Enem53

Prévia do material em texto

Esta página foi obtida através do recurso de impressão, disponível na Biblioteca A. Uso restrito a usuários com acesso a plataforma. Todos direitos reservados ao Grupo A
(https://grupoa.com.br/)
b7v3bÁvI57
7 ehguC GN gNjhThjCg C zNTC 1C UhA9çãh hg9t91CT, hcNGNjN1Gh Ch 
FSN eh9 NAzCcNTNj9Gh, é t9gC1Gh-C Nu Su â1tSTh GN
iPX° 1h AN1z9Gh C1z9-phgág9h
aX° 1h AN1z9Gh phgág9h.
x0X° 1h AN1z9Gh C1z9-phgág9h.
OxM° 1h AN1z9Gh phgág9h.
xOM° 1h AN1z9Gh phgág9h.
E63VvÃZ aMf PM% 
(iXxi) QhtCg cCgCTph é SuC Cz9D9GCGN FSN 
NAz9uSTC h gCj9hjí19h. 6u whth zgCG9j9h1CT é C 
WCj9ê1j9C, FSN Sz9T9mC Mi jCgzCA. I19j9CTuN1zN 
Aãh ehguCGCA ANzN jhTS1CA jhu CA jCgzCA. 7 Ug9uN9gC jhTS1C 
zNu SuC jCgzC, C ANtS1GC zNu GSCA jCgzCA, C zNgjN9gC zNu zgêA 
jCgzCA, C FSCgzC zNu FSCzgh jCgzCA, N CAA9u ASjNAA9DCuN1zN Czé 
C Aéz9uC jhTS1C, C FSCT zNu ANzN jCgzCA, N h FSN AhcgC ehguC h 
uh1zN, FSN Aãh CA jCgzCA 1ãh Sz9T9mCGCA 1CA jhTS1CA.
7 FSC1z9GCGN GN jCgzCA FSN ehguC h uh1zN é
i0.
iH.
ix.
Ox.
if.
E63VvÃZ aMM Ma% 
(iXxi) Z ThAC1th gNUgNAN1zCGh 1C J9tSgC x eh9 
ehguCGh UNTC S19ãh GhA jN1zghA GCA FSCzgh 
j9gjS1eNgê1j9CA zC1tN1zNA, GN gC9hA GN uNAuC 
uNG9GC.
4hcgC1Gh-AN h gC9h GN GSCA GCA j9gjS1eNgê1j9CA jN1zgCGCA 
Nu Dégz9jNA hUhAzhA Gh ThAC1th N C91GC uC1zN1Gh-AN C 

9TSAzgCGC UNTC J9tSgC i.
Z UNgíuNzgh Gh ThAC1th GC J9tSgC i, FSC1Gh jhuUCgCGh Ch 
UNgíuNzgh Gh ThAC1th GC J9tSgC x, zNDN Su CSuN1zh GN
OXX%.
MX%.
xXX%.

Ugho9u9GCGN Gh CAzNgh9GN Nu gNTCçãh à vNggC, hS ANwC, C uN1hg 
G9Azâ1j9C FSN NTN UCAAhS GC ASUNgeíj9N zNggNAzgN.
49AUh1íDNT Nu: pzzU://1hz9j9CA.zNggC.jhu.cg (CGCUzCGh).
5hu cCAN 1NAACA 91ehguCçõNA, C uN1hg G9Azâ1j9C FSN h 
CAzNgh9GN Y6 MM UCAAhS GC ASUNgeíj9N GC vNggC é 9tSCT C
O,iM × xXi qu.
O,iM × xXH qu.
O,iM × xX
f
 qu.
O,iM × xX
O
 qu.
O,iM × xX
M
 qu.
E63VvÃZ aMO P0% 

jóU9C Nu UgNzh N cgC1jh GC zNTC FSCGgCGC 91z9zSTCGC 
Z UN9oN, GN bCgjhA W91zh, FSN eh9 jhThjCGC Nu SuC 




fM° jhu C T91pC Gh phg9mh1zN.
WCgC gNjhThjCg C zNTC 1C ASC UhA9çãh hg9t91CT, GNDN-AN t9gá-TC, 
gN1zN à UCgNGN, 1h uN1hg â1tSTh UhAAíDNT 91eNg9hg C OHX°
Esta página foi obtida através do recurso de impressão, disponível na Biblioteca A. Uso restrito a usuários com acesso a plataforma. Todos direitos reservados ao Grupo A
(https://grupoa.com.br/)
b7v3bÁvI57
E63VvÃZ aM0 Mi% 
(iXxM) Z CjgéAj9uh GN zNj1hTht9CA 1h A9AzNuC 
UghGSz9Dh 91GSAzg9CT zNu Uhg hcwNz9Dh gNGSm9g jSAzhA 
N CSuN1zCg C UghGSz9D9GCGN. Rh Ug9uN9gh C1h GN 
eS1j9h1CuN1zh, SuC 91GúAzg9C eCcg9jhS 0 XXX S19GCGNA GN Su 
GNzNgu91CGh UghGSzh. Rh C1h ANtS91zN, 91DNAz9S Nu zNj1hTht9C 
CGFS9g9 – Gh 1hDCA uáFS91CA N CSuN1zhS C UghGSçãh Nu MX%.
3Az9uC-AN FSN NAAN CSuN1zh UNgjN1zSCT AN gNU9zC 1hA Ugóo9uhA 
C1hA, tCgC1z91Gh Su jgNAj9uN1zh C1SCT GN MX%.
5h1A9GNgN W C FSC1z9GCGN C1SCT GN UghGSzhA eCcg9jCGhA 1h C1h z 
GN eS1j9h1CuN1zh GC 91GúAzg9C.
VN C NAz9uCz9DC ehg CTjC1çCGC, FSCT é C NoUgNAAãh FSN GNzNgu91C 
h 1úuNgh GN S19GCGNA UghGSm9GCA W Nu eS1çãh GN z, UCgC z>=x (z 
uC9hg hS 9tSCT C x)?
W(z) = 0XXX · (x,M)
z-x
W(z) = X,M · z-x + 0XXX
W(z) = fXXX · z-x + 0XXX
W(z) = MX · z
-x
 + 0XXX
W(z) = 0XXX · (X,M) z-x
E63VvÃZ aMa MX% 
(iXxO) 3u ANzNucgh GN xa0P, sh9â19C eh9 UCTjh 
Gh uC9hg Cj9GN1zN gCG9hCz9Dh hjhgg9Gh 1h LgCA9T, 
FSC1Gh SuC CuhAzgC GN jéA9h-xOP, gNuhD9GC 
GN Su CUCgNTph GN gCG9hzNgCU9C CcC1Gh1CGh, eh9 uC19USTCGC 
91CGDNgz9GCuN1zN Uhg UCgzN GC UhUSTCçãh. 7 uN9C-D9GC GN 
Su uCzNg9CT gCG9hCz9Dh é h zNuUh 1NjNAAág9h UCgC FSN C 
uCAAC GNAAN uCzNg9CT AN gNGSmC à uNzCGN. 7 uN9C-D9GC Gh 
jéA9h-xOP é OX C1hA N C FSC1z9GCGN gNAzC1zN GN uCAAC GN Su 
uCzNg9CT gCG9hCz9Dh, CUóA z C1hA, é jCTjSTCGC UNTC NoUgNAAãh 
b(z) = 7.(i,P)
qz
 h1GN 7 é C uCAAC 919j9CT N q é SuC jh1AzC1zN 
1NtCz9DC.
5h1A9GNgN X,O jhuh CUgho9uCçãh UCgC ThtxX
i
.
ESCT h zNuUh 1NjNAAág9h, Nu C1hA, UCgC FSN SuC FSC1z9GCGN GN 
uCAAC Gh jéA9h-xOP AN gNGSmC C xX% GC FSC1z9GCGN 919j9CT?
xXX
MX
Mf
OH
iP
E63VvÃZ aHX ff% 
(iXxP) RSu G9C GN zNuUNAzCGN, C CTzNgCçãh 1C 
UgheS1G9GCGN GN Su g9h, 1Su GNzNgu91CGh ThjCT, 
eh9 gNt9AzgCGC GSgC1zN Su UNgíhGh GN f phgCA. 

UgheS1G9GCGN p, gNt9AzgCGC àA xO phgCA, 1ãh eh9 C1hzCGC N, C 
UCgz9g GN p, jCGC S19GCGN AhcgN h N9oh DNgz9jCT gNUgNAN1zC Su 
uNzgh.
xMX%.
iXX%.
E63VvÃZ aMH MP% 
(iXxi) 7gzpSg GNANwC jhuUgCg Su zNggN1h 
GN 5TécNg, FSN TpN heNgNjN CA ANtS91zNA 
UhAA9c9T9GCGNA GN UCtCuN1zh:
• ZUçãh x: WCtCg à D9AzC, Uhg n$ MM XXX,XX;
• ZUçãh i: WCtCg C UgCmh, GC1Gh SuC N1zgCGC GN n$ OX XXX,XX, N 
uC9A SuC UgNAzCçãh GN n$ iH XXX,XX UCgC GCT9 C H uNANA;
• ZUçãh O: WCtCg C UgCmh, GC1Gh SuC N1zgCGC GN n$ iX XXX,XX, 
uC9A SuC UgNAzCçãh GN n$ iX XXX,XX, UCgC GCT9 C H uNANA N 
hSzgC GN n$ x0 XXX,XX UCgC GCT9 C xi uNANA GC GCzC GC jhuUgC;
• ZUçãh f: WCtCg C UgCmh GC1Gh SuC N1zgCGC GN n$ xM XXX,XX N 
h gNAzC1zN Nu x C1h GC GCzC GC jhuUgC, UCtC1Gh n$ Oa XXX,XX;
• ZUçãh M: UCtCg C UgCmh, GCT9 C Su C1h, h DCThg GN n$ HX XXX,XX.
7gzpSg zNu h G91pN9gh UCgC UCtCg à D9AzC, uCA CDCT9C AN 1ãh 
ANg9C uNTphg CUT9jCg h G91pN9gh Gh DCThg à D9AzC (hS Czé Su DCThg 
uN1hg) Nu Su 91DNAz9uN1zh, jhu gN1zCc9T9GCGN GN xX% Ch 
ANuNAzgN, gNAtCzC1Gh hA DCThgNA à uNG9GC FSN CA UgNAzCçõNA 
GC hUçãh NAjhTp9GC ehAANu DN1jN1Gh.

jh1G9çõNA CUgNAN1zCGCA, 7gzpSg jh1jTS9S FSN NgC uC9A 

i.
f.
O.
M.
x.
E63VvÃZ aMP MH% 
(iXxP) nC9hA GN TSm AhTCg NAzãh Cz91t91Gh C 


3u GNzNgu91CGCA jh1G9çõNA, UhGN-AN ASUhg FSN C 91zN1A9GCGN 
TSu91hAC GNAANA gC9hA, 1C ASUNgeíj9N Gh TCth, ANwC GCGC 
CUgho9uCGCuN1zN Uhg I(o) = q . AN1(o)

ESC1Gh o = OXº, C 91zN1A9GCGN TSu91hAC AN gNGSm C FSCT 
UNgjN1zSCT GN ANS DCThg uáo9uh?
MP%
OO%
PX%
MX%
0H%
Esta página foi obtida através do recurso de impressão, disponível na Biblioteca A. Uso restrito a usuários com acesso a plataforma. Todos direitos reservados ao Grupo A
(https://grupoa.com.br/)
b7v3bÁvI57
E63VvÃZ aHi fX% 
(iXxP) 6uC GNAN1p9AzC UghwNz9AzC GNDNgá GNAN1pCg 
SuC zCuUC GN UC1NTC Nu ehguC j9gjSTCg. WCgC 
gNCT9mCg NAAN GNAN1ph, NTC G9AUõN, 1h uhuN1zh, GN 
CUN1CA Su jhuUCAAh, jSwh jhuUg9uN1zh GCA pCAzNA é GN xX ju, 
Su zgC1AeNg9Ghg N SuC ehTpC GN UCUNT jhu Su UTC1h jCgzNA9C1h. 
WCgC NAchçCg h GNAN1ph GNAAC zCuUC, NTC CeCAzhS CA pCAzNA Gh 
jhuUCAAh GN ehguC FSN h â1tSTh ehguCGh Uhg NTCA ehAAN GN 
xiXh. 7 Uh1zC ANjC NAzá gNUgNAN1zCGC UNTh Uh1zh 5, C Uh1zC Gh 


Jh9 91ehguCGh FSN N1zgN xM phgCA N xH phgCA, C UgheS1G9GCGN Gh 
g9h G9u91S9S Nu xX%.
ÀA xH phgCA, FSCT é C UgheS1G9GCGN Gh g9h, Nu uNzgh, 1h ThjCT 
h1GN ehgCu eN9zhA hA gNt9AzghA?
fX
if
OH
iX
x0
E63VvÃZ aHx fi% 
(iXxO) 4SgC1zN SuC CSTC GN bCzNuáz9jC, h 

Su A9AzNuC GN jhhgGN1CGCA jCgzNA9C1CA (o, y) N 
gNUgNAN1zC 1C ThSAC C GNAjg9çãh GN j91jh jh1wS1zhA CTtécg9jhA, 
I, II, III, Id N d, jhuh AN ANtSN:
I — é C j9gjS1eNgê1j9C GN NFSCçãh oi + y i = a;
 i
C x;


Id — é h FSCGgCGh ehguCGh UNThA Dégz9jNA (x, x), (i, x), (i, i) N 
(x, i);
d — é h Uh1zh (X, X).
7 ANtS9g, h UgheNAAhg gNUgNAN1zC jhggNzCuN1zN hA j91jh 
jh1wS1zhA AhcgN SuC uNAuC uCTpC FSCGg9jSTCGC, jhuUhAzC GN 
FSCGgCGhAjhu TCGhA uNG91Gh SuC S19GCGN GN jhuUg9uN1zh, 


Esta página foi obtida através do recurso de impressão, disponível na Biblioteca A. Uso restrito a usuários com acesso a plataforma. Todos direitos reservados ao Grupo A
(https://grupoa.com.br/)
b7v3bÁvI57
E63VvÃZ aHf Ox% 
(iXxP) 6u NuUgéAz9uh eh9 eN9zh à zCoC uN1ACT GN 
9%, SAC1Gh wSghA jhuUhAzhA, Nu h9zh UCgjNTCA 

Z GNDNGhg zNu C UhAA9c9T9GCGN GN FS9zCg C GíD9GC 
C1zNj9UCGCuN1zN C FSCTFSNg uhuN1zh, UCtC1Gh UCgC 9AAh h 
DCThg CzSCT GCA UCgjNTCA C91GC C UCtCg. 7UóA UCtCg C Mª UCgjNTC, 
gNAhTDN FS9zCg C GíD9GC 1h Czh GN UCtCg C Hª UCgjNTC.
7 NoUgNAAãh FSN jhggNAUh1GN Ch DCThg zhzCT UCth UNTC FS9zCçãh 
Gh NuUgéAz9uh é:
E63VvÃZ aHM ia% 
(iXxP) WCgC gNCT9mCg C D9CtNu GhA Ah1phA, SuC 
UNAAhC UgNj9ACDC eCmNg Su NuUgéAz9uh 1h 
DCThg GN n$ MXXX,XX. WCgC UCtCg CA UgNAzCçõNA, 
G9AUõN GN, 1h uáo9uh, n$ fXX,XX uN1AC9A. WCgC NAAN DCThg GN 
NuUgéAz9uh, h DCThg GC UgNAzCçãh (W) é jCTjSTCGh Nu eS1çãh Gh 
1úuNgh GN UgNAzCçõNA (1) ANtS1Gh C eóguSTC
VN 1NjNAAág9h, Sz9T9mN X,XXM jhuh CUgho9uCçãh UCgC Tht 
x,XxO; i,HXi jhuh CUgho9uCçãh UCgC Tht fXX; i,MiM jhuh 
CUgho9uCçãh UCgC Tht OOM.
4N CjhgGh jhu C eóguSTC GCGC, h uN1hg 1úuNgh GN UCgjNTCA 

xf
xi
xP
xH
xM
E63VvÃZ aHH ia% 
(iXxH) 3u iXxx, Su zNggNuhzh GN uCt19zSGN a,X 
1C NAjCTC n9jpzNg jCSAhS Su GNDCAzCGhg zAS1Cu9 
1h QCUãh, UghDhjC1Gh Su CTNgzC 1C SA91C 1SjTNCg 
7UóA jh1jTS9g h GNAN1ph, NTC h N1jCu91pC UCgC h ANzhg GN 
UghGSçãh. 7h gNjNcNg h GNAN1ph jhu C 91G9jCçãh Gh gC9h GC 

h z9Uh GN uCzNg9CT C ANg Sz9T9mCGh 1C ASC eCcg9jCçãh, GN CjhgGh 
jhu hA GCGhA.
Z z9Uh GN uCzNg9CT C ANg Sz9T9mCGh UNTh ANzhg GN UghGSçãh ANgá
Id
III
II
I
d
E63VvÃZ aHO fX% 

UCAACtN9ghA, SuC NuUgNAC GN zgC1AUhgzN 
jhTNz9Dh SgcC1h NAzá eCmN1Gh NAzSGhA UCgC C 
9uUTC1zCçãh GN Su 1hDh Uh1zh GN UCgCGC Nu SuC GNzNgu91CGC 

Uhg Su ô19cSA 1NAAC ghzC N C ThjCT9mCçãh GN Gh9A GN ANSA CzSC9A 
Uh1zhA GN UCgCGC, gNUgNAN1zCGhA Uhg W N E.
ZA NAzSGhA 91G9jCu FSN h 1hDh Uh1zh v GNDNgá ANg 91AzCTCGh, 
1NAAN UNgjSgAh, N1zgN CA UCgCGCA wá No9AzN1zNA W N E, GN uhGh 
FSN CA G9Azâ1j9CA UNgjhgg9GCA UNTh ô19cSA N1zgN hA Uh1zhA W N v 
N N1zgN hA Uh1zhA v N E ANwCu 9tSC9A. 4N CjhgGh jhu hA GCGhA, 
CA jhhgGN1CGCA Gh 1hDh Uh1zh GN UCgCGC Aãh
(ffX ; X).
(fxX ; X).
(ffX ; iX).
(fxX ; iX).
(iaX ; iX).
Esta página foi obtida através do recurso de impressão, disponível na Biblioteca A. Uso restrito a usuários com acesso a plataforma. Todos direitos reservados ao Grupo A
(https://grupoa.com.br/)
b7v3bÁvI57
E63VvÃZ aH0 ix% 
(iXxM) 6u N1tN1pN9gh UghwNzhS Su CSzhuóDNT 
jSwhA D9GghA GCA UhgzCA G9C1zN9gCA ehgCu 
GNAN1pCGhA GN ehguC FSN ASCA chgGCA 
ASUNg9hgNA ehAANu gNUgNAN1zCGCA UNTC jSgDC GN NFSCçãh y = Tht 

7 ehguC Gh D9Ggh eh9 jh1jNc9GC GN uhGh FSN h N9oh o ANuUgN 
G9D9GC Ch uN9h C CTzSgC p Gh D9Ggh N C cCAN Gh D9Ggh ANwC UCgCTNTC 
Ch N9oh o. ZcNGNjN1Gh C NAACA jh1G9çõNA, h N1tN1pN9gh 
GNzNgu91hS SuC NoUgNAAãh FSN ehg1NjN C CTzSgC p Gh D9Ggh Nu 
eS1çãh GC uNG9GC 1 GN ASC cCAN, Nu uNzghA.
7 NoUgNAAãh CTtécg9jC FSN GNzNgu91C C CTzSgC Gh D9Ggh é
E63VvÃZ aHa aO% 
(iXxi) RSu UghwNzh GC UCgzN NTézg9jC GN Su 
NG9eíj9h gNA9GN1j9CT C ANg jh1AzgSíGh, jh1AzC 
FSN CA zhuCGCA GNDNgãh ANg jhThjCGCA C X,iX 
u Cj9uC Gh U9Ah, N1FSC1zh hA 91zNggSUzhgNA GN TSm GNDNgãh ANg 
jhThjCGhA C x,fP u Cj9uC Gh U9Ah. 6u jCGN9gC1zN, UhzN1j9CT 
jhuUgCGhg GN Su CUCgzCuN1zh GNAAN NG9eíj9h, Ch DNg zC9A 
uNG9GCA, CTNgzC UCgC h eCzh GN FSN NTCA 1ãh jh1zNuUTCgãh ASCA 
1NjNAA9GCGNA. ZA gNeNgN1j9C9A GN CTzSgCA (Nu uNzghA) UCgC 
Cz9D9GCGNA FSN 1ãh No9tNu h SAh GN ehgçC Aãh uhAzgCGhA 1C 

GN JSqSAp9uC. 3u iXxO, hSzgh zNggNuhzh, GN uCt19zSGN P,X 1C 
uNAuC NAjCTC, ACjSG9S V9jpSC1 (ASGhNAzN GC 5p91C), GN9oC1Gh 
jN1zN1CA GN uhgzhA N u9TpCgNA GN eNg9GhA. 7 uCt19zSGN GN Su 
zNggNuhzh 1C NAjCTC n9jpzNg UhGN ANg jCTjSTCGC Uhg 
AN1Gh 3 C N1Ngt9C, Nu q2p, T9cNgCGC UNTh zNggNuhzh N 3X SuC 
jh1AzC1zN gNCT UhA9z9DC. 5h1A9GNgN FSN 3x, N 3i gNUgNAN1zCu 
CA N1Ngt9CA T9cNgCGCA 1hA zNggNuhzhA hjhgg9GhA 1h QCUãh N 1C 
5p91C, gNAUNjz9DCuN1zN.
49AUh1íDNT Nu: lll.zNggC.jhu.cg. 7jNAAh Nu: xM Cth. iXxO (CGCUzCGh).
ESCT C gNTCçãh N1zgN 3x N 3i?
3
x
 = xXi * 3
i
3
x
 = 3
i
 + i
3
x
 = a/P * 3
i
3
x
 = xXO * 3
i
3
x
 = xX
a/P
 * 3
i
E63VvÃZ aHP ia% 

Nu Su cCTC1çh 1h UCgFSN. 7 jhgGC FSN UgN1GN 
h CAAN1zh Gh cCTC1çh Ch zhUh Gh ASUhgzN uNGN 
i uNzghA. 7 jg9C1çC zhuC jS9GCGh UCgC 1ãh AhegNg Su Cj9GN1zN, 
N1zãh AN cCTC1çC GN uhGh FSN C jhgGC 1ãh jpNtSN C CTjC1çCg C 
UhA9çãh phg9mh1zCT.

Gh CAAN1zh Gh cCTC1çh, 1h FSCT C hg9tNu NAzá ThjCT9mCGC 1h zhUh 

h N9oh Y zNu hg9N1zCçãh UhA9z9DC UCgC j9uC.
7 jSgDC GNzNgu91CGC UNTC zgCwNzóg9C Gh CAAN1zh Gh cCTC1çh é 

e(o) = f – o²