9ye
X .BtQM M/ _X GxBÉ
#2ir22M i?2 mTT2` M/ HQr2` #QmM/b- #mi `2+2MiHv i?2b2 ?p2 #22M BKT`Qp2/ iQ
MQM@2H2K2Mi`v HQr2` #QmM/ (d) M/ M +F2`KMMBM mTT2` #QmM/ (kR)X
h?2 }`bi +QKTH2i2 H;Q`Bi?K 7Q` `2+?#BHBiv Bb /m2 iQ Jv` (k9)- bBM+2 7m`@
bi`BFBM;Hv bBKTH2 #mi MQi v2i T`+iB+H H;Q`Bi?K rb Q#iBM2/ #v G2`Qmt (ky)#b2/ QM 2MmK2`iBM; S`2b#m`;2`@/2}M#H2 BMp`BMibX AM i?Bb TT2` r2 rBHH 7Q@
+mb QM EQb`DmǶb H;Q`Bi?KX h?2 Hii2` Bb i?2 bm#D2+i Q7 M 2MiB`2 #QQF #v
_2mi2Mm2` (kN)- bBM+2 i`MbHi2/ BMiQ 1M;HBb? (k3)- M/ KQ`2 `2+2MiHv T`2b2Mi2/
BM MQp2H- `2/#H2 7Q`Ki rBi? +QMi2KTQ``v MQiiBQM #v GbQi (RN)X
AM bTBi2 Q7 i?2b2 bm#biMiBH M/ bmbiBM2/ i?2Q`2iB+H /2p2HQTK2Mib- i?2 `2
?b b22M HBiiH2 BM i?2 rv Q7 T`+iB+H BKTH2K2MiiBQMX q2 b22F iQ //`2bb i?Bb
;T #v KFBM; i?2 7QHHQrBM; +QMi`B#miBQMb,
Ĝ q2 T`2b2Mi iQQH- E_2+?- r?B+? r2 #2HB2p2 iQ #2 i?2 }`bi +QKTH2i2 BK@
TH2K2MiiBQM Q7 /2+BbBQM T`Q+2/m`2 7Q` i?2 ;2M2`H S2i`B M2i `2+?#BHBiv
T`Q#H2KX
Ĝ LQiBM; i?i i?2 `2+?#BHBiv T`Q#H2K Bb BM7KQmb 7Q` Bib +QKTH2tBivě#Qi? BM
i2`Kb Q7 Bib rQ`bi@+b2 `mMiBK2- M/ i?2 BKT2M2i`#BHBiv Q7 Bib /2+BbBQM T`Q@
+2/m`2b 7Q` M2r+QK2`běr2 Qz2` M ++2bbB#H2 BKTH2K2MiiBQM Q7 EQb`DmǶb
H;Q`Bi?K- r?B+? +M #2 mb2/ b /2iBH2/ H2`MBM; B/X
Ĝ q2 ?p2 /2bB;M2/ i?2 BKTH2K2MiiBQM BM KQ/mH` M/ 2ti2MbB#H2 rv r?B+?
Bb +QM/m+Bp2 iQ /2p2HQTK2Mi Q7 7mim`2 BKT`Qp2K2Mib iQ i?2 H;Q`Bi?KX
Ĝ q2 BM+Hm/2 MmK#2` Q7 T`K2i2`Bb2/ 2tKTH2 M2ib r?B+? /2KQMbi`i2
+Q``2+iM2bb M/ T2`7Q`KM+2- M/ +M #2 mb2/ iQ bb2bb 7m`i?2` rQ`FX
Ĝ q2 T`QpB/2 7mHH bmBi2 Q7 HB#``B2b r?B+? B/ T`Q;`KKBM; rBi? o2+iQ` /@
/BiBQM avbi2Kb UrBi? aii2bV BM i?2 >bF2HH T`Q;`KKBM; HM;m;2X
k .2bB;M M/ AKTH2K2MiiBQM
H;Q`Bi?K q2 rBHH MQr ;Bp2 #`B27 Qp2`pB2r Q7 EQb`DmǶb +HbbB+ `2+?#BH@
Biv H;Q`Bi?K 7Q` S2i`B M2ib- M/ 2tTHBM i?2 i`MbHiBQM BMiQ +Q/2X LQi2 i?i
EQb`DmǶb H;Q`Bi?K QT2`i2b Qp2` oaaěi?2 i`MbHiBQM #2ir22M i?2 irQ Bb
BKK2/Bi2- M/ +M #2 T2`7Q`K2/ r?BH2 T`bBM; i?2 T`Q#H2K BMbiM+2X
q
1, 0
r
0, 0
t0 [−1, 1]
t1 [0, −1]
UV q2 /2MQi2 +QMbi`BMib M/
[i`MbBiBQMb]X h?2 bii2b Q7 Qm` Q`B;BMH
oaa `2 q M/ rc i?2 i`MbBiBQMb `2 t 0
M/ t1X >2`2 r2 `2 i2biBM; `2+?#BHBiv
7`QK q(1, 0) iQ r(0, 0)X
q
1, 0
r
0, 0
t0 [−1, 1]
[0, −1]
U#V Gex 7i2` a** /2+QKTQbBiBQMX q2
MQr ?p2 irQ +QKTQM2Mib- i?2 b2+QM/
Q7 r?B+? Bb i`BpBHX h?2 /DQBMK2Mi Bb
K`F2/ #v /b?2/ ``QrX h?2 b?/2/
`2+iM;H2b `2 b2T`i2 +QKTQM2MibX
6B;X R, bBKTH2 :oaa- G ex X
X .BtQM M/ _X GxBÉ
#2ir22M i?2 mTT2` M/ HQr2` #QmM/b- #mi `2+2MiHv i?2b2 ?p2 #22M BKT`Qp2/ iQ
MQM@2H2K2Mi`v HQr2` #QmM/ (d) M/ M +F2`KMMBM mTT2` #QmM/ (kR)X
h?2 }`bi +QKTH2i2 H;Q`Bi?K 7Q` `2+?#BHBiv Bb /m2 iQ Jv` (k9)- bBM+2 7m`@
bi`BFBM;Hv bBKTH2 #mi MQi v2i T`+iB+H H;Q`Bi?K rb Q#iBM2/ #v G2`Qmt (ky)#b2/ QM 2MmK2`iBM; S`2b#m`;2`@/2}M#H2 BMp`BMibX AM i?Bb TT2` r2 rBHH 7Q@
+mb QM EQb`DmǶb H;Q`Bi?KX h?2 Hii2` Bb i?2 bm#D2+i Q7 M 2MiB`2 #QQF #v
_2mi2Mm2` (kN)- bBM+2 i`MbHi2/ BMiQ 1M;HBb? (k3)- M/ KQ`2 `2+2MiHv T`2b2Mi2/
BM MQp2H- `2/#H2 7Q`Ki rBi? +QMi2KTQ``v MQiiBQM #v GbQi (RN)X
AM bTBi2 Q7 i?2b2 bm#biMiBH M/ bmbiBM2/ i?2Q`2iB+H /2p2HQTK2Mib- i?2 `2
?b b22M HBiiH2 BM i?2 rv Q7 T`+iB+H BKTH2K2MiiBQMX q2 b22F iQ //`2bb i?Bb
;T #v KFBM; i?2 7QHHQrBM; +QMi`B#miBQMb,
Ĝ q2 T`2b2Mi iQQH- E_2+?- r?B+? r2 #2HB2p2 iQ #2 i?2 }`bi +QKTH2i2 BK@
TH2K2MiiBQM Q7 /2+BbBQM T`Q+2/m`2 7Q` i?2 ;2M2`H S2i`B M2i `2+?#BHBiv
T`Q#H2KX
Ĝ LQiBM; i?i i?2 `2+?#BHBiv T`Q#H2K Bb BM7KQmb 7Q` Bib +QKTH2tBivě#Qi? BM
i2`Kb Q7 Bib rQ`bi@+b2 `mMiBK2- M/ i?2 BKT2M2i`#BHBiv Q7 Bib /2+BbBQM T`Q@
+2/m`2b 7Q` M2r+QK2`běr2 Qz2` M ++2bbB#H2 BKTH2K2MiiBQM Q7 EQb`DmǶb
H;Q`Bi?K- r?B+? +M #2 mb2/ b /2iBH2/ H2`MBM; B/X
Ĝ q2 ?p2 /2bB;M2/ i?2 BKTH2K2MiiBQM BM KQ/mH` M/ 2ti2MbB#H2 rv r?B+?
Bb +QM/m+Bp2 iQ /2p2HQTK2Mi Q7 7mim`2 BKT`Qp2K2Mib iQ i?2 H;Q`Bi?KX
Ĝ q2 BM+Hm/2 MmK#2` Q7 T`K2i2`Bb2/ 2tKTH2 M2ib r?B+? /2KQMbi`i2
+Q``2+iM2bb M/ T2`7Q`KM+2- M/ +M #2 mb2/ iQ bb2bb 7m`i?2` rQ`FX
Ĝ q2 T`QpB/2 7mHH bmBi2 Q7 HB#``B2b r?B+? B/ T`Q;`KKBM; rBi? o2+iQ` /@
/BiBQM avbi2Kb UrBi? aii2bV BM i?2 >bF2HH T`Q;`KKBM; HM;m;2X
k .2bB;M M/ AKTH2K2MiiBQM
H;Q`Bi?K q2 rBHH MQr ;Bp2 #`B27 Qp2`pB2r Q7 EQb`DmǶb +HbbB+ `2+?#BH@
Biv H;Q`Bi?K 7Q` S2i`B M2ib- M/ 2tTHBM i?2 i`MbHiBQM BMiQ +Q/2X LQi2 i?i
EQb`DmǶb H;Q`Bi?K QT2`i2b Qp2` oaaěi?2 i`MbHiBQM #2ir22M i?2 irQ Bb
BKK2/Bi2- M/ +M #2 T2`7Q`K2/ r?BH2 T`bBM; i?2 T`Q#H2K BMbiM+2X
q
1, 0
r
0, 0
t0 [−1, 1]
t1 [0, −1]
UV q2 /2MQi2 +QMbi`BMib M/
[i`MbBiBQMb]X h?2 bii2b Q7 Qm` Q`B;BMH
oaa `2 q M/ rc i?2 i`MbBiBQMb `2 t 0
M/ t1X >2`2 r2 `2 i2biBM; `2+?#BHBiv
7`QK q(1, 0) iQ r(0, 0)X
q
1, 0
r
0, 0
t0 [−1, 1]
[0, −1]
U#V Gex 7i2` a** /2+QKTQbBiBQMX q2
MQr ?p2 irQ +QKTQM2Mib- i?2 b2+QM/
Q7 r?B+? Bb i`BpBHX h?2 /DQBMK2Mi Bb
K`F2/ #v /b?2/ ``QrX h?2 b?/2/
`2+iM;H2b `2 b2T`i2 +QKTQM2MibX
6B;X R, bBKTH2 :oaa- G ex X