Gabarito P1 2015 2 (1) Prof Daniele Sepe

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- Ek 112 . Consider a qe acute a vs extremes .
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teen ft ' ' anti; ftxinxdx II HE 9 onu y=k×
= ftp.llny#nt=tnjmaYnl1nH - Ink3) ] = + a
Portmh a sine diverge .
# : €Et 'Pn÷h . Un a ni Knie das sin . es alternators : a nqsenaa an = In (h 23) e' decrees an tee
bnisma an . . Logo a Knie converge .
Portmb ° interval de came rgynaa E |1<\⇒
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Sabres qe smx = x - ¥, + ¥at . . . Park to
smlmxtsenx - 'h¥+t¥E÷l×¥t¥p 't . ¥l×¥p¥I . .tt#lxItxEt..j5e. .
=× . ¥ ' ¥t¥t , sat '¥tt¥t÷=× . Itx4÷+÷d+ . .=× . It¥t .
b) ten
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( mlm×h¥#f= xhjmofotttwmosquonkmpekninspoalirashx ) = of .
4a) lxtnplxt 471×+11×2+4 - F) x - Fly 't lxtx - Hy to
Primi a renfro te os uefientes possum Zeros com vns :
Ecxhlxtnplxizj = 1×+431×-421×+4
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EH = lxtn ) kith - klx - F) = lxtn ) ( xtn ) ( x - k ) = (xtnflx - k )
Folxl = x ' - x -2 = ( xtn ) ( x - 2)
Portmt posse divider as tries terms for 1 xtn ) :
1 xintlx - kltxtffy ' 't 1×+1) Ix - Hy ' +1×-2)y=o
Os points sing Ines da EDO si × = - 1 , K , - F e os ordinaries sio RY - 1 , if , - F ] .
Venfo se cada ponto srnglwei regular on irregular :
sjam PH=YxtlYF¥yc×+ri ixthhtrttxrdi ' ' "*h÷xFFA "
Logo , x = - 1 e x =p so regimes e x = - K e
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+⇐g2a , xrtk +2=0
P#2 : relays de borne ncia :
(A) 2r 1 r - 1) t3r - 1=0 ( ao.to ) ⇒ 2m+r - 1=0 ⇒ ( 2ndlrtn)=o⇒r= 'how r= - I ( du as sol . )
( B )§lrtHrt3lrtH - Ha , =o
( a) [Eg[21h th ( ktr - Ht 31kt ) - 1) an xhtrt¥o2aknh§=o
÷{ dan . , xhtr
⇒ €z[(21h tr ) ( ktr - n) +3 ( htr ) -Dan +2 an . if xhtra
⇒ pare to do k 22 (21h tr ) ( htr - 1) +31 ktr ) - 1) an +2 an -2=0
⇒ parted k 't an = - µ!YrYµ#y+s#.
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Se r± : ( B) (211+1) 'k +3 / Yen) - 1) a , =o
⇒ (Eta - n ) a ,=o ⇒ of
an ;h?;j÷ .to#.iEfaiiF=iznFiII
= -
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