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Curs electronica

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curs electronica
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euRS q \e?\ th*dd rq)*sq\q.l.r\A dt *qs^.Gt A u: * ,r*r "q*t\i. eo. \t'.d i""?d* & h,ndd a .,.*nui {t[h," i&& a,$,!. s lo,.f"s-.r "tq\d' e^r [*t"l*o iHqrr,\r",ibd "1" +"tb."] \raq qi'"d )s isds,ow ^[ "p]&*A: *ge*"d "\lo . Nur = .t?*t*u: =6sriB(o) $[*u) lJo Atu ("r") A(*) r" cn"pli{od,*qq, k rJ"I"t {*#d & so*^l$ o {SS\'\n \ro\, Ro * \o\aos&q" 1* *tod-* " \,r,x&!i ols ur "^'$ss-$lr\"+rb Io.- rb1.,squ {til*s'^,I"t ko\ $e*S tsi'dd sd.n*!.*ld o\St,nr\8 d" lt*'Xi."'.rq qh, r.&i de s,*L "tt{gr-td dL l,f;s''1".^rc dr 1.";Jd -3drJ. M,qdi"al&o" gB t*l = (*) -l-x = *fiitu * S\*US*, \"*So & +s.,ql"rr\$ o. *T*o $th* aesq r,lo\s*o.ld oqrs*d lx**rnlo\"s"' ^lud"** (, *^itrrilto ns\ nS) "p*+ d,r r.u.dilr,i. t r\\\ ^ n* r.k) =,* Jx(a)da -Po 6 = 6,_D J6= 66t 6 =*$ 6t =* oaoL*os,r- prdt*J*3 t*,-r*I "L*"ish s att" xt^rrql. John* q. r$f)t,.} ^+J *f^o,d6 -*I;n a D)du = _0a ,h * f&(e)-n{a-{ra *.Do ^*-D - * J xta)da = -F $[*u) 5*" Nuqri,I d.,[0.6t Iq.6 d,ed nrdor*q uosio.tifii mu qr.l
Transcript
Page 1: Curs electronica

euRS q

\e?\

th*dd rq)*sq\q.l.r\A dt *qs^.Gt

A u: * ,r*r "q*t\i. eo. \t'.d i""?d* & h,ndd a .,.*nui {t[h,"i&& a,$,!. s lo,.f"s-.r "tq\d' e^r [*t"l*o iHqrr,\r",ibd

"1" +"tb."] \raqqi'"d )s isds,ow ^[ "p]&*A: *ge*"d

"\lo .

Nur = .t?*t*u: =6sriB(o)$[*u) lJo Atu ("r")

A(*) r" cn"pli{od,*qq,k rJ"I"t {*#d & so*^l$ o

{SS\'\n \ro\,Ro * \o\aos&q" 1* *tod-* " \,r,x&!i ols

ur "^'$ss-$lr\"+rb

Io.- rb1.,squ {til*s'^,I"tko\

$e*S tsi'dd sd.n*!.*ldo\St,nr\8 d" lt*'Xi."'.rq qh, r.&i de

s,*L "tt{gr-td dL l,f;s''1".^rc dr 1.";Jd

-3drJ.

M,qdi"al&o"

gB t*l = (*)

-l-x= *fiitu

*

S\*US*, \"*So & +s.,ql"rr\$

o. *T*o $th* aesq r,lo\s*o.ld oqrs*d

lx**rnlo\"s"' ^lud"**

(,

*^itrrilto ns\nS)

"p*+ d,r r.u.dilr,i. tr\\\ ^ n*r.k) =,* Jx(a)da

-Po

6 = 6,_DJ6= 66t6 =*$6t =*

oaoL*os,r- prdt*J*3 t*,-r*I "L*"ish s att" xt^rrql. John*q. r$f)t,.}

^+J*f^o,d6 -*I;n a D)du =

_0a ,h

* f&(e)-n{a-{ra*.Do

^*-D- * J xta)da =

-F

$[*u)

5*" Nuqri,I d.,[0.6t Iq.6 d,ed nrdor*q uosio.tifii mu qr.l

Page 2: Curs electronica

"*o\i*rord eoe$qlio., :

-.luntbtnr

x(+)

-xt e -D) ui*lH"(5.^r\

Hnltr*\ = \ ,

+Loi*_b!=,-ib*b S(*):Hr-(i*\ = i[*]

Cl-d a xixh.r-r ,lfiios,t ro*-JqJ \I*r"r*.S"t { )"ourrrro eo\AF, & {**f

\t5*) =,*-\*)

b",-,-*d*ohrtu ts\r-'"[q\e {"*+tl ol& *l$^dtsr rc)^t t"[",ih

tr t\"d lr h"l8 i- p*olrl ^,'oi ,-oth ,\ift*,!" "hionq , {*d" &tnora*$a o&i'*oN*\d

"HU T$d eu \ur,oo, {"-oj,bilot da fnq^',',[h qh ,{rtU,'nht

es'rDpslr\$dr.

ra

y (tr*)= A)*(5*) =

m:: x{tr"r) H*(5*) =K=L

= x (5*,)i u* (l*)

Ht(5*\=

W, =[^He(go)

&f.dt ?,'" No1il, {.,",S* d" $al 4&

"tt" b"",t-(rn .

2

mLl1ie

Page 3: Curs electronica

6 b".3 n'q! ,*,',!ttdr .ls.q*,\*b.

"d**o$n*$ .r

*rr*r\sh asscofCIff\$i+9",

Xq-,") Ynt;; \-

'-. -. -G-Y(l*lHorio)= ffi = ffi ,

HSI, . . . & . Hs " W =

,-f)

=s$(5*)

=.p$i$;-l,ee!u:NlH3(5*';)=*

rr (5.J = iil*b '*o ST.^mdis d. r.s-,d$,r )"$) o o*rJn.i {tJh^^ " #,".r*{gn-do Ts^rsrrh

i*.,rs,r3, T ih,l*r: =\(+)Vof'$oSl

frlJu.*f oo$o olr\ s qls.tr L'nto, +"t+ dr)& murmgfo. +Ss \"td , -

Slb* rx. I""gd ?m

-{:- .* *f,*"thRsut |60.$ i* o"mdd , tr.*rqti*{*,"ailloh "h

S,q*{$ "[o

*-

3.

Page 4: Curs electronica

Q-os\-r

\,,\

"\aloS, pl-0Jo. hRJ.rntvn-

xt*) "*r h$) rK. x&$-Zo)lhe)

gs-)d*Ard K= \ ,-,*,'*\-\ x(-*) "*" x*,r$ie {"i$ dr o'xo, """[.CI!d

q o*f,t"d i$., \]sd..on[ i']$n*rs".lo. 4 , * "o&\q' en iro t 1*d,f\(*\ =Jior,*-b**ot* =Ift (*-C. u- L*1 di

Tjicb."J o.do$o* ,ta {os.^-o. }"r.,,r"!r.t;Nh, "A*i,-" *c* \q, ; 'roliassr P"nf,*^lqr'i o.

s ^.,o*dn., clr x$) ,T,*-g$'o. ols ,ao-ot!hr- . {i}*r'. '}.,.,L adup{o*

-*+ 6o=^"

#:-J-I =6.-x-b -b

A (\"i =Iia .iL* tc *\d * =Ji*t . *I* ^ . _i5*6J,^ =

-('4 *ba

= *-t*6o . S*(*) ,",'.1- 5. (*) '* esi*tda" ,.*r'*$-I^lt Sf*)

LIJ^jJolno.,

\s*3 Io- *.rhonm- Slt"'\,* dT;" +t ,.*-"il i"I$,qs,**$^$'

& Io., A\\ir.e ..o $ S*"'{.t"-"*" i*"ltUd a. t""^,rJ'!.tt & [q ,i]i],!..)

$ ol?_1 [t(i*\S (*))= y$*)5(*)-l 'lF

\u) =ftff*) Htp .o\**J* = *,rF) . $*(*)

"L'"

(*- 4)d*-(Y -p

\"S5os,!a r-"il,"-8 o. !slr"too}o-t^i t(+)

xt s[#r"* tt ^tts^"rtfir,l J= 6,

tn-"- = {*= 6.1 =*f;(*)le J,u = E --x -*nu$o, rK'" *atl^i"

^*(*) r,sd! U "$*ff ry\ etr *\.+s""$- ^'s\sj.

;* t*q,'o\" ''tq 'as),^ l*$''*iq 'u *\"t+' ,\rn d l^. ''

${) = Jo,.l*t*-a)dz =Jota)'"[-f+-6 - 6"!dn =Jjb)"F* * 6+ q]d6 =-Fe-oo - 0o

= ?,^$-A\

Page 5: Curs electronica

Aar$. S.tlr.- -Q. ^rro

s*.rle$. taa [o ,i]* \*4o. "la ""d*eo*l.$il o. ]!LMI)-

*.\*\*l- t (r\).0il-a ,s**"$*$ & I" i*$os',-r- A aro M*'*I

"U$"1 d! gGl) [q i+$-'r *-eb$'n \.r.afio. d!- es$,r\o*,[ n-"*oo\d dirdr.! "rb e ,.d$.,-/relo,'

Xtr) =_ffirl,ht+-a)da =ffii#+*z+A!a =&n\(*-4.)-lb

h"J*o/*u" t*"*h}"9''-s\uu p"J" di- Jco"oo, douaulO *"*ixlio U",ps.*"rd c^^ Jc$."o" {i[-t\&

h,ii eplir, *U * &enfo,, !rJ-i.'-o:-rri' ;oonurmrbri"kh.' l'^edo\.,\ ',ror.r.i

,.ttfu"r *l aA.+* xrrymlsle:ffiK

6$-t roo*d &\€ldd de .*-xqr 0K.\t4 -t r.".,u&&dso\ ens.r p"b;nfo e p*s*E{oo$& & Io. T*$'dstt $ d,i'

,.m\+f'rL u"os$, tx-*"h \K. I ' I u

\

$.K -o r*n'.*.Is. \saT$s'-qh .? km I0^ x \oe ehhR\.,di l* la.r\ olociu. d seS,! x.ts-* e.s'*'uri'dt "Ai.hgo**o!"'i..

€,.ild am rn\$rds' l&i* "tt -t:t- mr $lc* d$tro- ran""-ch n*. h4dt*

h$o, o pd" \rl el.^ )str,*It otr*rurnbrirdrtu:crr r,st -rah" "t"tr-"hird-

I,sr\ arr 't****!" o\o*sow . I

C" lc,. ,r.\" d"l*r..i*._r$ * So rSn- S*_n Xrruslotd rro(*),r.ntt).^."\-ft)C" tsr**,-h qs-&*is^m* dsl$'ynirrau*I + NK dirorlrnl rnu rnurwnf, olr r6"',lp

ci $ oh .,.ro *n' & Ponormdrru"'

5o'3n,'^"Snn-n & eetqry*-d I

roo(* , on . ., o-) , \n(d on,..O-), , " .

t* \&"^"da "Ns\sob* -* q,Sn., .,. {.-n -t^ y.(+), tn({) ..,,..Y*_nS),

b\ed.',\q., t{ N.r lo* S ptr- rr{Itr.;l . Sr.,'i"fir,ion,^}. en-olu}.*i., lsf }.,^r',J

"\+"*" an s\o^-st -\d',\ qqiiiloF,q, $*d es",.nid!ho* qofu*i., . /o r*gp{u , hj* I'\ ' I ",1."""* *-Jor*,* l,q.' i,n rmg^r'qr#.-R ot 6CIde ok t*"p, ;8-,\*^n8t;&

F*** e* ffao

m*sarisrd-rr-r*- *b*nuu$i,? l*eo \s\ X \ot ^po{ru $ 1g lqr^ olqat$i :

q

5-o

SorSn..,,q*-n * Ho,,Hn,",-'.H*-n *bo,bn '--- -.)*-o

Page 6: Curs electronica

l&"\ , ceuxr-o"odu.Jo, .itr#u n*sq.N g3"r.lDq* & l'rhxd rl drai*;,h l*qh,S$ t*,,t"*i ,d*' ^f"or*,r1"

,1"d {' S {-ti. . fuX"Llt dr drci+ir +{h* ,r{ th* "y $ "\s>&

**\$ t-aAI pr luoto. *rnoui qr-;Jqlto du- {rUr}r+* rd }&

u\i"3 r'ls"t\ddr q,t".'a.*f!" -o r-rno.r! f"r"d ot;u", t E{i*\ -us,tir\stt

U *f\-

ffi:ffiJ3- r"*"d d;" \.4"y n-u{u-

**S* fr. e^'qJ1.t"*,.tm de,w.miw tor xodi-N .^rr.*J"it "ogdrt\d.. ^l .' 0 A ot r ll

t'€r.*,>A\afiNq & h >uurp{il d S Nos..iql*}q q\qo*oor.r d".i -"d^.,$&[.ri&

'* \o r- nnoernart! da #*.T di.;"d-' nJ. pxsesh( n}rOs$..t doo.d .""dlust&l*i[t

n \uc ee'rliror.rrr.,

('h,rS,.,**q t*, c".s*^rqh "tih,$'dr n *.mnn*$r*!6 \*fS"'**

G*$o\s,dm rs.o ost- $.+iaJo,\ ?ro eos,i. - u-dn"\ d, r*'.n%t fv\ {- l*.*\*\o er, $,rr.xq ti\elds .\o. r', 'oerrurd.

qlo* /r*J- T*" \r* "t"ry+ S" \" Sn.

Xo. *isis.,rq ..sl*\qfos'"\i p"J. lpdnro" 1o8*) ry* MH). Q fo,^tct'J, * *Vd**,^r*\-\.. h(*) f\'b"d^j. "fu n "dl.rnot ilns -.^rD ;".,lns"q\ & J"-f D ol"

^^ns."ou$nit, cno"-db,' d.l shi $ g" b^*s ,oed.oh n-,,in*E\t" P"b t st"tti,\6. t*"o dlto

Td.*$" {t**Hq . U" r-j*o,* * ed l-o. r,",*A So , Hn $nxqrnm( sd A^a rnntA

3n.S\.d*\',\. !i.*rr,-&n dc lrrqm^rdd,.r e

No

\\

Page 7: Curs electronica

ehAso-'\ *1" pl,xaie^r p$. ["i \-xN.p,d,\. tso"^Sie *m tl..i+$\iw r e \ufo.hqCd conr $-poilo y+$ "ts""q(-

\S, tso $ r,oqt$.L d.l dreibi "

N=b L

N".d ub\'\ *d*"I.n R ls $xrfu iro >o1i,*o^ro. ho w. i* dta*^o" )o os-o b**nn*i*. $o , h.oi '..Alq$ *d*.N',iB I iro tili** An$N. Iq.otooiuqln

$ ttor\Rql.!.d ed h-q So""orrix 54.

N"ai$ih cnu n*cl isr#&R!$nn- eshrai. Sd""+^,l" cns-,r. pct T3** rrw*

$"*s"re. er* "1-tlorJ ^!$c^,J. +ahr!. , {trass,l. olqqig*l pso*r qslq.

^*, es,il. e,cs'! &F..t*

"$I dq d'qa,*id

[* ;T $ dq t&**,"\"\ inq,",rrn ^x,

s. p." gnol

Sn LCon Cnn -J?".i- *l& Li thy* \"{i."1 "[xnu$;.,tO

,. r'*.10ffi ]n e" ds,-'"".ilt"S$ **.,s *.qdl^ .\ &oiaid. l^*dr d {is "'-ir'n* .{eq* .s* *,tdir^ dt

q^^ Qi $c (R) ,

?o = e* ?(\, DS) * eno?(tn n S) + 0or? (No nSn) r C,,nP 6^ n6n )?(Xon$o1 =;ur*habi\'ld** & q rx loq &q.aiq ]o d*nno. en-d ,N-qr-

)nro"r*ir, So.

5- es ru*d.ud q^s",enqrrb- f."lel.i,t"ld+i" & ,tq trwi^iir ol.l. o. )& $,qmrv"i,Jd

S*fs\*$J.q >u.xprdiur

f{so) =??(sA\ = g?, = %Jr.?(\o/So) * enJ,?(un/6) * %n ??(U /S)+ e4n?r?f[a /5,rJ

A.n"ilq"\ {.[o'**i p"l".h&l$,0lon as-dt#o-ah r- cd nn fCIdr ry"^il

\X*",**\o\ od.' pnohotil.{d#h ;'u ?(\"/s,) =ft6/s,)da

ao ?.

o*\$

"rs\d.r',

Page 8: Curs electronica

?(\^ fs) = Ip(f /s")d?,An

t (0, /3n) = {' p tR ts^t aR"A"

?(\^lSJ = 'lp$

/sn)di\M

\srro -\,b"i-e ,O'*rffJil* p- dsr^r,'-"\ Sn 4irrA-d |&q.ryno.r od f*ffi-lr\J"a cp. "n^\.$ \"lq hd {i" .r'1$1o, -e- pneholo*td*o- so$o^r-,r"t[*-[r^t *B*

ptf, /a) =pffi/oo) " p(*/an) = r

f$/s)dR,= r- Jrs/s'w*ao s"

$t*K^ldR,= r- SR/s^)de

\1 \

6- *bJ,i",,t , ?u= e""?$N/r")an * 0nn?oln-Jtt*lS,)an] *\. At

* h$o [t -I?N/ql{ * %^?}6."/sn ) d?,\No

s

t = Cnn?n *CnJo - le""t" - CnoG J . ffd/tJan *Fnfi + gqfl .

5o n**d*d Qd daaitiilo. {"I}* xomt nmol

rls x.d"ox&, Cno-%o=e4) g"^ -c,\l = o.-

-R, = c,o?" r cn,r?n + e4?o *_l&..ip^16"/sn) * ef/ptt lal]re

?**"* eo$uq l^'i R, r rnrcar$$' ea, ffiT,*dJ "d h rmgo*iv,

ef"i(*/sJ, e,JPo1ff /s^)

?(F/s^) 9l 9F"offi/S^\ x< 0..,3^

-- aA,rd "$q$ l'i'.R oodr iso ruXiusnrs.

No (o ro d'sw{q Do) ,

" Jt(*/sn)aR,ao

'"^^,y* .trait .-tL esndl

8.

Page 9: Curs electronica

Sct\\N+Q-uL q

bE?i

!,-) Sq qs*ni-doo& {.*,4* *r(*) =If ., xe f, K , Kl

gR x dshss.,rs^r p*,s* p=r, +"ffi .r*&r tu*lt o,'f*) ^d

p*-\R

\ e^\*+\ dst darvrdsla& O. p"et "t+,.!rVfo q. t+rr^!i tqs.iqkir\q

"Iqotsosra l.ir nfr r*

eNa'S*e$ \.'*9:* J" \."J"+ ol;sqiq\d , r.*ts*d;So. p--*"- e,ot"$ 1.,,'*""\ rJutt-)dx = 1-

^,Ko -t'4

J*d* = tt-15

dt" =\ :b, d= I =of(=36fLo-- '-5-*- vIr(*) =Jiur*-,['id* =Jr\,=f]r- _ ,ul' _ t'*]

-,,o -o. + -qg 3l-yr-ivr

vo\ob'Id dson t'(-t<,, rc)

?"'X* x <:K =*T tx) =O

ao x>K "'oT(1)=1 . n -9 . r. ,5d r*. d*r*rnrsnr ,rJsouo. "^*&s , u*\eouu r rolh p,8{""[od 3t o[*gl*,1o,

F".ilN- oc"**\R tL\oalh . k , v. !f-y

F = t3**r- =I5.,\d* = ?:lT = *" = * l6f = * (*)",.; -K s/-G 5 5\\'rl

f,=f -g* =r=#.€)"" i

A,) S* c.**d*d s w(*)= (L , lxl <q

JJFF(o , lr,o Surt

ffi b& s, og.\$ t'"aA* 'u"(*) d h {.,-d'h do dc"*ldr "tap*u\o\i,\rfo+." 6,. ,r-$ndr ros'iutol\o'"\"&N ;. Sd x *$*-\n** \;.f.- "tt

xpn*'ifiL.r"S $ p,sb..h$ifof"". ca ,-p,\sos*o-

^r""r.ti nq!"Adt"rt pod"c^Nos.l d 1* l-

i*.i$Br\s\*\ ('O", r-) .

Page 10: Curs electronica

Da

f*t.lax = \-O€

g.il=\ =sJp.

/txT(*) = I \^tt'.)

J_Do

t\qat x <-l-

^L-s t +- dx = n. cnCrxroI

-

J rJ.8-xa-t

*l: = A' ii : I\lr

d.x = -\- I 't d*iiJ Vir*_()0

=o+tx)= +Fd_ =oMed xeFn.,o]=o,T(x)=+[:n, *^ = ]*o6*]!l* :

":r-\JGqL rr 1l--e-

T(x) = \I\sud x> !- *, T(x) = $a.,."--o

? =+l# = lL *il" = {[i-ol=]o

b) 5" **d*3 ln*oh\o "I.ofsonr f *".r{enr- otir$$nt"i.{d i,., (-q,a).

S r* dd.^,*t"* &*n$dso dr poh"[''\ihJu. E-\*ro]ia d" mparJ"].r. o vos.iq.kQ\

"\u"Ses,r *L= y.

q,u[*) = {r< '' Y€ Flo)Lo , ifr, ".rhlro€ nA .,q.

f"'Ulax = L *J*d" - \ =s- *- l:= o

,i! (""0 )$.'")L .$

-{)9 -q.

+K- tI.0.

"r*.,(o ,

.*(q)=.1rr(x)- \ *ry(q\=+6 lt(.il\ o rt=| =o{,(il=_ft,

*= \ ^1-n(tt=-f,*

ur(1) = f," '{"t ,,tet-,a-}]ud

[o ,, im $.&\t

xe(-q.,eJbo l,ril.


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