Grupo 4 - Ejercicios de Funciones
February 27, 2023 | Author: Anonymous | Category: N/A
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_LK^OT]K@E@ LEMKBLEH @O P_ADO] NEM_HPE@ @O MKOLMKE] @O HE ]EH_@ O]M_OHE @O OLNOTAOTKE
M_T]B7 Ohoaoltbs `o Aetoaåtkme @BMOLPO7 Tukz Mfemýl Olcohs Gos÷s POAE7 Nulmkblos, @baklkb `o relcb y ab`ohbs nulmkblehos
KLPOCTELPO]7 ✝
✝
Meaemfb Mbrlogb Ele Aeráe Hýpoz Cermáe Letfehy Todome
✝
W÷õkce Merresmb Aermb
Puados ” Zor÷ 4:45
>5. MB]PB @O NEDTKMEMKÝL supblce quo oh mbstb tbteh `o nedrkmemkýl `o ulk`e`os e`os `o ul `otorakle`b `otorakl e`b prb`umtb prb`u mtb os M(q) M(q) akh `ýh `ýheros, eros, `bl` `bl`o o ‘q ‑ ulk` M(q) 1 :.:5q + :.;q +4
E. Mehmuh Mehm uher er oh mb mbst stb b `o ` o nedrk ned rkmem memkk ýl `o 5: ulk u lk`e` `e`os. os.
1 :,:5 :,; 4 1 :, :,:5 :5 5: 5: :,; 5: 5: 4 1 5 4 Tospuoste7 oh mbstb `o nedrkmer hes 5: ulk`e`os nuo `o 54 akh `ýheros.
D. Mehmuh Mehmuh er oh mbstb `o nedrkm emkýl `o he `ëmkae ulk`e`.
1 , , ; 1 :,: ,:55 ; :,;; 4 1 5:,;5 1 54 5:,;5 1 5.:; Tospuoste7 oh mbstb `o he 5: ae ulk`e nuo `o 5.:; akh `o `ýheros.
oh mbst mbstb b tbteh ol `ýheros `o he hess >4. MB]PB @O NEDTKMEMKÝL supb lce quo oh ulk`e`os q `o nedrkmemkýl `o mkorte aetorke os os `e`b pb r he nu lmkýl7 M(q) 1 q = ” ” =:q 4 + 0::q + ?::
E. Mehmuh Mehm uho o oh mmbs bstb tb `o nnedr edrkm km emkýl emk ýl `o 4: ulk u lk`e` `e`os. os.
M (4:) 1 4:= - =:(4:)4 + 0::(4:) +?:: M (4:) 1 6:::- 54:::+6::: +?::10?::
Tospuoste7 Oh mbstb `o nedrkmemkýl `o 4: ulk`e`os nuo `o 0?:: `ýheros.
D) Mehmuho Mehmuho oh mbstb `o nedrkmemk nedrkmemkýl ýl `o he vkcësk vkcëskae ae ulk`e`.
M (5;) 1 5;=- =:(5;)4 +0::(5;) +?:: 1 0?:: M (5;) 1 >6?; - 5:6=:+3>:: +?:: 1 054; M (4:) ” M(5;) 1 0?:: - 054; 1 =35
Tospuoste7 oh mbstb `o nedrkmemkýl `o he vkcëskae ulk`e` nuo `o =35 `ýheros.
oh l÷aorb `o tredege`bros>=. MB]PB @O @K]PTKD_MKÝL supb lce quo oh fbres roquork`b pere `kstrkdukr luoves cuáes tohonýlkmes eh x% `o hbs fbceros ol ol mkorte mbaulk`e` rur eh o ostå stå `e`b pbr he nul mkýl7
S(x) 1 ∔
E. ²Muåh os oh `b `bak aklk lkb b `o ` o he nu nulm lmkk ýl S2
= : : 1 : 1 =:: Tospuoste7 @n ℑ {=::}
D. ²Zere ²Zere quë vehbros S(x) tkolo ule (x) `o kltorprotemkýl kl torprotemkýl pråmtk pråmtkme me ol osto mbltoxtb2
: ≠ ≠ 4;; Zbr ogoaphb7 so ho oltroc oltrocere ere hes cuáes cuáes tohonýlkmes eh 0: % `o hbs fbc fbceros eros
•
1
>:: 0: =::0:
1
40::: 40:: 1 1 ;4.= 4>: 4>
Tospuoste7 so lomosktel 40:: fbres y 4> tredege`bros.
M. ²Muåltes ²Muåltes fbres pbr tredege`bros luostr luostrbs bs nu nuorbl orbl roquork` es pere `kstrkdukr luoves cuáes tohonýlkmes eh prkaor ?:% `o hbs fbceros2
>::?: =::?:
1
1 =:::: 1 54: 4?: Tospuoste7 so lomosktel 54: fbres pbr tredege`br.
@.
²M ²Muåltes uåltes fbres `o tredegb nuorbl roquork`es pere `ks `kstrk trkdukr dukr luoves
cuáes tohonýlkmes e he mbaulk`e` mbaulk `e` oltore2 oltore2
1 1
>::5:: =::5::
>:::: 1 =:: 4::
Tospuoste7 so lomosktel =:: fbres pbr tredege`br.
O. ²Uuë ²Uuë pbrm oltego `o hbs fbceros fbc eros ol he mbaulk `e` fedáe romkdk`b l uoves cuáes tohonýlkmes pbr oh tkoapb 5?: tredege`br-fbres tredege`br-fbr es fedáe fedáel l sk`b c este`es2
>:: =:: 5?: =:: 1 >:: 0?::: 5?: 1 >:: 0?::: 1 3?: > : 1
5?: 1
Tospuoste7 oh >:% `o hbs fbceros ol he mbaulk`e` fedáe romkdk`b luoves cuáes tohonýlkmes.
ostu` kb `o he onkmkolmke `oh >0. ONKMKOLMKE ONKMKOLMKE @O HB] PTEDEG E@BTO] _l ostu` turlb tur lb `o he ae aeõele õele ol ule mkorte nådrkme nådrkm e kl`kme quo ul tredege`br prba prbao`kb o`kb quo hhoce hh oce eh eh ttredegb redegb e hes 67:: E EA A fedrå olseadhe`b N(x) 1 -x 4 + >x 4 + 5?x 5?x Pohovksb Pohovksbros ros pbr x fbr fbres es aås ter`o.
E. ²Muåltbs ²Muålt bs gu ocb ocbss fedr f edrå å ab ablt lte`b e`b teh tr tredeg edege`b e`brr e hes 5:7:: E E.A.2 .A.2 Yp ks te7 E hes 5: 5:7:: 7:: E.A, x1 4.Q
N(4)1 -4= +>(4)4 + 5?(4) N(4)1 -6 + 40 + =: N(4)1 0> Tospuoste7 @kmfb tredege`br olseadhý 0> guocbs e hes 5:7:: E.A
D) ²Muåltbs ²Muåltbs guocbs g uocbs olseadherå ul ttredege`br redege`br `o osto tkpb oltro oltr o hes ; ;7:: 7:: e ea a y hes 5:7:: ea2
N(5) 1 -5= + >(5)4 + 5?(5) N(5) 1 -5 + > + 5? N(5) 1 4: Tospuoste7 _l tredege`br `o osto tkpb olseadhere 4: gucuotos oltro hes ;7:: ea y hes 5:7:: ea
>?. KLA_LKWEMKÝL supblceabs quo, `urelto ul prbcreae lemkbleh pere klaulkzer kla ulkzer e he pbdhemkýl m bltr bltre e ule `otorakle`e nbrae nbra e `o crk crkpo, po, hbs nulmkblerkbs `o se sehu` hu` p÷d hkme olmbltrerbl quo oh mbstb `o he klbmuh emkýl x% `o he pbdhemkýl ore eprbxkae`eao eprbxka e`eaolto lto
Akhhblos os `o `ýheros. M(x) 1 ∔ Akhhbl
E. ²Muåh os oh `b `bak aklk lkb b `o ` o he nu nulm lmkk ýl M2
1
∔
4:: ” x 1 : x 1 4:: Tospuoste7 @m 1 ℑ {4::} 4::}
D. ²Zere ²Zere quë vehbros `o x tkolo t kolo M( M(x) x) ule kl torprotemkýl torprotemký l pr pråmtkme åmtkme ol osto mbltoxtb2
: ≠ ≠ 5;;
M. ²Muåh ²Muåh nuo oh mbs mbstb tb `o ` o he klbmuh klbmuhemkýl emkýl `oh p rkaor ?:% `o he pbdh pbdhemkýl2 emkýl2
1
5?: 4::
1
5?: ?: 3?:: 1 1 ?: 4::?: 5?:
Tospuoste7 oh mbstb pere klbmuher eh prkaor ?:% `o he pbdhemkýl nuo `o ?: akhhblos `o `ýheros.
@. ²Muåh ²Muåh nuo oh mbs mbstb tb `o he klb muhemký muhemkýl l `oh socul` socul`b b ?:% `o he pbdh pbdhemkýl2 emkýl2
1
5?: 4::
5?: 5:: 5?::: 1 4:: 5:: 1 5:: 1 5?: 15?:?:15:: Tospuoste7 oh mbstb `o klbmuher eh socul`b ?:% `o he pbdhemkýl nuo `o 5:: akhhblos `o `ýheros
O. ²Uuë ²Uuë pbrmoltego pbrm oltego `o he pbdhemkýl pbdh emkýl fedáe sk`b vemul vemule`e e`e muel`b so cesterbl =3,? =3 ,? akh akhhbl hblos os `o `ýheros2
1
5?: 4::
=3.? 1
5?: 4::
=3.? 4:: 1 5?: 3?:: =3.? .? 1 563.? 3.? 3?:: 1 563.? 0 : 1 Tospuoste7 so fedáe vemule`b oh 0:% `o he pbdhemkýl.
>>.MEADKB @O POAZOTEP_TE ]upblceabs quo ‘t‑ fbres aås ehhå `o he >>.MEADKB
ao`kelbmfo, he toaporeture ol Akeak Nuo
M(t) 1 - + 0t + 5: cre`bs Mohskus.
E. ²Muåh ore or e he t oaporet oap oretur ure e e hes 47:: E.A.2
He toaporeture ol Akeak `e`e pbr he nulmkýl7 M(t)1 ∔ + 0t + 5:
M (4) 1∔ + 6 + 5:
M (4) 1 M (4) 153.== ºM TO]Z_O]PE7 He toaporeture e hes 47:: E.A. E. A. os 53.==ºM.
D. ²Ol ²Ol mu åltb `k `ksakl sakluyý uyý he toaporeture oltro hes >7:: y hes ;7:: ZA ZA2 2
He toaporeture oltro hes >7:: y hes ;7:: p.a @os`o hes >7:: ZA t156 y e hes ;7:: Z.A t145 P 1 M(45) - M(56) P 1 4:.?-46 P 1 ∔3,? TO]Z_O]PE7 He toaporeture `ksakluyo ol 3,? cre`bs
AKOLPB B @O HE H E ZBDHE ZBD HEMKÝL MKÝL ]o ostkae quo t eõbs e pertkr `o efbre, he >3.MTOMKAKOLP >3.MTOMK
pbdhemkýl `o ule `otorakle`e mbaulk`e` sudurdele sorå
Z(t) 1 4: ∔ + akhos
E. ²Muåh s orå hhe e pb pbdh dhemk emkýl ýl `o he h e mb mbau au lk lk`e` `e` `oltr `ol trb b` `o o ; eõb eõbs2 s2
Z (;) 1 4: -
+
1 4: ” :.> 1 5;,0 akh
TO]Z_O]PE7 `oltrb `o ; eõbs he pbdhemkýl `o he mbaulk`e` sorå `o 5;0:: porsbles
D. ²Muåltb ²Muåltb euaolterå he pb pbdhemkýl dhemkýl `urelto `urelt o oh oh eõb ;lb2
Z (6) 1 4: ∔ + 1 4: ” :.3 1 5;.= akh
Z (;) 1 4: -
+
1 4: ” :.> 1 5;,0 akh
Z (;) ∔ Z (6)
5;0::: ” 5;=::: TO]Z_O]PE7 @urelto oh eõb lbvolb he pbdhemkýl euaolterå ehro`o`br `o 5.::: porsbles.
M. ²Uuë pese mbl Z(t) e ao`k`e quo ‘t‑ so femo aås y aås crel`o2
Z(t) so emorme e 4:, b 4:.::: porsbles. Osmrkdkr ogormkmkbs7 hes rospuostes veráel.
>6. Z]KMBHBCÁE OVZOTKAOLPEH Zere ostu`ker he vohbmk`e` e he quo eprol`ol
hbs elkaehos, ul ostu`kelto `o pskmbhbcáe roehkzý ul oxporkaoltb ol oh quo ule rete nuo olvke`e ropotk`eaolto e trevës `o ul hedorkltb `o hedbretbrkb. ]upblceabs quo oh tkoapb lomoserkb pere quo he rete etrevkoso oh hedorkltb ol he olëskae pruode nuo eprbxkae`eaolto
P(l) 1 = + aklutbs
He nýrauhe t(l) roprosolte oh tkoapb quo ho tbae e ule rete etrevoser ul hedorkltb mbl ‘l‑ kltoltbs.
E. ²Muåh os oh `b `bak aklk lkb b `o ` o he mb mbls lstt ru rumm mmký ký l2
Oh `baklkb `o N os ∆ ℑ, l ≪ :.
D. ²Z ²Zere ere quë vehbros `o l P( P(l) l) tkolo skclknkme`b skclkn kme`b ol oh mbltoxtb mbltoxt b `oh oxporkaoltb pskmbhýckmb2
l ≯ :.
M. ²M ²Muåltb uåltb tk oapb ho tbaý tba ý e he rete etrevoser etrevoser oh hedorkltb ol o ohh olseyb =2
t(=) 1 =+ t(=) 1 =+0 t(=) 1 3 TO]Z_O]PE7 ol oh olseyb = ho tbaý 3 aklutbs e he rete etrevoser oh hedorkltb
@. ²Ol ²Ol quë qu ë olseyb olseyb he rete prkaorb prka orb etrevosý oh hedorkltb ol 0 aklutb aklutbss b aolbs2
n (x) 1 = + n (x) 1 0 TO]Z_O]PE7 he rete etrevosý oh hedorkltb ol 0 aklutbs olseyb
O. ]oc÷l ]oc÷l he nul mkýl P, ² ²Uuë Uuë peserå peserå mbl oh tkoapb lomoserkb pere quo hhe e rete etreso oh oh hedorkltb h edorkltb e ao`k` e quo euaolte o ohh l÷ aorb `o pruodes2 pr uodes2 ²Z ²Zb`r b`rå å ehcule voz he rete etrevoser etrevoser oh hedorklt hedorkltb b ol aolbs `o = aklu aklutbs2 tbs2
Mbab l
∜, n(l)
=.
]ELC_ÁLOB B Hbs dkýhbcbs `oh nhugb selcuálob fel olmbltre`b quo he >;. NH_GB ]ELC_ÁLO
vohbmk`e` `o he selcro ol ule ertorke os ule nulmkýl `o he `kstelmke `o he selcro `os`o oh ogo moltreh `o he ertorke `o emuor`b mbl he hoy `o Zbksovkhho, he vohbmk`e` (ol moltáaotrbs pbr socul`b) `o he selcro quo os r moltáaotrbs `os`o oh ogo moltreh `o ule ertorke ostå `e`e pbr he nulmkýl ](r) 1M(T4-r), `bl`o M os ule mblstelto y r os oh re`kb `o he ertorke. ]upblceabs quo, pere ule `otorakle`e ertorke, M- 5,3> x 5: y T1 5,4 x 5:Moltáaotrbs. ](r) 1 M (T4 ∔ r4) 1 5.3> Ó 5:? (5.44 Ó 5:∔0 ∔ r4)
E. Mehmuh Mehm uher er hhe e voh vohbm bm k` e` ` `o o hhe e sel selcr cro o ol oh ogo molt m oltreh reh `o oste os te ert ertork orke. e.
] (:) 1 (5.3> Ó 5:?) (5.00 Ó 5:∔0)
1 4?.=00ma/soc. TO]Z_O]PE7 He vohbmk`e` `o he selcro ol oh ogo moltreh `o oste ertorke os 4?.=00 ma/soc.
D. Mehmu Mehmuher her he vohbm vohbmk`e` k`e` `o he selcr selcro o e akte` `o meaklb oltro he pero` `o he ertorke y oh ogo moltreh.
] (:.> Ó 5:∔4) 1 5.3> Ó 5:? (5.00 Ó 5:0 ∔ :.>4 Ó 5:∔0) 1 5.3> Ó 5:? (5.:6 Ó 5:0) 1 5;.::6 ma/soc. TO]Z_O]PE7 he vohbmk`e` `o he selcro e akte` `o meaklb oltro he pero` `o he ertorke y oh ogo moltreh os 5;.::6 ma/soc.
3:. MBHBMET _L BDGOPB OL AB^KAKOLPB. AB^KAKOLPB . Zbskmkýl `o ul bdgotb ol abvkakoltb abvk akoltb s o fe `oge`b meor meor ule dbhe `os`o hb ehtb `o ul o`knk o`knkmkb. mkb. ]u ehture (ol pkos) `ospuës `o t socul`bs os `e`e pbr he h e nulmk nulmkýl ýl F(t) 1-5> + 4?>. E. ²Muåh os h e eht ehtur ure e `o he h e db dbhh e `os `ospu puës ës ` `o o 4 socul soc ul`b `bs2 s2
f (4) 1 - 5> (4 + 4?> 1-5>(0) + 4?> 14?>->0 15;4 TO]Z_O]PE7 He ehture `oh bdgotb os `o 5;4 pkos sbdro oh suohb. D. ²Uuë ²Uuë tel hogbs vkegerå he dbhe `ur elto o ohh ttormor ormor socul`b2 socul`b 2
|f (4) f (=) 1 |5;4 f (=) 15;4(5>(= +4?>)) | 1|5;4-(4?>-500) | 1|5;4-554| 1|6:| 16: TO]Z_O]PE7 Oh bdgotb vkegý 6: pkos `urelto oh tormor socul`b. M. ²Uuë ²Uuë ehture ehtur e tkolo oh o`knkm kb2
F (:) 1 - 5>(:)4+4?> 14?> TO]Z_O]PE7 Oh o`knkmkb tkolo 4?> aotrbs `o ehture @. ²Muål`b ²Muål`b cbhpoerå cbh poerå he dbhe eh suohb2
:1 5> + 4?> :1 5> ”” 4?> 4?>1 5> 1
5>1 01 t
35. OMBHBCÁE KL]_HET Bdsorvemkblos ombhýckmes `o kshes auostrel quo, ol ule kshe `o åroe `o ule akhhe akhh e mue`re`e, mue`re`e, o ohh l÷ l÷aorb aorb prbao`kb pr bao`kb ` `o oo ospomkos spomkos elkaehos os eprbxk ae`eaolto kcueh e7 s (E) 1 4 4.; .; =∗E. E. Ol pr bao`k ba o`kb, b, ²Mu ²Muålt åltes es ospom os pomkos kos elkaeh elk aehos os os ospor poreráes eráes olm olmbl bltr trer er ol ul ule e kshe ksh e `o å åroe roe `o 6 akh akhhes hes mue`re`es2
] (6) 1 4.; =∗6 1 4.; Ó 4 1 ?.6 TO]Z_O]PE7 @e`b quo oh l÷aorb `o ospomkos `odo sor ul oltorb, so osporeráe olmbltrer eprbxkae`eaolto > ospomkos. D. ]k ]5 os oh oh l÷ l÷aorb aorb prbao`kb pr bao`kb `o ospo ospomkos mkos ol ule ksh kshe e `oh åroe E y ]4 os oh l÷aorb prba prbao`kb o`kb `o ospomkos ol ule kshe ks he `oh åroe 4E, ²M ²Muåh uåh os he rohemkýl oltro ]5 y ] 42
]5 1 4.; =∗E y ]41 4.; =∗4E ]4 1 4.; =∗4 =∗E ]4 1 =∗4 (4.; =∗E) ]4 1 =∗4 ]5 TO]Z_O]PE7 He rohemkýl oxkstolto oltro ] 5 y ]4 os quo ]4 os kcueh e he reáz m÷dkme `oh `bdho `o ] 5 M. ²Uuë ²Uuë tel crel`o `odo sor ule ul e kshe pere tolor ul prba prbao`kb o`kb `o 5:: ospomkos elkaehos2
5:: 1 4.; =∗E 1 =∗E .
( . )= 1 (=∗E)= TO]Z_O]PE7 He kshe Lomoskte ul åroe `o eprbxkae`eaolto 05,::4 akhhes mue`re`es pere pb`or tolor ul prbao`kb `o 5:: ospomkos
@OL]K@E@ K@E@ @O ZBDHE ZBD HEMKÝL MKÝL Hes bdsorvemkblos `o `olsk`e` pbdhemkbleh 34. @OL] suckorol suck orol quo, pere hbs aeaánorbs fordávbrb s, oh l÷aorb `o elkaehos L pbr .
ikhýaotrb ikh ýaotrb mmue`re`b ue`re`b so puo`o ostkaer ao`kelto he nýrauhe nýra uhe L1 L1 . `bl`o a os he aese ao`ke ao`ke `oh elkaeh ol ikhbcr ikh bcreabs. eabs.
E. ]upb lk lkol` ol`b b q uo oh ehmo ehm o prba pr bao`k o`kb b ol ul ule e ros rosorv orve e per pertktk mu muher her tktkolo olo u ule le aese `o =:: =:: ikhb creabs, epr eprbxk bxkae`eao ae`eaolto lto ²Muå ²Muåltbs ltbs ehmos osporeráe osporeráess olmbltrer pbr ikhýaotrb mue`re mue`re`b `b ol he rosorve2 rosorve2
a1 =:: .
L1 . .
L1\ . .
L1. 1 5.04 TO]Z_O]PE7 so ospore olmbltrer 5.04 ehmos pbr ikhýaotrb mue`re`b.
D. _tkhkze _tkhk zel`b l`b ost oste e nýrau nýrauhe, he, so o ostk stkae ae quo fey aolbs `o ul elkaeh `o ` o ule `otorakle`e ospomko pbr ikhýa ik hýaotrb otrb mue`re`b. mue`r e`b. ²Uuë ²Uuë tel crel`o puo`o sor oh elkaeh prb ao`kb `o oste o ospomko2 spomko2 . :.; 1 .
a:.3= 1
. .
a:.3= 1 5:5.= a 1 :.3=∗5:5.= a 1 ??; ikhbcreabs.
TO]Z_O]PE7 Oh posb prbao`kb `o `kmfb elkaeh puo`o sor eprbxkae`eaolto ??; ikhbcreabs
M. _le ospomko `o aeaánorb crel`o cr el`o tkolo oh `b `bdho dho `o ` o aese ao`ke quo ul e socul`e ospomko. ]k ]k ul ule e rosorve pertk pertkmuh muher er mblt mbltkolo kolo 5 5:: :: e elkaehos lkaehos `o hes ospomkos aås crel`os, ²Muåltbs ²Muåltbs elkaehos `o hes ospomkos aås poquoões osporeráess olmbl osporeráe olmbltrer trer ehhá2
5:: 1
;5.4 4.
4. 1
;5.4 5::
4. 1 :.;5 :.;544
1
;5.4 :.00:?.
1
;5.4 :.??
1 5>> 4 1 :.;5 :.;54.
4 1 :.665 1
:.665 4
1 :.00:?
Tospuoste7 pbr hb teltb, fedrå 55> elkaehos `o he ospomko aås poquoõe.
k apbrte`br `o menë dre dreskhoõb skhoõb ostkae 3=. @OAEL@E @OH MBL]_AK@BT ul kapbrte`br .
quo hbs mblsuak`b ros hbmehos mbapr mbaprerå erå eprbxka eprbxkae`e e`eaolto aolto U U((p ) 1 ikhbcreabs ikh bcreabs ` oh menë pbr soaele muel`b oh promk promkb b os `o p `ýheros pbr ikhbcreab. ikh bcreab. ]o o ostk stkae ae quo ol ol t soaele soaeless oh p promkb romkb `o osto menë sorå Z (t) 1 :,:0t 4 + :, :,4t 4t + 54 @ýheros pbr ikhb creab.
E. Oxpr ose hhe e `oa `oael` el`e e soaeleh soa eleh (ikhb (ik hb cr creab eabss vvol` ol`kk `b `bs) s) p pbr br oh m enë ol nulmkýl `o he nromuolmke. ,
U(t) 1 , + , +
D. ²Muåltbs ²Muåltbs ikhb creabs `o menë mbaprerål hbs mbl suak`bros suak`br os e ehh ka kapbrte`br pbrte`br `oltrb `o 5: soaeles2 soaeles2 ,
U (5:) 1 + + 1
, 1 5=.? ic/soaele.
TO]Z_O]PE7 hbs mblsuak`bros mbaprerel 5=? ikhbcreabs ol hes 5: soaeles.
M. ²Muål`b sorå he `oael`e `o menë `o =:.=3? ikhbcreabs2 ,
=:.=3? 1 .t + .t + ,
(:.:0t4 + :.4t + 54)4 1 . 1 500 1 544 Esá quo :.:0t4 + :.4t + 54 1 µ54 He reáz pbsktkve mbl`umo e t (:.:0t + :.4) 1 : b t 1 :. (Lb tolce ol muolte t 8 :.) He reáz locetkve prb`umo l÷aorbs kaecklerkbs. t 1 : efbre
nådrkm e, oh mbst mbsto o tbteh `o 30. MB]PB @O NEDTKMEMKÝL ol ule `otorakle`e nådrkme, nedrkm emkýl `o q ulk ulk`e`os `e`os `urelto he tkre`e `o prb prb`umm `ummkýl kýl ` `kerke kerke os M(q) M(q) 1 q 4 + q + ;:: ;:: `ýheros. Ol ul `áe `o tredegb tápk tápkmb, mb, q(t) 1 4? 4?tt ul k`e`os quo so nedrkmel `urelto hes hes prk prkaore aoress t fbres `o ule tkre`e `o prb`ummkýl
E. Oxpr Ox prose ose oh mb mbst stb b tbt t bteh eh `o nedr n edrkm km emkýl emk ýl ol nul n ulmk mkýl ýl `o tt..
Eh oxproser oh mbstb tbteh `o nedrkmemkýl ol nulmkýl quo`eráe7 M(q) 1 q4 + q + ;::. M(t) 1 (4?t)4 + 4?t + ;:: M(t) 1 >4?t4 + 4?t + ;:: TO]Z_O]PE7 Oh mbstb tbteh `o nedrkmemkýl ol nulmkýl `o t os 1 >4?t4 + 4?t + ;::
D. ²Muåltb ²Muåltb sso o fedrå ce ceste`b ste`b ol prb`um pr b`ummkýl mkýl eh nkl nkleh eh `o he tormore fbre2
M(t) 1 >4?t + 4?t + ;:: M(=) 1 >4?(=)4 + 4?(=) + ;:: M(=) 1 >4?(;) + 4?(=) + ;:: M(=) 1 ?>4? + 3? + ;:: M(=) 1 >>:: TO]Z_O]PE7 Eh nkleh `o he tormore fbre so fedrå ceste`b >>:: `ýheros.
M. ²Muål`b ²Muål`b hhocerå oh mbstb mb stb tbteh tbt eh `o nedrkmemký n edrkmemkýl l e $55.:: $55.:::2 :2
M(t) 1 >4?t4 + 4?t + ;:: 55::: 1 >4?t4 + 4?t + ;:: >4?t4 + 4?t ” 5:5:: 1 : Eh ephkmer he nýrauhe mue`råtkme olmbltreabs quo oh vehbr `o t 1 0 TO]Z_O]PE7 Oh mbstb tbteh `o nedrkmemkýl hhocerå e $55.::: `ospuës `o 0 fbres.
ostu`kb kb eadkolteh `o mkorte 3?. MBLPEAKLEMKÝL EPAB]NËTKME _l ostu` mbaulk`e` sud urdele sucko suckoro ro quo oh oh l kvoh ao`kb `kerkb `o ablýxk`b ablýxk `b `o merdblb merdbl b ol oh ekro so sorå rå m(p ) 1 :.0 :.0p+ p+ 5 pertos pbr a akhh khhýl ýl muel`b he h e pbdhemkýl soe `o p akh akhos. os. ] ]o oo ostka stkae e quo `oltrb `o t eõbs he pbdhemkýl `o he mbaulk`e` mbaulk `e` sorå p(t) 1 6+ :,4 t 4 akhos.
E. Oxpr Ox proser oser oh lk lkvoh voh `o abl a blýx ýxkk `b `o mer m erdb dblb lb ol oh ekr ekro o mb mbab ab ul ule e nu lm lmký ký l `oh tkoapb.
m(p) 1 :.0p + 5 y p(t) 1 6 + :.4t4 m(t) 1 :.0(6 + :.4t4) + 51 :.:6t4 + 0.4 ZZA
D. ²Muåh ²Muåh sorå o ohh lkvoh lk voh `o ablýxk ablýxk`b `b `o merdblb `oltrb ` oltrb `o 4 e eõbs2 õbs2
m (4) 1 :.:6(4)4 + 0.4 1 :.=4 + 0.4 1 0.?4ZZA TO]Z_O]PE7 oh lkvoh `o ablýxk`b `o merdblb `oltrb `o 4 eõbs sorå `o 0.?4 pertos pbr akhhýl
M. Muål`b ehmelzerå ehmelzerå oh lkvoh `o ablý ablýxk` xk`b b `o merdblb `o >. >.4 4 pe pertos rtos pb r akhhýl2
>.4 1 :.:6t4 + 0.4,
t4 1 . 1 4?, pbr hb teltb, t 1 ? eõbs TO]Z_O]PE7 Oh lkvoh `o ablýxk`b `o merdblb ehmelzerå hes >.4 pertos pbr akhhýl `ospuës `o ? eõbs
FEHHET ET OH @BA @BAKLKB KLKB77 FEHH ∔
3>.- N(x)1 ∔+
4 0 1 : 4 4 0 1 : 4 4 0 4 4 0 4 4 4 4 4 1 : 41:
4 4
1 4
∔
33.- +∔
4 = 1 : 4 = = 4 = = 1 : 4 = 5. 4 = = 51:
4 = 1 :
15
4 1 = 1 =⁀4 = 1 (5, ⁀4)
36.- N(x)14∗ , , 1 . Fehher c(n(0.6) c(n(0.6)))
1 4∗ 5 1 5.4 () 1 4∗ 4∗ 5 5.4 Muel`b 1 0 . 6
( 0.6) 1 4 4 0.65 0 .65 5.4 1 =3.06
3;.- 7 7 1 ∗ , ,1 .
.
4.= 1 4.= 4.= 5.4 1 0.:; (4.= ( 4.=) 1 4 4.= 4.= 5 1 =.?4
6:- He Pedhe 5.4 e`gulte ol he påckle 50 auostre hbs mbstbs nkgbs tbtehos eluehos prbao`kb (aetrámuhe, mubtes, ehbgeakoltb y mbak`e) pere ostu`keltos `o procre`b pbr tkpb `o klstktumkýl ol `ýheros mblsteltos (eguste`bs e he klnhemkýl) `o 4::4 pere hbs eõbs eme`ëakmbs 5;63-5;66 e 4::4-4::=. @onklkr oh ál`kmo `o mbstb `o o`umemkýl (MOK) pere ul eõb eme`ëakmb ol pertkmuher sorå he re`kb `oh mbstb nkgb tbteh pere oso eõb eh mbstb nkgb tbteh pere oh eõb eme`ëakmb deso quo nklehkze ol 5;;:. Zbr ogoaphb, pere klstktumkblos p÷dhkmes `o 0 eõbs ol oh åadktb eme`ëakmb eõb quo toraklý torak lý ol 4: 4::: ::,, oh oh ál`km o `o mbstb `o he o`umemkýl nuo7
4:: 4:: 1
6,=55 1 5.46 >,03>
e) Mehmu Mehmuho ho o ohh MO MOKK `o su tkp tkpb b pertkm uher `o klstk klstktumk tumkýl ýl pere me`e ulb `o hbs 5> eõbs eme`ëakmbs quo so auostrel auostr el ol he tedhe. ² ²Muåh Muåh nuo oh euaoltb elueh prbao`kb prb ao`kb ol MO MOKK `urelto oh oh poráb`b `o 5> eõbs pere su tkpb tkp b `o klstk klstktumk tumk ýl2
Zere 0 eõbs, eõb quo toraklý 14::4 5º) MOK (4::4) 1
, , 1
5,=?
,
4º) MOK (4::4) 1, 1 5,=0 ,
=º) MOK (4::4) 1, 1 5,== ,
0º) MOK (4::4) 1 , 1 5,=4 ,
?º) MOK (4::4) 1 , 1 5,4? >º) MOK (4::4) 1
, ,
1 5,4:
,
3º) MOK (4::4) 1 , 1 5,53 ,
6º) MOK (4::4) 1 ,1 5,5? ,
;º) MOK (4::4) 1 , 1 5,54 5:º) MOK (4::4) 1 , , 1 5,55 ,
55º) MOK (4::4) 1 , 1 5,:3 ,
54º) MOK (4::4) 1 , 1 5,:? ,
5=º) MOK (4::4) 1 , 1 5,:0 ,
50º) MOK (4::4) 1 , 1 5,:4 5?º) MOK (4::4) 1
, , 1 5,:: ,
5>º) MOK (4::4) 1 , 1 :,:>
V1
+, + ,+ ,+ , + , , , + , , , 1
1 :,:43
d) Mehmu Mehmuho ho o ohh MOK MOK pe pere re hbs muetrb tktkpbs pbs `o klstk klstktum tumkblos kblos pere o ohh eõb e eme`ëakmb me`ëakmb quo nklehkze nk lehkze o ol l 4::= 4::= o kltorproto sus rosuhte`bs .
Zere 4 eõbs p÷dhkmbs7 MOK (4::=) 1
, ,
1 5,?;
,
Zere 4 eõbs prkve`e7 MOK (4::=) 1 , 1 5,4 ,4== ,
Zere 0 eõbs p÷dhkme7 MOK (4::=) 1 , 1 5,05 ,
Zere 0 eõbs prkve`e7 MOK (4::=) 1 , 1 5,0>
TO]Z_O]PE7 Oh MOK (4::=) pere hes 0 Klstktumkblos tkolo ul prbao`kb `o 5,0:.
m) Osmrkdo ul pårrenb s bdro oh ál`kmo `o mbstb `o he o`umemkýl. ²Zuo`o ²Zuo`o so socuk cukrr euaoltel`b mbab mb ab hhb b fe fomfb2 ²Uuë mroo mrooss quo peserå o ovoltuehaolto2 voltuehaolto2
Ál`kmo `o mbstb `o o`umemkýl Os he verkemkýl `o mbstb `o o`umemkýl quo tkolol hes Klstktumkblos Z÷dhkmes b Zrkve`es, tbae`es `o hbs Mbstbs Nkgbs Pbteh pere ul eõb ol muostkýl y oh Mbstb Nkgb Pbteh `oh eõb tbae`b mbab deso. -
]k puo`o socukr euaoltel`b mbab so bdsorve ol he tedhe. Hbs mbstbs nkgbs tbtehos `oh eõb ol muostkýl euaolterål.
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