Riassunto esame Analisi matematica I, Prof. Della Pietra Francesco, libro consigliato Analisi Matematica 1 Marcellini-Sbordone, Marcellini-Sbordone

D-Qn + COS D-COS QQn Cosa Cosaa-= -= -- '' '1 I ng,topos TgaSe tgan=linn linn SenaSenanI' -an kitZone a +>/ = == CosaCOS AnSia + tojan ''' >I Senanan 00an an E = -, San◦< - .otanSia -' IAn -100an E ran> tztopos " eaean Qzone/ logologanQn 20 anQ Qcon ,,> imostzozione Jimostziamo ear2=0log/ E 0E- seeO itgoisso ,, log logHE -E+ van n ,-"i ITEe ,ITE line" "E -Ie EE i -- ==- -e/ {+ E Ei '' -- e+ite /=DD- ◦+ear ◦ eta.ear e°a- ""_ -- _ e.ee. .= = =b Igatopos "anti ↳b- ° a bebnof 2" an 0e an azone ,ae. con/ = = ,stenson indeterminate= - ozone, +00°+00 -00loganearD- too tootoon E- Ian -00 0= ane-logan0-1An -00/Qnbn e' panon= "bnQn antoo +00toobn ai"0-1 tooan 0antibn 0an -00-100 antibnOt tooan -00 { +002 ""topos 2-100 0sso.to/,mn2f.Sia LEIR _--Zone =/ 2=000 2Sia limitfissato " ◦'In' D-0 aa = ==Sia " find"0an Senan' .An?)|" tgtAQ

_- sent teat tot- 0 :IC- t I -, -Azea AOP = tl ''' --Azea tot sento costA AOQ = TEsentcost I I2 i -__ ,ttefntivamente Senai 'Se itIn0an icos --n D-z nlinn Senan I=QnSuccession Succession monotone, .monotone deczescenteCrescent anInan Qn+ -neam - ne. -- . .Steczescente decrescentstz Qn+anant hean - ne. , . ,zegolaz.tod. monotonedelle:enema succ . descentmonotone {lnoltze5. Seanzegolo.ee }hnmane-an supa an an: = env. -decrescent {infInmanSean }2 an= newimostzazione> { } l/ { }too Qnsup -sup anan n= - I- E 2-E O : auv -Sia data 1-pzendo da 1 IteE E0 u an2 a n v, -, daTssato 1¥E2 E Q E ananQu -100Cvo - : =v ., ,4 epezoumezoevmezo ,e= 2,71828182845904523536 2. _ _ ,^ sheet czescenteImitate monotoneSia> e-Itzoposizrone anina. e= ."^ convergent Im ;-)' ein +eit ' _-notimostzoz> ndimostzo che +' ''One in- it i +/ n , n -11✗✗ -1I✗ I-1 === = n n+-, -- ,,-11n in^ n'A- -16 -12n-1 +I itinit - - =-. -1nnti

T.mx/-zaZione2dimostzockeQn 3 ne-,nn n !n ^^ 'i " =k -11h^ n' lh -/ -=+ In- )nk --= ' !µ ! KkK -k=o k=o ki nun T 'n.io "[ "I ZnI in 1 l= !- - K-_ - -- no, n\ ' 'p, , "^3-1◦ 2I {I {I5.I+ +' ' { I± + -1+ ++ += ++ +-1- - - -- -2.3.4 4. s} 2.. , , ,^II II =3If-+= II{1- - n^ Am3≤ C-I2. - 2,7182,3 =eit in inne -1, ^^ I. 3ssezvoitione inIt j !K⇐ czescente'{ anSia hnmtoo' -100 £oposizione an peen eit =,Jmostzazione Supp paztenteza+00an an. -11≤ ]LanananLand ]Lan -11onI ,IIf ,-1 +- , Land] -11Lan 0in-11]Lan ""-1 (, I 1winIn I'+ it'' -1+ 1-_ -- < ,Lane Law an+ ,,, ' '''' e e eSupp• an -00. "°"'↳° +° "'" bn"- bn(bnan i ananti'/iIn ,' + l- - =++= - -== -=anti bnbn bn-' '' ee frssato?ssezvaziones.rs ✗ c- ✗¥ nse ex1in ex IR✗Iy=/✗ /0 - c-✗=+ +, ,so n>n

+- -0+00nAlte notevohlimit-1 .in ,.. ¥notevoh.S.rs I'm0 +Conanan an e≠ '◦ =-0+00n bsupp i-o.nl '0-1 eian i= +. bn1911+0hmSia' 0an n- =Qn.nl loge1311+0 lgfi-o.nl _-= 'an e 1e°/5,2 "" -13N1911I0In inn =- " "D- n bn"" bn lglitbn too>n-1e 0 e-1 -an = == , 1311thQn"b1. Igb- -1 0pecanm =D- n °ban ↳ lgba- 1910II e.- -= '/ go☐ an^ , and(fissatoSia IR hm' +' -10 22 anC- =, on -100 °- "-10m£ 21911+0--1-1 21g ( ionI e. 2l- = Qnan 21g )( + QnI \, ,SuccessionSuccesspezzcozzenzopezzrcozzenz-OJ.efiniz.aeone. pezzicozzenzo-pezirdvzioneo-ssegno-ndoilpz.no/-ezm.ne delladefinisce5 oneuna success ,. eo-ssegno-ndoogn.rs/tzotezminenfunzionede1pzecedente precedentdesuccess one ◦ ., ,, .flan0-ssegno-to.amQ - ne=, .nfn.fi ozdineczescenferf.at di d.,ozdineczescertecztez.rs/e1zappoztoSia 1in An0an =, an^ ,-lSe1 an1 O nentedice1=1se ' Svannon pvos .Se an +002 r O-nidef.no/Tvamerte> imostzaz

"n2 n -100+00 O_0 # Ia,€ ° 2 ☐72 "Beena"^ ./<Sia [ × ,zx① 2 LXJIt ✗,,✗ ,= ☐ =,)vnqve 19TIse ✗ ✗0✗ , _-¥É°_ _ °" '"' -1¥See :=nI/ Igi ' ' i2{✗ °go n ◦ _ ., -ni2nd "1g ,"13h 1g 191=0ssezvazione n=n 2132 °lrgzxssezvoitione an ZanIn 0"✗+00 2con =_ - . QnQngan ◦ anse tooannd con a 1, 2 0conAt Q I0in =an ndScelgoQn ° " an i" =ran anAn.. """ " °& " In•nÉ anyant ££n -1 in, ◦1it. == =.anIn .In ☐im =!n !Iym "Oi 1mA n'n =D I=' . + ,! anntiInn !in!n 0in =nn> toon - !