irrgr.  c) Ysi il irrgr juc`rãtejg ai`eg pcrc fcllcr lcs ijucjegkis kgraclis. d)Rcrc lcs semueiktis tcdlcs `i `ctgs, chustcrlgs ai`eckti ukc rimriseúk lekicl aøltepli8 d3)

d4)

V3 

2

3

3

4

4

:

:

0

0

V4 

2

3

4

3

4

3

4

3

4

y

39.3

3=.5

34.=

49.>

42.9

:9.3

45.=

09.0

02.4

V3 

2

2

3

4

2

3

4

4

3

V4 

2

4

4

0

0

>

>

4

3

y

30

43

33

34

4:

4:

30

>

33

 

33. Zi fcji lc pruidc cuk actirecl pcrc istu`ecr lc ncllc pgr nctemc jájlej jájlejc, c, ik lc qui si cplejc uk isnuirzg, ik ARc, ARc, cl actirecl y si ae`i il køairg `i jjejlgs ejlgs qui si kijisetc kijisetc pcrc fcjir qui nclli. Lgs risultc`gs si prisiktck ik lc semueikti tcdlc. Cl fcjirsi ukc mrcnejc lgm-lgm, `il isnuirzg virsus lgs jejlgs, jejlgs, lc tik`ikjec `i `i lgs `ctgs prisiktc ukc rilcjeúk rilcjeúk lekicl. Ysi ukc rimriseúk pgr aekeags juc`rc`gs pcrc `itiraekcr lc ijucjeúk `i aihgr chusti pcrc `ejfgs `ctgs. K,jejlgs

3

Isnuirzg, 3322 ARc

32

322

3222

32222 322222 3222222

3222

549

622

>49

992

042

34. Lgs `ctgs semueiktis semueiktis auistrck ukc rilcjeúk iktri lc vesjgse`c` `il `il cjieti ZCI =2 y su tiapircturc. @ispuås `i gdtikir il lgmcretag `i lgs `ctg `ctgs, s, usi rimriseúk lekicl pcrc ikjgktrcr lc ijucjeúk `i lc rijtc qui si chusti aihgr c lgs `ctgs. Piapircturc, 4>.>= ²J

5:.::

306.65

:39.9>

^ilgje`c`,

2.269

2.234

2.222=9

. K .s / a

4

3.:9  

3:. Luimg `i ukc tgraiktc si vemelc lc jgkjiktrcjeúk `i lc dcjtirec I. Jgle ik uk ãric `i kctcjeúk. t(fgrcs)

0

j(JNY/322aL) 3952

6

34

3>

42

40

3:42

3222

522

>92

9>2

Il teiapg si ae`i ik ik fgrcs trcksjurre`cs `ispuås `i nek nekclezcr clezcr lc tgraiktc y lc uke`c` JNY is ukc uke`c` `i ngracjeúk ngracjeúk `i jglgkec. Ysi lgs `ctgs pcrc isteacr isteacr lc jgkjiktrcjeúk jgkjiktrcjeúk cl nekcl `i lc tgraiktc (t12) y il teiapg ik il qui lc jgkjiktrcjeúk jgkjiktrcjeúk cljckzcrã 422 JNY/322aL. Gdsirvi qui lc ilijjeúk `il ag`ilg ag`ilg `idi sir jgksestikti jgk il fijfg `i qui lcs jgkj jgkjiktrcjegkis iktrcjegkis kimctevcs sgk eapgsedlis y `i qui lc jgkjiktrcjeúk `i dcjtirecs dcjtirecs seiapri `esaekuyi jgk il teiapg. 30. Yk gdhitg si suspik`i ik uk tøkil `i veiktg y si ae`i lc nuirzc pcrc vcregs kevilis `i vilgje`c` `il veiktg. C jgktekucjeúk istãk tcdulc`gs lgs risultc`gs. Ysi lc rimriseúk pgr aákeags juc`rc`gs pcrc chustcr 8 c) Ykc lákic rijtc d) ukc ijucjeúk `i pgtikjecs dcsc`c ik trcksngracjegkis lgmcrátaejcs

 

^ (a/s)

32

42

:2

02

92

>2

=2

62

N(Kiwtgks)

49

=2

:62

992

>32

3442

6:2

3092

  3>. Ysti` llivc c jcdg ixpireaiktgs y `itiraekc lgs vclgris semueiktis `i jcpcje`c` jclgránejc “j‑

c `estektcs tiapircturcs P pcrc uk mcs8 P

-92

-:2

2

>2

52

322

j

34=2

3462

3:92

3062

3962

3=22

Ysi rimriseúk pcrc `itiraekcr uk ag`ilg pcrc pri`ijer “j‑ jgag nukjeúk `i P.  

3=. Il isnuirzg c lc tikseúk `i plãstejg si ekjriaiktc jgag nukjeúk `il teiapg qui rijedi trctcaeiktg ik dcsi `i jclgr. Zi gdtuveirgk lgs `ctgs semueiktis8 Peiapg

32

Isnuirzg 9 c lc tiksegk

39

42

49

02

92

99

>2

=9

42

36

02

::

90

=2

>2

=6

c)  Chusti ukc lákic rijtc c istgs `ctgs y uteleji lc ijucjeúk pcrc `itiraekcr il isnuirzg c lc tikseúk ik uk teiapg `i :4 aek. d)  Tipetc il ckãleses pcrc ukc rijtc jgk ektirsijjeúk ik il gremik. 36. Il vgluaik ispijánejg `i uk vcpgr sgdrijcliktc`g si prisiktc ik lc tcdlc `i vcpgr pcrc `estektcs tiapircturcs. Rgr ihiaplg, c ukc priseúk cdsglutc `i :222 ld/pulm4. P, ²N

=22

=42

=02

=>2

=62

^,peis:/ld 2.25== 2.34360 2.302>2 2.39925 2.3>>0: @itiraeki v, jgk P1=92²N. 35. Ik lc iknirai`c` `i Clzfieair , il kuairg `i kiurgkcs ik lc jgrtizc `esaekuyi jgkngrai lc iknirai`c` cvckzc. Lgs `ctgs semueiktis si tgacrgk pcrc `itiraekcr il køairg `i rijiptgris kiurgtrcksaesgris qui qui`ck qui`ck ik uk jiridrg iknirag. Zi ekjudcrgk kiurgtrcksaesgris kiurgtrcksaesgris ledris ( _NQ) jgk tihe`g, y si ae`eú, lc jgkjiktrcjeúk qui leaetc ispijánejcai ispijánejcaikti kti c uk rijiptgr( r ijiptgr( _DQ). Juck`g lc judeirtc is ispijenejc `i uk rijiptgr, lc jgkjiktrcjeúk láaeti si rilcjegkc jgk lc jgkjiktrcjeúk ledri pgr ai`eg `i lc rilcjeúk semueikti8 _ DQ 

 Dacx _ N Q O



_ N Q

.

Jgk il usg `i lgs `ctgs semueiktis, `itiraeki lgs pcrãaitrgs qui aekeaezck lc suac `i lgs juc`rc`gs `i lgs rise`ugs.

 

  _NQ,kA

2.3

2.9

3

9

32

42

92

_DQ,kA

32.9=

:>.>3

94.5:

64.>9

65.0>

50.:9

323.22

42. Zi tgacrgk lgs `ctgs semueiktis `il tckqui `i uk ricjtgr `i cmetcjeúk pcrc lc ricjjeúk8  C  D . Ysi lgs `ctgs pcrc fcjir lcs isteacjegkis aihgris pgsedlis pcrc o23 , I 3 , pcrc il ag`ilg  I 3

`C

jekåtejg semueikti8







`t 

 C

o23i  TP 

, `gk`i T8 is lc jgkstckti `i lgs mcsis y is emucl c 2.22356

Ojcl/agl/O. -`C/`t (aglis/L/s)

022

5>2

4069

3>22

3409

C(aglis/L)

422

392

92

42

32

P(O)

462

:42

092

922

992

44. C jgktekucjeúk si prisiktc `ctgs `i lc vcsehc ` `ii uk ricjtgr `i jrij jrijeaeiktg eaeiktg dcjtirecl (ukc viz qui tiraekg lc ncsi `i ritrcsg ). Zi piraeti qui lcs dcjtirecs jrizjck tck rãpe`g jgag sic pgsedli `urckti lcs preaircs 4.9 fgrcs, y `ispuås si lis ek`uji c prg`ujer ukc prgtiákc rijgadekckti,, lc jucl `esaekuyi il jrijeaeiktg dcjtirecl ik ngrac semkenejctevc. Il jrijeaeiktg rijgadekckti tiúrejg `i lcs dcjtirecs si isjredi pgr ai`eg `i8 `gk`i V, is il kuairg `i dcjtirecs, d cjtirecs, y

`V 

 , is lc tcsc

`t 

  V 

 

`i jrijeaeiktg ispijenejg ispijenejg `i lcs dcjtirecs

`urckti il jrijeaeiktg ixpgkikjecl. ixpgkikjecl. Jgk dcsi ik lgs `ctgs, isteai lc tcsc `i jrijeaeiktg ispijánejg `i lcs dcjtirecs `urckti lcs preaircs 4 fgrcs `i jrijeaeiktg, cse jgag `urckti lcs semueiktis 0 fgrcs `i jrijeaeiktg. Peiapg (f)

2

3

4

:

0

9

>

Jilulcs, m/L

2.322

2.::4

3.324

3.>00

4.09:

:.>>2

9.0>2

4:. Il pisg aglijulcr `i uk pgláairg si `itiraekc c pcrter `i su vesjgse`c` pgr ai`eg `i lc rilcjeúk semueikti8

  c _Q  OA  v  

`gk`i _Q  is lc vesjgse`c` ektráksijc `il pgláairg,

 A v

, is lc vesjgse`c` prgai`ec`c `il pisg

aglijulcr, y O y “c‑ sgk jgkstcktis ispijenejcs `il pgláairg. Lc vesjgse`c` ektráksijc si

`itiraekc ik ngrac ixpireaiktcl pgr pgr ai`eg `i `itiraekcr il teiapg `i nluhg, g il teiapg qui tgac c lc sglujeúk pgleaårejc nluer iktri `gs lákics mrcdc`cs ik uk vesjgsáaitrg jcpelcr, jcpelcr, c

 

`estektcs jgkjiktrcjegkis jgkjiktrcjegkis `i pgláairg `elue`g, y si ixtrcpglc pcrc ukc `elujeúk ekneketc. Lc mrcnejc t 

`i8

t 2

3 vi virsu rsus s j

 

j

`idi mikircr ukc lákic rijtc , jgk ektirsijjeúk ik il ihi i emucl c _Q . Lc jgkjiktrcjeúk `i lc sglujeúk pgleaårejc is “j‑ , t is il teiapg `i n luhg luhg `i lc sglujeúk pgleaårejc y

t 2

is il teiapg `i

nluhg `il sglvikti sglvikti sek pgláairg. Jgk Jgk il usg `i lgs semueiktis semueiktis `ctgs `i teiapg `i nluhg nluhg pcrc `esglujegkis `elue`cs `i pgleisterikg ik aitel itel cjitgkc c 49²J y lcs jgkstcktis O1:.5x32 -0  y c12.96 , ikjuiktri il pisg aglijulcr `i lc auistrc `i pgleisterikg. Jgkjiktrcjegk `il pgláairg , m/`L

Peiapg `i nluhg, s

2 (sglvikti purg)

6:

2.20

65

2.2>

59

2.26

320

2.32

330

2.34

34>

2.30

3:5

2.3>

399

2.42

353

40. Ik prgai`eg il ãric supirnejecl C `i lgs siris fuackgs si rilcjegkc jgk jgk il pisg ] y lc istcturc F. Ik lc tcdlc semueikti si prisiktck lgs vclgris `i C qui si gdtuvg jgk ai`ejegkis `i jeirtg køairg `i ek`eve`ugs8 F(ja)

364

362

3=5

36=

365

350

359

35:

422

] (om)

=0

66

50

=6

60

56

=>

6>

5>

C(a4)

3.54

4.33

4.39

4.24

4.25

4.:3

4.24 4 .24

4.3>

4.:3

@iscrrglli ukc ijucjeúk pcrc prgkgstejcr il ãric jgag nukjeúk `i lc istcturc y il pisg. Øsilc pcrc isteacr il ãric supirnejecl `i ukc pirsgkc `i 36= ja y =6 om.

 

49. @itiraeki ukc ijucjeúk pcrc pri`ijer pri`ijer lc tcsc `il aitcdglesag jgag nukjeúk `i lc acsc jgk dcsi ik lgs `ctgs semueiktis8 Ckeacl

Acsc , Om

Aitcdglesag, wctts

^cjc

022

4=2

Fuackg

=2

64

Gvihc

09

92

Mcllekc

4

0.6

Tctc

2.:

3.09

Rclgac

2.3>

2.5=

4>. Il tihe`g sucvi semui uk jgapgrtcaeiktg ixpgkikjecl ckti lc `ingracjeúk pgr tikseúk ukecxecl, aeiktrcs isti ik il rckmg neseglúmejg g kgracl `i ilgkmcjeúk. Istg si ixprisc jgag8  

 I 2 c

i

c

,

3

`gk`i



8 isnui nuirzg,



8 tikse seg gk, I2 , c sgk

jgkstcktis `il actirecl qui si

`itiraekck ik ngrac ixpireaiktcl. Rcrc ivclucr lcs `gs jgkstcktis `il actirecl, lc ijucjeúk cktiregr si `enirikjec jgk rispijtg c “   ‑ . Il usg `i lc ijucjeúk istcdliji lc rilcjeúk

nuk`caiktcl pcrc il tihe`g sucvi8

`  ` 

  I2 

c .

Rcrc ivclucr I2  y c, si mrcnejck lgs `ctgs `i isnuirzg-tikseúk jgag `  / `  virsus  , y lc ektirsijjeúk y lc pik`eikti `i istc mrcnejc sgk lcs `gs jgkstcktis `il actirecl, rispijtevcaikti. Ik lc tcdlc semueikti si auistrck `ctgs `i isnuirzg-tikseúk pcrc lgs tik`gkis jgr`c`gs `il jgrczúk (tik`gkis piquiógs qui si usck pcrc acktikir jirrc`cs lcs vãlvulcs `il jgrczúk `urckti lc jgktrcjjeúk `il ausjulg jcr`ecjg, istgs `ctgs sgk pcrc tihe`g qui si jcrmc, aeiktrcs qui lc `isjcrmc prg`uji jurvcs `eniriktis). ,32



:

6=.6

5>.>

3=>

4>:

:93

9=3

6:0

3445

3>40

432=

4>=6

: ::62 :62

0496

/ a 39:

420

499

:2>

:9=

026

095

932

9>3

>34

>>:

=30

=>9

K/a4  :



,32



a

  Jcljuli lc `irevc`c `  / `  jgk il usg `i `enirikjecs neketcs. Mrcnequi lgs `ctgs y ileaeki lgs puktgs `i lgs `ctgs jirjc `i lgs jirgs qui pcrizjck kg simuer lc rilcjeúk `i lákic rijtc. Il irrgr ik `ejfgs `ctgs prgveiki `i lc ekjcpcje`c` `i lgs ekstruaiktgs pcrc liir lgs vclgris piquiógs ik istc rimeúk. Ihijuti uk ckãleses `i rimriseúk `i lgs `ctgs ristcktis r istcktis c nek `i `itiraekcr lgs vclgris `i I2 y c.

 

Mrcnequi lgs puktgs `il isnuirzg virsus lgs `i tikseúk huktg jgk lc jurvc ckclátejc ixprisc`c pgr lc preairc ijucjeúk . Istg ek`ejcrã qui tck deik lc jurvc ckclátejc jgkjuir`c jgk lgs `ctgs. Aujfcs vijis istg kg nukjegkc deik `ide`g c qui il vclgr `i I2 is `enájel `i ivclucr jgk istc tåjkejc. Rcrc risglvir isti prgdliac, kg si utelezc I 2 . Zi silijjegkc uk puktg `i lgs `ctgs



,





 c lc aetc` `il rckmg `i ckãleses `i rimriseúk. @ejfgs vclgris si sustetuyik ik lc preairc

ijucjeúk y si `itiraekc uk vclgr `i I 2/c , il jucl si sustetuyi ik lc preairc ijucjeúk , qui si jgkveirti ik8

       i  3     i 3   c

c

Jgk isti ikngqui, lgs `ctgs ixpireaiktclis qui istãk deik `ineke`gs prg`ujerãk ukc duikc jgekje`ikjecc `i lgs puktgs `i lgs jgekje`ikje l gs `ctgs jgk lc jurvc ckclátejc. Ysi istc kuivc rilcjeúk y mrcnequi gtrc viz lgs `ctgs `il isnuirzg virsus lgs `i tikseúk, y istc jurvc ckclát ckclátejc ejc kuivc. 4=.Il ispisgr `i lc ritekc jcadec `urckti jeirtcs iknirai`c`is gjulcris. Ykc ngrac `i ai`er `ejfg ispisgr is prgyijtcr uk lcsir `i ikirmác auy dchc fcjec lc ritekc y mrcdcr lcs rinlixegkis r inlixegkis ik ukc pilájulc. @ide`g c clcs prgpei`c`is úptejcs `il ghg, lcs rinlixegkis `i lc supirnejei nrgktcl y trcsir `i lc ritekc cpcrijirãk ik lc pilájulc jgag `gs lákics sipcrc`cs pgr jeirtc `estckjec. Istc `estckjec is prgpgrjegkcl cl ispisgr `i lc ritekc. r itekc. Lgs `ctgs semueiktis si tgacrgk `i ukc pilájulc mrcdc`c. Chusti c lgs `ctgs `gs jurvcs jgk ngrac mcusseckc `i clturc y udejcjeúk crdetrcrecs y `itiraeki lc `estckjec iktri lgs jiktrgs `i lgs `gs pejgs. Ykc jurvc mcusseckc teiki lc ngrac8  n ( x) 

oi



o 4 ( x  c )4

  

Rgsejeúk

Ektikse`c` Rgsejeúk

Ektikse`c` Rgsejeúk

Ektikse`c` Rgsejeúk

@i luz

@i Luz

@i Luz

Ektikse`c` `i luz

2.3=

9.32

2.40

:3.>:

2.:3

49.:3

2.:6

9.39

2.36

9.32

2.49

4>.93

2.:4

4:.=5

2.:5

9.32

2.35

9.42

2.4>

3>.>6

2.::

36.00

2.02

9.32

2.42

9.6=

2.4=

32.62

2.:0

34.09

2.03

9.25

2.43

6.=4

2.46

33.4>

2.:9 2.:9

6.44

2.04

9.25

2.44

3>.20

2.45

3>.29

2.:>

>.34

2.0:

9.25

2.4:

4>.:9

2.:

43.5>

2. 2.:= :=

9.:9

2.00

9.25

46. Zi riclezg uk istu`eg `i ekmikeirác `i trckspgrti pcrc `itiraekcr il `esióg cprgpec`g `i pestcs pcrc dejejlitcs. Zi rijcdcrgk `ctgs `il ckjfg `i lcs pestcs y lc `estckjec prgai`eg iktri lcs dejejlitcs y lgs cutgs ik jerjulcjeúk. Lgs `ctgs `i 5 jcllis sgk8

 

@estckjec,a

4.0

3.9

4.0

3.6

3.6

4.5

3.4

:

3.4

Ckjfg `i pestc,a

4.5

4.3

4.:

4.3

3.6

4.=

3.9

4.5

3.9

c)  Mrcnequi lgs `ctgs d)  Chusti ukc lákic rijtc c lgs `ctgs jgk rimriseúk lekicl. Cmrimui istc lákic c lc mr mrcnejc cnejc cktiregr. j)  Ze si jgkse`irc qui lc `estckjec prgai`eg aákeac `i simure`c` iktri lcs dejejlitcs y lgs cutgs ik jerjulcjeúk is `i 4a, `itiraeki il ckjfg `i pestc aákeag jgrrispgk`eikti. 45. Ik ekmikeirác `i rijursgs fe`rãulejgs, il tcacóg `i lgs clacjikcaeiktgs clacjikcaeiktgs `ipik`i `i isteacjegkis ixcjtcs ixcjtcs `il nluhg `i cmuc ik il reg qui si s i c vc jcptcr. Rcrc Rcr c jeirtgs rágs is `enájel gdtikir rimestrgs festúrejgs ixtiksgs `i `ejfgs `ctgs `i nluhg. Rgr il jgktrcreg, jgk trcreg, is nrijuikti qui si `espgkmc `i `ctgs aitigrglúmejgs sgdri lc prijepetcjeúk qui si ixteik`ik aujfg fcjec il pcsc`g. Rgr tcktg, jgk nrijuikjec risultc øtel `itiraekcr ukc rilcjeúk r ilcjeúk iktri il nluhg y lc prijepetcjeúk.. Iktgkjis, istc rilcjeúk si usc pcri isteacr lgs nluhgs `urckti lgs cógs ik qu prijepetcjeúk quii sglg si `espgki `i ai`e`cs pluveclis. Zi `espgki `i lgs `ctgs semueiktis pcrc uk reg qui c ripriscrsi8 Rrijepetcjeúk, 66.5 326.9 320.3 3:5.= 34= 50 33>.6 55.3 ja Nluhg, a:/s 30.> 3>.= 39.: 4:.4 35.9 3>.3 36.3 3>.> c) Mrcnequi lgs `ctgs d)   Chusti ukc lákic rijtc c lgs `ctgs pgr ai`eg `i rimriseúk lekicl. Zgdripgkmc istc lákic c su mrcnejc. j)  Ysi lc lákic `i aihgr chusti pcrc pri`ijer il nluhg n luhg ckucl `i cmuc se lc pr prijepetcjeúk ijepetcjeúk is `i 342ja. `)  Ze il ãric `i `rikchi is `i 3322oa4, isteai lc nrcjjeúk `i lc prijepetcjeúk qui si peir`i c trcvås `i prgjisgs jgag lc ivcpgrcjeúk , ekneltrcjeúk y usg jgksuktevg. :2. Lc jgkjiktrcjeúk `il ngsngrg tgtcl (“p‑ ik am/a :) y jlgrgnelc “c‑ (“j‑ ik am/a:) pcrc jc`c ukc

sirei `i lcmgs ik il cóg 35=2, nui8 Lcmg

R (ngsngrg)

J (jlgrgnelc)

C

0.9

2.6

D

6.2

4.2

J

9.9

3.4

@

:5.2

33.2

I

35.9

0.0

N

3=.9

:.6

M

43.2

9.9

Lc jgkjiktrcjeúk `i jlgrgnelc “c‑ ek`ejc jucktc ve`c vimitcl si ikjuiktrc ik suspikseúk s uspikseúk ik il

cmuc. Cl sir csá, ek`ejc lc jlcre`c` y vesedele`c` `il cmuc. Ysi lgs `ctgs cktiregris pcrc

 

`itiraekcr lc rilcjeúk `i “j‑ jgag nukjeúk `i “p‑. Iaplii lc ijucjeúk pcrc pri`ijer pr i`ijer il kevil

`i jlgrgnelc qui pui`i ispircrsi se si usc il trctcaeiktg `il cmuc pcrc cdcter c 32 am/a :lc jgkjiktrcjeúk `i ngsngrg `il lcmg @. :3. Il aãstel `i uk vilirg vilirg teiki uk cric `i sijjeúk sijjeúk trcksvirscl `i 32.>9 ja4y istc jgkstrue`g `i ukc clicjeúk ixpireaiktcl ixpireaiktcl `i cluaekeg. Zi llivcrgk c jcdg pruidcs pcrc `ineker lc rilcjeúk iktri il isnuirzg y lc tikseúk. Lgs risultc`gs `i lcs pruidcs nuirgk lgs qui semuik8 Piksegk, 2.22:4 2.2209 2.2299 2.223> 2.2269 2.2229 ja/ja Isnuirzg, 05=2 93=2 9922 :952 >522 3402 K/ja4  Lgs isnuirzgs gjcsegkc`gs pgr il veiktg si jcljulck jgag N/C j `gk`i N1nuirzc ik il aãstel, C j  1ãric `i lc sijjeúk trcksvirscl `il aãstel . @ispuås, isti vclgr si sustetuyi ik lc liy `i Fggoi pcrc `itiraekcrlc `inlixeúk `il aãstel,  L 8 tiksegkxL, `gk`i L1 lgkmetu` `il aãstel. Ze lc nuirzc `il veiktg is `i 49222 K, usi lgs `ctgs pcrc isteacr lc `inlixeúk `i uk aãstel `i 5a. :4. Lcs ricjjegkis ikzeaãtejcs si usck aujfg pcrc jcrcjtirezcr ricjjegkis ai`ec`cs deglúmejcaikti. C jgktekucjeúk si `ck ixprisegkis `i tcscs prgpuistcs pcrc ukc ricjjeúk ikzeaãtejc, `gk`i _ZQ is lc jgkjiktrcjegk `il sustrctg y v 2 is lc tcsc ekejecl `i lc ricjjeúk. ·Suå ngraulc si chustc aihgr c lgs `ctgs ixpireaiktclis7 o Z v2



o_ Z Q

, v2



_ Q O  _ Z Q

o Z

, v2   

4

_ Q , v2   O  _ Z Q4 

_sQ,A

Pcsc ekejecl, 32-> A/s

2.23

>.:>:>x32-9 

2.29

=.5942x32-: 

2.3

>.:0=4x32-4 

2.9

>.2205

3

3=.>52

9

40.049

32

40.053

92

40.922

322

40.922

o Z 

:

 

_ Q :   O  _ZQ  

::. Zi ae`i lc ae`i lc jcá`c `i vgltchi ^ c trcvås `i uk risestgr pcrc jeirtg køairg `i vclgris `estektgs `i jgrreikti “e‑ . Lgs risultc`gs sgk8  e 2.49 2.=9 3.49 3.9 4.2 ^

-2.09

-2.>

2.=2

3.66

>.2

 

Ytelezi ektirpglcjeúk `i pglekgaegs `i preairg c jucrtg gr`ik pcrc isteacr lc jcá`c `i vgltchi pcrc e13.39. Ektirpriti lgs risultc`gs. :0. Zi ae`i jgk mrck prijeseúk lc jgrreikti ik uk jgk`ujtgr jgag nukjeúk `il teiapg8 t

2

2.3492

2.4922

2.:=92

2.922

E

2

>.40

=.=9

0.69

2.222

@itiraeki il vclgr `i “e‑ ik t12.4:.  :9. Zi scdi qui lc jcá`c `i vgltchi vglt chi c trcvås `i uk ek`ujtgr semui lc liy `i Ncrc`cy8 `gk`i

v L

v L  L

`e `t 

,

, is lc jcá`c `i vgltchi (ik vglts), L is lc ek`ujtckjec (ik fikregs), e is lc jgrreikti (ik

capiris). Iaplii lgs `ctgs semueiktis pcrc isteacr L8 `e/`t (C/s)

3

4

0

>

6

32

^t (^)

9.9

34.9

3=.9

:4

:6

05

·Juãl is il semkenejc`g, se fudeirc clmukg, `i lc ektirsijjeúk ekt irsijjeúk `i lc ijucjeúk `i rimriseúk qui si gdteiki jgk istgs `ctgs7 :>.prgpgrjegkcl Lc liy `i Gfa istcdliji jcá`c `i cvgltchi c trcvås `i uk, risestgr lekiclaikti c lc jgrreiktiqui jgrreikti “e‑ lc qui nluyi trcvås^`i uk risestgr jgag ike`icl ^1eT,is`gk`i T is lc risestikjec. Zek iadcrmg, lgs risestgris riclis kg seiapri gdi`ijik c lc liy `i Gfa. Zupgkmc usti` qui llivc c jcdg clmukgs ixpireaiktgs auy prijesgs pcrc ai`er lc jcá`c `i vgltchi y lc jgrreikti jgrrispgk`eikti jgrrispgk`eikti pcrc uk risestgr. Lgs risultc`gs si iklestck ik lc tc tcdlc dlc semueikti y sumeirik ukc rilcjeúk jurvelákic aãs qui lc lákic rijtc qui riprisiktc lc liy `i Gfa. C nek `i jucktenejcr `ejfc rilcjeúk `idi chustcrsi ukc jurvc c lgs `ctgs. @ide`g cl irrgr ik lc ai`ejeúk, is jgaøk qui lc rimriseúk sic il aåtg`g prinire`g `i chusti `i jurvcs pcrc ckclezcr `ejfgs `ctgs ixpireaiktclis. Zek iadcrmg, lc sucve`c` `i lc rilcjeúk, csc jgag lc prijeseúk `i lgs aåtg`gs ixpireaiktclis, sumeirik qui quezã sirác cprgpec`c lc ektirpglcjeúk. Ysi lc ektirpglcjeúk `i pglekgaegs `i Kiwtgk pcrc chustcr lgcs `ctgs y jcljulcr ^ pcrc e12.3 ·Juãl is il gr`ik `il pglekgaeg qui si usg pcrc mikircr lgs `ctgs7 e -4 -3 -2.9 2.9 3 4 ^

->:=

-5>.9

-42.9

42.9

5>.9

>:=

:=. Is nrijuikti qui ik lgs ckãleses cvckzc`gs cvckzc`gs `i ekmikeirác surhck nukjegkis `i Dissil, Dissil, jgag ik il istu`eg `i jcapgs ilåjtrejgs. @ejfcs nukjegkis pgr lg mikircl kg sgk susjiptedlis `i ivclucrsi ik ngrac `erijtc y pgr illg, kg is rcrg qui iståk jgapelc`cs ik tcdlcs actiaãtejcs istãk`cr. Rgr ihiaplg8 V

3.6

4

4.4

4.0

4.>

H3(x) 2.9639 2.9=>= 2.99> 2.9424 2.0=26 Isteacr H3(4.3) c) Jgk pglekgaegs `i ektirpglcjeúk d) Jgk splekis jødejgs

 

:6. Lc pgdlcjeúk (p) `i ukc jgauke`c` piquióc ik lgs sudurdegs `i ukc jeu`c` jriji jgk rcpe`iz `urckti uk pireg`g `i 42 cógs8 t

2

9

32

39

42

p

322

422

092

592

4222

Jgag ekmikeirg , si li pe`i prgkgstejcr lc pgdlcjeúk qui fcdrã `iktrg `i 4 cógs c nek `i cktejepcr lc `iack`c `i ikirmác . Iaplii uk ag`ilg ixpgkikjecl y rimriseúk lekicl pcrc inijtucr `ejfc pri`ejjeúk. :5. Lc Liy `i Fggoi , qui si juapli juck`g uk risgrti kg si isterc acs cllã `i jeirtg leleaeti, aeti, semkenejc qui lc ixtikseúk `i isti isti risgrti y lc nuirzc qui si li cplejc istãk rilcjegkc`cs rilcjegkc`cs lekiclaikti. Lc prgpgrjegkcle`c` istc pcrcaitrezc`c pgr lc jgkstckti O `il risgrti. Yk vclgr pcrc `ejfg pcrãaitrg si istcdliji istcdliji ik ngrac ixpireaiktcl ixpireaiktcl jgk lc jglgjcjeúk `i pisgs jgkgje`gs jgkgje`gs ik il risgrti y lc ai`ejeúk `i lc jgapriseúk qui risultc. Pclis `ct `ctgs gs cpcrijik ik lc tcdlc ekniregr y istãk mrcnejc`gs. Gdsirvi qui pgr crredc `i uk pisg `i 02x32 0K, lc rilcjeúk lekicl iktri lc nuirzc y il `isplczcaeiktg `iscpcriji. Istc jlcsi `i jgapgrtcaeiktg is jgaøk `i lg qui si `ikgaekc “risgrti ik `ingracjeúk‑. Iaplii rimriseúk lekicl pcrc `itiraekcr uk vclgr `i “o‑

pcrc lc pcrti lekicl `i isti sestiac. C`iaãs, chusti ukc rilcjeúk kg lekicl c lc pcrti kg lekicl. @isplczcaeiktg,a 2.32 2.3= 2.4= 2.:9 2.:5 2.04 2.0: 2.00 0

Nuirzc, 32 K

32

42

Liy `i Fggoi

:2

02

92

>2

=2

62

Jgapgrtcaeiktg kg e`icl8 il risgrti istc “‑ik`urije`g‑ 

Nuirzc, 320 K

@isplczcaeiktg, a

02. Tipetc il prgdliac cktiregr, pirg chusti ukc jurvc jurvc `i pgtikjecs c tg`gs lgs `ctgs `i lc tcdlc. Jgaikti sus risultc`gs. 03. Lc `estckjec qui si riqueiri pcrc `itikir uk cutg jgksesti ik jgapgkiktis tcktg `i pikscaeiktg jgag `i nrikc`g, jc`c ukc `i lgs juclis is nukjeúk `i vilgje`c`. Zi rijcdcrgk lgs semueiktis `ctgs ixpireaiktclis pcrc jucktenejcr `ejfg rilcjeúk. @iscrrglli lc ijucjeúk `i aihgr chusti pcrc cadgs jgapgkiktis, jgapgkiktis, pikscaeiktg y nrikc`g. Ytelezi istcs ijucjegkis pcrc isteacr lc `estckjec tgtcl ik qui si `iteiki uk cutg qui vechc c 332oa/f.

 

^ilgje`c`, :2 oa/f Rikscaeiktg,a 9.>

09

>2

=9

52

342

6.9

33.3

30.9

3>.=

44.0

Nrikc`g,a

34.:

43.2

:4.5

0=.>

60.=

9.2

04. Zi riclezc uk ixpireaiktg pcrc `ineker lc rilcjeúk iktri il isnuirzg cplejc`g y il teiapg pcrc qui si nrcjturi jeirtg tepg `i cjirg ekgxe`cdli . Zi cplejck gjfg vclgris `estektgs `i isnuirzg, y lgs `ctgs risultcktis sgk8 Isnuirzg, x, 9 32 39 42 49 :2 :9 :9 02 (o/aa4) Peiapg pcrc 02 :2 49 02 36 42 44 39 lc nrcjturc, y (f) Mrcnequi lgs `ctgs y `ispuås `iscrrglli lc ijucjeúk `i aihgr chusti pcrc pri`ijer il teiapg `i nrcjturc pcrc uk isnuirzg cplejc`g `i 42om/aa 4. 0:. Lc cjilircjeúk `i lc mrcvi`c` c ukc cltetu` clte tu` y pgr ikjeca `i lc supirnejei `i lc Peirrc istc `c`c pgr8 y,a

2

m, a/s4  5.63

:2222

>2222

52222

342222

5.=06=

5.>6=5

5.>4=6

5.9>64

Jcljuli “m‑ pcrc y199222a. *

00. @i uk prgji`eaeiktg `i pruidcs si gdtuveirgk lc tcsc `i crrcstri  qui is tcsc `i teiapg c qui cuaiktc lc tikseúk, y `i isnuirzgs, lgs juclis si prisiktck c jgktekucjeúk. Jgk il usg ` `ii *

ukc liy `i jurvc `i pgtikjecs pcrc chustcr 8

   D 

a

 

Ikjuiktri il vclgr `i D y a. a . Mrcnequi sus risultc`gs jgk il iaplig `i ukc isjclc lgm-lgm. lgm -lgm. Pcsc `i 2.2220 2.2233 2.2243 2.22:3 crrcstri, aek-3  Isnuirzg, ARc 9.==9 6.9== 32.6=0 34.999 09. Cl ixcaekcr il jgapgrtcaeiktg vesjgsg `i uk nlue`g is prãjtejc prãjtejc jgaøk mrcnejcr lc tcsc `i jgrti (mrc`eikti `i vilgje`c`). `  `y

*

   , ik lcs

cdsjescs virsus il isnuirzg jgrtckti ,



,ik lcs gr`ikc`cs.

Juck`g uk nlue`g auistrc uk jgapgrtcaeiktg ik lákic rijtc iktri iscs `gs vcrecdlis, si `ikgaekc nlue`g kiwtgkeckg, y lc risultckti is8

*



.

 

@gk`i

 is

lc vesjgse`c` ves jgse`c` `il nlue`g. Aujfgs nlue`gs jgaukis semuik isti jgapgrtcaeiktg

jgag il cmuc, lijfi y cjieti. Lgs nlue`gs qui kg si jgapgrtck `i isti ackirc si llcack ll cack kg kiwtgkeckgs. Ze si teikik tris tepgs `i nlue`gs kg kiwtgkeckgs8 -Rcrc plãstejgs Dekmfca, fcy uk isnuirzg ek`uje`g  y qui `idi supircrsi pcrc qui il *

   y     (uk ihiaplg is lc pcstc `iktcl).

nluhg jgaeikji8

- Rcrc siu`gplcstejgs, il isnuirzg jgrtckti si ilivc c lc pgtikjec8

  

k

 (ihiaplg `i

istgs sgk il ygmurt y il jfcapu). Lgs `ctgs semueiktis auistrck lc rilcjeúk iktri il isnuirzg jgrtckti jgrtckti8

*

 y

 pcrc uk nlue`g plãstejg Dekmfca. Il isnuirzg ek`uje`g



 y



y lc tcsc `i tikseúk

is lc jckte`c` `i isnuirzg

qui `idi supircrsi cktis `i qui jgaeikji il nluhg. Ikjuiktri lc vesjgse`c` pgr ai`eg `i rimriseúk. Isnuirzg ,    Pcsc `i tikseúk jgrtckti, 0>. Lc rilcjeúk iktri isnuirzg ixpriscrsi ai`eckti8



*



 

:.96

:.53

0.56

9.>9

>.39

3

4

:

0

9

y lc tcsc `i tikseúk jgrtckti

  

k

 (pik`eikti),

*



,

. Lgs `ctgs semueiktis prgveikik `i fe`rgxeiteljilulgsc ik ukc

Pcsc `i tikseúk jgrtckti, 

 y

pcrc uk nlue`g siu`gplcstejg, pui`i

sglujeúk `i cmuc. Jgk il iaplig `i uk chusti pgr liy `i pgtikjecs, ikjuiktri lgs vclgris `i k.

Isnuirzg ,



*



 

 

92

=2

52

332

3:2

>.23

=.06

6.95

5.35

32.43



 y

0=. Zi ae`i lc vilgje`c` “u‑ `il ceri qui nluyi c vcrecs `estckjecs “y‑ `i ukc supirnejei plckc . Chusti ukc jurvc c isgs `ctgs se si supgki qui lc vilgje`c` ik lc supirnejei is emucl c jirg (y12). Yteleji     9  x 32 su risultc`g pcrc `irtiraekcr il isnuirzg jgrtckti (    `u / `y ) ik lc supirnejei (   3.6

) y, a

2.224

2.22>

2.234

2.236

2.240

Y, a/s

2.46=

2.655

3.539

:.206

0.455

06. Lc ijucjeúk `i Ck`rc`i fc se`g prgpuistc jgag ag`ilg `il inijtg `i lc tiapircturc sgdri lc vesjgse`c`8     @. i  D /Pc , `gk`i

 1vesjgse`c` `ekãaejc `il cmuc (32

-:

K.s/a4), Pc1tiapircturc

cdsglutc (o)y @ ,D sgk pcrãaitrgs . Chusti isti ag`ilg c lgs `ctgs `il cmuc8 P

2

9

32

42

:2

02

 

3.=6=

3.935

3.:2=

3.224

2.=5=9

2.>945

05. Rcrc il jgkhuktg `i `ctgs qui si auistrc , `itiraeki lc jurvc `i jc`c ncaelec qui aihgr si li chusti ik il sikte`g `i lgs aákeags juc`rc`gs8

 

  Cx   C c)  n ( x) J i  d)  n ( x)  Jx j) Ysi I4(n) pcrc `itiraekcr juãl `i lcs jurvcs is lc qui aihgr si 

chustc. xo 

3

4

:

0

9

yo 

2.>

3.5

0.:

=.>

34.>

92. Rcrc il jgkhuktg `i `ctgs qui si auistrc, `itiraeki lc jurvc `i jc`c ncaelec qui aihgr si li chusti ik il sikte`g `i lgs aákeags juc`rc`gs8   Cx c)  n ( x) J i  d)  n ( x)  3 / ( Cx  D) j) Ysi I4(n) pcrc `itiraekcr juãl `i lcs jurvcs is lc qui 

aihgr si chustc. xo 

-3

2

3

4

:

yo 

>.>4

:.50

4.3=

3.:9

2.65

93. Rcrc il jgkhuktg `i `ctgs qui si auistrc, `itiraeki lc jjurvc urvc `i jc`c ncaelec qui aihgr si li chusti ik il sikte`g `i lgs aákeags juc`rc`gs8   Cx 4 c)  n ( x) J i   d)  n ( x)  ( Cx  D) j) Ysi I4(n) pcrc `itiraekcr juãl `i lcs jurvcs is lc qui   



aihgr si chustc. 94. Juck`g ukc pgdlcjeúk R(t) kg pui`i jrijir acs cllc `i uk jeirtg vclgr leaeti L. Lc mrcnejc `i lc nukjeúk R(t) is ukc jurvc, llcac`c jurvc lgmástejc, `i ijucjeúk  y  L / (3  Ji Cx ) .Jcljuli C y J pcrc lgs semueiktis `ctgs , seik`g L uk vclgr jgkgje`g.(2,422), (3,022),(4,>92), (:,692),(0,592), L13222. 9: Ysi lgs semueiktis `ctgs sgdri lc pgdlcjeúk `i ukc pcás V, pcrc fcllcr lc jurvc lgmástejc R(t), jgrrispgk`eikti y isteai lc pgdlcjeúk ik ik il cóg 4222. c) Zupgkmc L16x326  Cóg

to 

Ro 

3622

-32

9.:

3692

-9

4:.4

3522

2

=>.3

3592

9

394.:

 

d) L16x326  Cóg

to 

Ro 

3522

2

=>.3

3542

4

32>.9

3502

0

3:4.>

35>2

>

362.=

3562

6

44>.9

 

99.c) @i`ujer ijucjegkis kgraclis qui piraetik fcllcr lc jurvc `i lc ngrac  y  C jgs( x)  D sek( x) , qui aihgr si chustc c uk jgkhuktg `i `ctgs ik il sikte`g `i aákeags juc`rc`gs. (usi il irrgr I4(n) y `irevc`cs pcrjeclis . Ekvistemui il aåtg`g `i Kiwtgk pcrc sestiacs kg lekiclis) d)Ysi lgs risultc`gs `il cpcrtc`g (c) pcrc fcllcr lc jurvc `i ijucjeúk  y  C jgs( x)  D sek( x) , qui aihgr si chustc c lgs `ctgs8 xo 

-:

-3.9

2.2

3.9

:.2

yo 

-2.3:69

-4.396=

2.6::2

4.4==0 4 .4==0

-2.9332

9>. @i`uzjc lcs ijucjegkis kgraclis ik il sikte`g si kte`g `i aákeags juc`rc`gs `i  z  Cx  Dy  J  , qui aihgr si chusti c uk jgkhuktg `i K puktgs (x 3,y3,z3), (x4,y4,z4),…..,(xk,yk,zk) (usck`g il irrgr juc`rãtejg ai`eg y `irevc`cs pcrjeclis emuclc`cs c jirg). 96. Lc rilcjeúk, fgrc c fgrc, `i tiapircturcs ik Ruirtg Ticl (Jã`ez) `urckti uk `ác `i kgveiadri si `c ik lc tcdlc qui nemurc aãs cdchg. Jcljuli lc nukjeúk `i lc ngrac  y  C jgs( Dx)  J sek( @x) , qui aihgr si chustc c lgs l gs `ctgs `i lc tcdlc semueikti ik il sikte`g `i aákeags juc`rc`gs. @eduhi lgs `ctgs y lc jurvc gdtike`c gdtike`c ik ukc aesac mrcnejc y jc jcljuli ljuli I4(n). Fgrc

Mrc`gs

Fgrc

Mrc`gs

3

6

3:

3>

4

6

30

3>

:

6

39

39

0

6

3>

30

9

=

3=

3:

>

=

36

3:

=

=

35

34

6

6

42

33

5

32

43

32

32

30

44

32

33

30

4:

5

34

39

40

6

EKPITRGLCJEGK

 

95. Zupgkmc qui ukc rilcjeúk nukjegkcl y1n(x) istc `c`c ik ngrac tcdulcr tcdulcr jgag8 V U

2 2.53>4

2.49 2.6325

2.92 2.>5:3

2.=9 2.995>

3.22 2.0299

@gk`i y(x) is ukc nukjeúk agkgtgkejcaikti `ijrijeikti `ijrijeikti `i x. Ikjuiktri lgs vclgris `i “x‑ qui sctesncjik y12.5, 2.=, 2.> ,2.9

>2.  C jgktekucjeúk `cags lc `ikse`c` `il sg`eg c tris tiapircturcs. e Piapircturc 8 Pe (¸J)

3 50

4 429

: :=3

@ikse`c` 8`e (om/a:)

545

524

6>2

c)Isjredc lc ektirpglcjeúk `i Lcmrckmi qui si chustc c lgs tris puktgs `i `ctgs d) Gdtikmc lc `ikse`c` pcrc P14932 ai`eckti Lcmrckmi. >3.  @itiraeki il pglekgaeg ik ngrac `i sirei `i pgtikjecs qui pcsc pgr jc`c ukg `i lgs semueiktis jgkhuktgs `i `ctgs8 c)  (-3,3),(3,0) d)  (-4,4),(2,-3),(4,3) j)  (-3,-3),(2,4.9),(3,3),(4,-3) `)  (-3,-3),(2,2),(3,4),(4,9) Ysck`g 8 pglekgaeg `i Lcmrckmi, Kiwtgk, aåtg`gs actrejeclis. >4.  Is jredc ukc ngraulc `i ektirpglcjeúk lekicl qui cprgxeai sik(x) ik il ektirvclg 2   x        / 0 , usck`g lgs vclgris `i x12 y  x       / 0 . >:.  Zcdeik`g qui

acx

 n  ''  



2.:64=  ik 2   x        / 0 , pri`emc il irrgr aãxeag

pgsedli `i lc

ektirpglcjeúk lekicl `itiraekc`c ik il prgdliac cktiregr >0.  c)Isjredc il pglekgaeg y(x) ik ngrac `i sirei `i pgtikjecs chustc`g c lgs semueiktis puktgs `i `ctgs8 E 3 4 : 0 V 2 2.9 4.2 4.9 U 3.43 3.:4 3.29 2.5= d) Ivcluå lc `irevc`c ik x13.=9 >9. c)Isjredc lc ektirpglcjeúk ektirpglcjeúk `i Lcmrckmi qui pcsc c trcvås trcvås `i lgs semueiktis puktgs ` `ii `ctgs8 V 2 2.0 2.6 3.4 U 3.2 3.053 4.449 :.:42 d) Jgkgjeik`g  n  '''' ''''((2.>) 2.>) 3.644 3.644 isteai il irrgr ik x12.4, 2.>, 3.2  



j) @c`g il fijfg `i qui lc tcdlc `i `ctgs si gdtuvg `i  n ( x)   i x , ivclui il irrgr `i lc ngraulc `i ektirpglcjeúk ik x12.4,2.>,3.2 ai`eckti8 i( x)  n ( x)  m ( x)  i x  m ( x)  

 

>>. Chusti  x.sik( x ) ik

2   x        / 4 , jgk il pglekgaeg `i ektirpglcjeúk `i Lcmrckmi `i

gr`ik 0, utelezck`g puktgs iqueispcjec`gs. Jcljuli il irrgr `i jc`c ngraulc `i ektirpglcjeúk ik jc`c ekjriaiktg `i    / 3>   >=. Isjredc lc ngraulc `i ektirpglcjeúk `i Lcmrckmi chustc`c c8 V U

2.9 U3 

3.2 U4 

3.9 U: 

4.2 U0 

@gk`i yo sgk vclgris `isjgkgje`gs. Isjrádclg ik sirei `i pgtikjecs y `i`uzjc lc preairc `irevc`c `il pglekgaeg. >6. Cprgxeai8

 y



3   x 3  4 x  : x

4

ik

y ivclui simøk il irrgr 8 i( x)



2   x  9 ai`eckti lc ektirpglcjeúk `i Lcmrckmi `i gr`ik 0 y



m ( x) . Rrgji`c semueik`g lgs semueiktis pcsgs8 c)

@itiraeki lgs puktgs d) Isjredc lc ektirpglcjeúk `i Lcmrckmi j) Jcljuli il irrgr pgr jc`c ekjriaiktg `i 2.4 ik “x‑.  >5. ·Rcrc qui tepgs `i kg`gs il pglekgaeg `i ektirpglcjeúk `i Lcmrckmi ri`uji su irrgr7 (prgdliac >6) =3. simøk Il piktúxe`g `i eúk `eketrúmikg `eketrúmi kg mcsigsg purg ricjjegkc ik uk ektiraetikti ukc ricjjeúk ricjj queaejc. Zi jcljulc lc jgkjiktrcjeúk `iricjtgr Riktgxe`g `i `eketrgmikg ik jeirtgs ekstcktis, gdtikeik`g lgs semueiktis `ctgs8 Ze lg P (s) 2 422 022 >92 3322 3522 4:22 J 9.9 9.20 0.:> :.09 4.:= 3.:4 2.=3 tikiags ik il ricjtgr uk teiapg aãxeag `i :9 aekutgs (4322 simuk`gs), ·juãl is lc jgkjiktrcjeúk `i piktúxe`g `i `eketrúmikg qui qui`c sek ricjjegkcr7 =4. Isteai il lgmcretag kcturcl `i 32 pgr ai`eg `i lc ektirpglcjeúk lekicl. Ektirpgli iktri lgm61 2.52:2522 y lgm3413.2=53634 Ektirpgli ikti lgm512.5904049 y lgm 3313.203:54= Rcrc jc`c ukc `i lcs ektirpglcjegkis jcljuli il irrgr rilctevg pgrjiktucl jgk dcsi ik il vclgr `i jcljulc`grc. =:. Chusti uk pglekgaeg `i ektirpglcjeúk `i Ki Kiwtgk wtgk `i simuk`g gr`ik pcrc pcrc isteacr il lgm32, jgk lgs `ctgs `il prgdliac cktiregr ik x16 , 5 y 33. Jcljuli il irrgr rilctevg pgrjiktucl vir`c`irg. =0. Chusti uk pglekgaeg pglekgaeg `i ektirpglcjeúk ektirpglcjeúk `i Kiwtgk `i tirjir tirjir gr`ik pcrc isteacr lgm32 jgk lgs `ctgs `il prgdliac 3:. =9. Isteai il lgmcretag 9 usck`g ektirpglcjeúk lekicl c) ektirpgli ikti lgm 012.>242> y lgm >12.==6393: d) ektirpgli iktri lgm 0.912.>9:4349 y lgm 9.9 2.=02:>4= j) ik jc`c ukc `i lcs ektirpglcjegkis, jcljuli il irrgr rilctevg pgrjiktucl jgk dcsi ik il vclgr vir`c`irg. Ysi ektirpglcjeúk `i Lcmrckmi =>. Chusti uk pglekgaeg `i ektirpglcjeúk `i Kiwtgk `i simuk`g mrc`g pcrc isteacr lgm 9 usck`g lgs `ctgs `il prgdliac =9.

==. Jgk lgs `ctgs

 

x 3 4 4.9 : 0 9 N(x) 3 9 = 6 4 3 Jcljuli n(:.0) usck`g ektirpglcjeúk `i Kiwtgk `i mrc`g 3 c : =6. @iscrrglli splekis juc`rãtejcs pcrc lgs preairgs 9 `ctgs `il prgdliac : y pri`emc n(:.0 )y n(4.4) =5. @iscrrglli splekis jødejcs pcrc lgs semueiktis sem ueiktis `ctgs8 y x 3 4 : 9 > N(x) 0.=9 0 9.49 35.=9 :> jcljuli n(0) y n(4.9) 62. Gdtikir il pglekgaeg `i lcmrckmi `i lgs semueiktis `ctgs8 V 3 4 : 0 9 N(V) 4.3>=50 3.63>:6 4.26564 4.:4035 4.40>2= N(V) 4.003:= 3.060:> 4.2:344 3.5::9= 3.69909 N(V) 4.=545: 4.6939: 4.545>9 4.6=32> 4.6939: N(V) 4.9:52: 4.==:0 4.>5946 4.=9:6= 4.==:0 63. Lgs tiragstctgs si usck pcrc ai`er lc tiapircturc `i lgs juirpgs. Il prekjepeg `i su nukjegkcaeiktg si dcsc ik il jcadeg `i lc Tisestikjec jgk lc tiapircturc. Rcrc ai`er su tiapircturc, lgs ncdrejcktis prgviik cl ekstruaiktg `i ukc jurvc `i jcledrcjeú jcledrcjeúk k `i tiapircturc vs risestikjec. Ze si ae`i risestikjec, risestikjec, pui`is fcllcr lc tiapircturc. Yk ncdrejckti `i tiragstctgs fcji vcrecs gdsirvcjegkis lcs qui si risuaik ik lc tcdlc8 T (gfa) 3323.2 533.: >:>.2 093.3 P(²J) 49.33: :2.3:3 02.342 92.346 @itiraekcr lc tiapircturc jgrrispgk`eikti jgrrispgk`eikti c =90.6 gfas usck`g uk pglekgaeg `i Lcmrckmi `i preair gr`ik. Ivcluå cfgrc lg aesag usck`g pglekgaegs `i ektirpglcjeúk `i simuk`g y tirjir gr`ik. 60. Cyu`c`g pgr lc ektirpglcjeúk `i Kiwtgk, fclli il vclgr `i “x‑ qui jgrrispgk`i c n(x)12.69 pcrc lgs `ctgs tcdulc`gs8 V 2 3 4 : 0 9 n(x) 2 2.9 2.6 2.5 2.5033=> 2.5>39:6 Gdsirvi qui lgs vclgris `i lc tcdlc si mikircrgk jgk lc nukjeúk  n ( x)  x 4 / (3  x 4 )   Jcljuli il vclgr vir`c`irg y il irrgr rilctevg pgrjiktucl. 69. @iscrrglli splekis juc`rãtejgs y jødejgs pcrc lgs `ctgs8 V 3.> 4 4.9 :.4 0 0.9 n(x) 4 6 30 39 6 4 y prgkgstequi n(:.0) y n(4.4) 6>. Jcljuli lc pcrãdglc qui pcsc pgr lgs tris ølteags puktgs `i lc tcdlc `il ihirjejeg cktiregr c) Actrejeclaikti Actrejeclaikti d) Ysck`g Lcmrckmi, Lcmrckmi, 6=. Iaplii lc pgrjeúk `i lc tcdlc `i vcpgr qui si `c pcrc il cmuc supirjcliktc`c c 422 ARc, pcrc8 c) Ikjgktrcr lc iktrgpác jgrrispgk`eikti “s‑ pcrc uk vgluaik ispijenejg “v‑ `i 2.326 a:/om jgk ektirpglcjeúk lekicl d) Ikjgktrcr lc aesac iktrgpác jgrrispgk`eikti cl usg `i ektirpglcjeúk juc`rãtejc, juc`rãtejc, j) Fcllcr il vgluaik jgrrispgk`eikti jgrrispgk`eikti c ukc iktrgpác `i >.> jgk iaplig `i ektirpglcjeúk ekvirsc. ^ (a:/om) 3.> 4 4.9

 

Z (ol/om.O)

>.030=

>.909:

>.=>>0

65. Lc tcdlc `i vclgris `c`c c jgktekucjeúk, jgrrispgk`i cl vclgr `i 8

Z ( x)

 x     si  k  t 4  2 4 

`t , 

pcrc `eniriktis vclgris `i “x‑8  x 2 2.20 2.26 2.34 2.3> 2.42 v(x) 2 2.2222: 2.2224> 2.2225 2.22430 2.22035 Gdtikir uk pglekgaeg ektirpglckti `i Kiwtgk `i mrc`g 9 pcrc Z(x) , luimg jcljulcr Z(4) y isteacr su irrgr. 52. Zi `ck c jgktekucjeúk lgs `ctgs `i tiapircturc (²J) iktri lcs 6822ca y lcs 6822pa `il 4: `i gjtudri `il 4234 ik ukc jeu`c`. Isteacr lc tiapircturc c lcs 9pa Fgrc 6822c.a 34822a 0pa 6pa Piapircturc :2 := 0: :6 53. Il pcmg aiksucl aiksucl pgr ukc fepgtijc c :2 cógs `i $322,222. pcrc `gs tcscs `i ektirås `eniriktis istc `c`g ik lc tcdlc semueikti. Ysi ukc ektirpglcjeúk lekicl pcrc isteacr il pcmg p cmg aiksucl jgrrispgk`eikti jgrrispgk`eikti c ukc tcsc `i ektirås ektirås 6.49% cl cóg. Pcsc `i ektirås ckucl eo 

=%

32%

Rcmg aiksucl Co1n(eo)

$>>9.:2

$6==.9=

54. Zupgkmc qui si `espgki `i `gs `ctgs c`ejegkclis sgdri lc tcsc `i ektirås ektirås y il pcmg aiksucl ik il prgdliac cktiregr. Lc kuivc `ctc , si risuai ik lc tcdlc semueikti. Isteacr il pcmg aiksucl pcrc 6.49% ckucl usck`g ukc ektirpglcjeúk `i simuk`g gr`ik (usi ukg `i lgs `gs puktgs c`ejegkclis pcrc istg). Pcsc `i ektirås =% 32% 6% 5% ckucl eo  Rcmg aiksucl $>>9.:2 $6==.9= $=::.=> $620.>4 Co1n(eo)

 

KGPC8 Zuder il crjfevg `emetcl cl culc vertucl (risuiltg ik Actlcd ) FCZPC IL huivis :2 @I ACUG y iktrimcrlg ik násejg il veirkis :3 `i acyg pgr lc acóckc acóckc jgk su `ilimc`g `ilimc`g/c. /c. K²

CRILLE@GZ U KGADTIZ

Ihirjejegs csemkc`gs

3

CMYITG TG@TEMYIX, ACTEC NITKCK@C

3

95

4

DITKCDI TYEX, @CKEIL

:

>3

:

JFCRE ZYUG, EZCECZ CL@G

9

>:

0

@YTCK TE^ITC, ACTU JIJELEC

=

>9

9

IZREKGXC TIUKCNCTHI, RCPTEJO LYEZ

32

=:

>

NEMYITGC ^CLITECKG, @CK HCTG@

34

=>

=

MCDTEIL TG@TEMYIX, HCOILEKI ZPFINCKU

4

=5

6

FYCACK YAITIZ, JTEZPECK ACTJILG

30

>2

5

LGDCPGK PCTCXGKC, MTIJEC EZCDIL

3=

>>

32

SYEZRI C^IK@CÓG, OIL^EK AEZCIL

42

>6

33

TCAETIX CLDITPG, CKMEI LEXDIPF

0

=4

34

TCAETIX JCDILLG, ACTEC MTCXEC

5

>4

3:

TCAGZ AGTCLIZ, HGEJI UGTILE

49

=0

30

ZCL^C@GT PGTEDEG, RCYL OIKKI@U

>

63

39

ZCL^CPEITTC JCRJFC, OCPITEK

3>

>0

3>

ZEL^ITC MCTJEC, OCPPUC TGZZJILUK

:2

==

3=

YTECTPI DCTTCXC, OCPFITEK LGYT@IZ

33

62

36

^IT@I TGDLIZ, CKUILC DTELLUPF

36

60

35

AGTCK REZJG HYLEG JIZCT

4=

>=

42

CLECMC XIMCTTC, GLEADIT GJPC^EG

3:

6>

43

DCLPCXCT ACTECKG, CLIVEZ @EG]EL

4:

6=

44

FYCACK JCT@IKCZ, PFIG CLIZZCK@TG

:3

>5

4:

LEHCTXC TCNCELI, UIEZGK UIKJG

35

69

40

LLCKC CKCUC, UIE@E ACULEK

40

=3

49

ACJFJG FYCACK, ^E@CL NITKCK@G

4>

64

4>

ACTC^E RITIX, CKPFGKU ACKYIL

46

=9

4=

RCLAC ACMCTEÓG, JIZCT TIKCPG

44

=6

46

RGTPELLC JCTTCZJG, CKCPGLLU IYLIT

92

65

45

ZITCNEK NCYZPEKG, IZPIT

:>

52

:2

^CTMCZ NLGTIZ, NTCKJEZ ZPCTLUK

02

53

:3

^ILC HCTCAELLG, ZYAAIT KCEK

9>

54