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  • 8/8/2019 Zbirka Zadataka-matematika I

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    / tsRKAZADATAI(A7T,ZTT,

    7\11ZW,Lv"R.

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    223ZI V*&f*i

    1,0rvr***@ Al, "NAr.,rX"i"1; ,rrh* a T_W ^rr,,,&2 c,vw?-t * tuv--4 ,#/,X**27 ,4A L ^ .z,\^,1,i*" ^,J,Jffi'A y 3 c.rrvvYtAfu p fuW dJ-* -5alt,y=yfi f *'n,,{.u'nl.y't,^ WxlI-tud ) ",1,,

    5, V"U"; X;i 4 ,>tf^Le**- i ,,,aj^'4.'U^/ * r[*"u,|),Nr),L"wu=^ia i +tsL X= +A *i,6. Vr,l"l'ri. Ll z^t^^$ ,Lf nL qno", i i" 4 z w t * A^-q/" 3 uftL ,\L "dh oJ^.e;t/ral/-tXM* a ;uf ,,ro,-oAio*rbr,* W A dJ-d A;i ,r"i*r+ h" &,,[*u,A 4 rt* 6 ;* , \*r"'ri tt ^rrAI-." p*'-L"*JJt * 7,;Y ,^r")^i,frr) l ; t n* **hrrv'L.a tl,*"*rti ,\t*toi*-

    l lza+4&l l L l l3d-4&t l ,t ,W,rr ] ' j - i i ;& W,Uf o*Gl", *r* |*4l l2 i l+g#lt .g. ,AI;[-o- ABoD w"'&br"*, 9r** A;4bq".,P^t,( r+ I 0*lllp4w nC; f'6 /izlrtLi, i"*rr'*A,^*,rril"Lot.l.,fi ; f,fr, 0 010. lL ,i""-e. I*"L-f* ABC,* tJqe,*.*,,.*h*"v*'-'^:= + ABt :,f oj, ?r*n"L r-),f.r*ALt irr^!/ri^^d.,t"rV ^;;f i, W-,t rtr; nfrvni"cz {C , d (

    I

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    230 ZL U"Al^*dtr . \ , to, ' , fu4 E*C7.f i 2,*y" t* ArB*LN Lrir t*,*y-t"wt2,La,W yw *r],t * a;E ,:fJ; l ld,+Eil={frl{ l lBll{3,N/.,l*k*Jd =AE,B: Ab B= t.?"*^-A" *,!.h"r,7,\Lt y;,f,"A*d,l-& A? c7 i -Bil,

    roil"U* lr*.+e*Ar*a,u*qunA*aBCDvnihh*ft *&I*,i ;=A-$,E=il6 ; d=dB 9*,*r;,, ^delffi,7,,\ ;t r,,1'b.l*r,L** {vI ' 'D o ,r i lu l , r "A^ 6C.TTT'Y$, Bn4A/*^rr)rl*i 8 ,t ; t, f^',",f'"nq^t4^tA 'I ' t turyi"I"k n *rl,rn A, f*^.;* t'h *d.L** Y i,;i, ,.l"jd ie , "ht yS

    ffi ?*;"" ^rctrhot',',X ;Z ,rrder"; tr].j"*

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    2, V*t*,"r{ w /eoaL,eq^know Ar"^ta"* 2312,V"!,*,^i ,w /t^tf,"",*

    zo.)A,,r*A,Lrt fr^r^*f,u .Jrh^* A f,erll*-* * tt'i',lr;A(-t,10)i r',,fr,11"* Lrirlri B(f , - 4,S),

    z.z. t*t** *1*^-d=5 + i - 2i' p *,arbJ,;il'*, V+ * p Y-i*i,a,l*, ,ZS,13ryj^rr,^t, d"'I;rr,*"r&t^* A - -2T+fi- SE "uiol"nL't"^ft [)^r*W *, lqi,Q,r:-*.ot,z+.0),+');W|"^L ^d,J-rriB (o,1 ,t\

    * 4'* ^'JJ'"t* g ' "k 1oA(t'e'Affi U n^"i,^*,ltt'*?,= 2Y tf -E ,AAd; rtLJ'rT-t- ry/vrA,/ tilZ.t"Ol.t 5 .26. r^;^r ^; d"^I;,t"*^r")rj*" 6 = t,*!T *,lTT- ^fT.o17.Wq /"'"^t

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    I, Sl,alnd,j"39. *^^-; l" a ,B = J.Z,oT' ,ho,Yo$tLn/;n"^o4;lr nt^^;

    ^^r**4",1r,W Prr^;irrA ^rrj-fd*4 M,&'^I' ,& 435o .U,T.irLo A,b;L tuw..,.' 'g,'"i tvkuhw Aa,Attrrt/'/,/,/4",,^A,W 4, 1"'*"!-rr*4- - AB,BC.

    \4, \^-;^^q *"A ,t;ky*&y,)" i=37*f* zL" t'^*;,,,* br""f'r-,- ,;^,>J\,

    lv

    43, 1a*;*-; %^."/*rr'^i ^",- *LrJtu .Rjrlttu A =LT -fT (!""**fe=:r- t l

    m \,r"^;"t*t lr"A ,hr*A* ,rtl-f*, 3, E , &" 'p( t t d=2T zi* i , t = i - +i(3) = T.i- i , E=eT-zi-t i '46, ^-r*^i,A* t* X= loT*Sf,+ oi--^hi"-st kil-; "r["f,ri fu"j--,hol,V-Ur&; l*^f ?*^j^x*^/ra4r\,ui"Ate"t[r;^,"{ l""r{ =si l_zT f E:3i+4i "^r, t*"di lA:f f i ,*Aer,"r*

    WS]\,2^-.*-n'y'* ^r-j&rrw--+a-3G,op "--! tt=3Ly=)c(i l ,?)=G0",(t l a= f-2f,*ei, E=zT rT-E(3)d=5i l* f ,B=A-2V,u=26\ A - -d +2&,8 =3i+i , r '+=

    ,E=E=i

    ,B=T-iir.riE=-T"3f )d'=Tzi.,z["-44i zi*+,fl"

    (e)(4)

    | -t , ^?, t C =-Lv

    "N"r"^tU,

    f2) i l +t T,B= i *T"t =3, y= t(Arf)= 60or=f r y=a (d,&\=1Oo

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    234 ZL U"*tni50, "!.t^'rlr*ry,"fud **E p ,r.Lfq3T*6fi.,Wf,vJafdffi

    0)A"^*+i 0l d ** -ttfl,Vn'l.W*o,trW 7,,*,t p -/rkdT-6l ,W f N*,,-&** yi@ v(n)+d, *t (il -27,"nt

    (o fi,c*il (s)Rc,n

    ffif"^4 *A^t,,+taia^"s " J"'W, ^!rort*^r

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    4, YrA*;.vtL; ill*,et^h *rlf-* 2355E. rt-;^^r,,'"t ^,&ffiL;, ,,r,*,*r;o/""rbf"r* a= fi-3]i" L I = - 3T 5 ,.59, ^;-,*t rt**"!"f';'A=-4i *2i ;I =i-St.x^^,Ut*Br"{-t**,*Efu f TT itil*( ,1) @,o,o\ (2)A(3,3,4)60.Ur*A^ )LMU ^p,LJ,r *y *'1"*t*7,*E , oJ*f d=zi++-3[ i od=i- f , .il, I,a),',ni w ",*j*i*; d=hT+3TLE=4i8T.t \^!it^"^ ^R!"f-r*

    AE ,r,^.4i0, ,",'hrr f ry ^y*t 4 *rkI",*Afr.U^d;" A,oJ,.o\h,-i, z)62.ffi

    t- I Y I Y Ib5, v?iu/uJlta*fz ^* U ,i t ;)

    vt ,b = .JL-25+u"y w,Q-\A=rt+zt4i,=i*f

    u = 4., = 3, y= x(A,&)=30ot t ,= 2, nf= 4, y =X(i^, ,?)=450'

    y;A^r^irr'," Abra;; b.

    4=

    , o,o) , B( , l , { ) L C (2,3,4)td.";"L Bc,-lxi- tt L =* -li

    \S^rx

    ? + t-+b = U +Icl ,

    ^,ddlnttx^eA ;t,

    ( t t d=-t7+5i t(3)a= Ai ln? ,(+)a=-3fi+24,

    -t--6= v -5b'i > ^-+b=-u+z\fE=5A-

    "rffX " ry uj* t*H,r*+a-(-r,o,L\,

    67' t-a-.:f [-6

    Fl*iL X^.|"^,t,7l.a.ztf?-igtr^.t'a

    7=i-+i,* mt*t.f.Jvq.6a,

    A=;/-ztr - E=31

    es,X.^ii,r i ^*Lhrnrb ^^**r4*.1" ^,*)tLtrrn- 6i, ;d""L ,^'*l'-*"'l-h"'* 1

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    L36 zT, \)i!"t t

    , t =+i- zi (W * "*h"b\i =T T tE G"f^s' * c'.'I;*'"h;*'"\

    ( { )a=T-si , \=Ti inzi , t=T- i \ ' .^y"e*)qr,^,k;^e') =37* i , B=T-T,Z=T-4T+2t, (Wr*&L*, \

    70.AA',r); *J,*.-,. (a*t\ ^Z ; a ^(g^i).,^,!* Z=11,*l*tL,

    Tf D"'L"o;;,^, (a*()"a= a"1)" I trb rSW ^^r)tJ."t-t 7t ^,a/ a.v^/vvt^/i4^LJ^A'rrr*t ^J-ttu*^.-; ^r&,f*;r.,*v+-, 1, ,v A,

    72, "A'"P ABc,5W /r*il^"X,n"4ry ^"'Li"'*(1)eTxc6 (z)r ^& (r) f t*et73.N"X*tri,tcUEFGVl'P;^,;^*"'"A*,\"*\W ^'"Lk**( t) {srf f i Q,, ACx CA (g) nG xBH

    d '/ AMl4/^,r/ph *J./.rtr*

    f ,=-ei*" i ; =-3f .8.

    7+.75,1LL"/,^.y 7w u-zi -,W /,*W (A"t)'7 ,? /-+ -o\4, t--> ?\ n 'b . \Axc) tu \Cxo l .a,Y6.\r,*;L y*W W"dJ^*i , t ;2,&tr( , t ) a"E) d = L (a" E).2" Q\ G, 8" t =L6". B*t)

    UnU*;-n'W W n,th*,,^*7,,i,1,fu({ )a=51*f*gf, ,E--uT(a) =47-i.2i , i =zi -V"YS,t ^";4 W tt^."A,* ^,*{J"V ^il'}o},tu*i,7 ii , Jd Jr,

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    0L . -, .- 24ly* fi1Jrrt^w 6, ,tt e- ,

    6,

    56,"^s;^r"4 Mry *o\*},n'* -.At -2T "k l, A=i- tl, ;E =3ll ri ,gY.YA^l-;f lr-^h rr,^"A*^rrAJLrr*Z=A-21 X= d*t , o'l.n ,ilJd'+r,aJV^; '" ,8E.1/^" !;" ^"XI-i 7,l ; t, lr""+I^"^ ".^, &n t(r) =-7*1-uL E=fn l ' , = 4T ttf(Lld=f,*aE,t zi-i, 7=2l - AT+U,

    (3)a" 3i-#, E =i+5&, 7, -2i +&

    *4 J.W Ni,tt,lr,W@ /fr^"";A0\,52", i^^W,U r,!,f,-i ,=T2L,T=sTi L =T-ulN """^;'; ?

    ffiffi0J^# \"M W . l^Lr )*. *,.11,,(2,-4,5),B({,,8),CG3,o 2) ; D o, '1, ) /*A'" k"-Il-",, ,r' -,s4,{rA*p ABCbEFGH

    H$,1/,

    ('t)AB"*) .e[

    *-ti-|oa=i, \ ,E=g7-sf(r) d.B)aG.Ae(g) '* (a.e)G]

    W /rtl^^r,\""oLrno7'(e) tts ffi). i (3) Z-BtrEF),')*)*)

    L 7= 2tr+V,")'r

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    2\E Zt. \h/,j,ei30,O)^dd Aw axl,Jst

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    ?,*",.^, 233ZLT to;\fung/1,**uorr2

    rc2,0),,r*)*1"*rl* pr^^*1,1,*o4iz ,rcg,O)4"d;r.r^."^rJ-"")pAdil,* W #,1-t*T@t,,+); fl+ p r^ryd, ^ rn 1,

    o I

    ffiJU,,.,V Wyp(1)

    (z) 0;* ,e,")ffil?4My* u h,"i,L.(o,,,tr?,)Lv( ,o, \y** * =+ =+ ?lo8,U lr^Xr*",,*1pg" )' l-^/*r,* ,t* "Jr,-t^,qto,A)*Ai q;b t")*n),^T14,Y,Y)

    (1) ,

    ( , i ) o; *,y)

    t06,

    z+3 ?0r+2 q= -T'.

    x-'l-9x-4-o

    x-{ y z,-3 :-3--=A=T ox+2 V-2 Z'-T-= 7=4 *x+5_ Y-4 _Z+Za,b3

    v

    v- ' l2Fd,;,IYw"

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    il|, U ,LtJ"*r,* 11*o-n'nr,*Lfr*r" # = * = T,V x+3 V-3 z-3-2 1-3'

    x-5 Vo , l-

    x Vt4 z-4-= += .-511

    Mj?.l^-l; 4 t"rilr""* (z,t+,3\4 Wb ^lVL f-""h ,(^,,1o*lL1.

    2,RfuM+,A)^

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    z,R^*,n ' 241ns,Q),+r); ,W ilrilril,ru 'twvr1,i,twx',t0va.)A'n*,ilWy W

    f"i,!"-'*T(2,t,4\"rryrA*" A $a^tuAlndr4txb,iffi W p^,'d;.fi",WW L,;Jr*,fi(t,yo),B(t,L,-z\ L c( ' t ,5 ' ,z)

    ffiffi U"rrh,pA**Jr,h ,rw,rrr;^^LY(,1)

    Vg,0)r"d'JA(a, ,o\$o,O.JaqA;T Gz,o,4\

    i3{ ,X* *,rW t.ot)vtArvw

    (zl

    bA^-ilrtl"-tu'r,,rr,t"W fu I'"{et"'*, , %(o,-s. ,o lc(o,or6\,l&"'ilrilr*410v$,;,w W * ftil"-"*, rry^d*" A ,-Ly+1n=4,

    Lrk.lro,A(,r,,,L\ tB(o,L,-l\ L L(-5/ - e, z\ n'i"3x-2u-x,+f=01,$2, 0)*); w ,\il,^*-,fi, ,L".r("r;ld- C D ,* X.-it kdjr*T(4,3,o) / ' ; ; rw -r-^,v* i"nL-2y+(ntD=O.l1l,0A4

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    2hZ ZTI.P^',; ; .ra",.;,R,il}Z.lW l*"*Q* rol.*dr;J"* ^W M,,w;,$a,[-"+t+2r=t p\ [ . -^-1 f , t t .+4y=o' l )| x +11-r- =-B t' ' l - 6x+Ly+3n=B Ls" -4!=o$E,U W n,,^rr i , t l ! ,t25 -2n=5 L 2x-21+r=O o|,ral-P'd"^d,erLrov'^ryJ*ql"^^h,ro^n^/J"i",$n,Y-w ^/y^dr*.ted,vi'r ltu *-Y+3a='l ,r,, *-Y +7r,=3 tJ^uJ; fu-

    A;r['* 'ft),rr"r^,{"^r, 4v"tq,;rt',1,

    I l . -22,=4L -* *4Y = ${rrf, -"J" (,-* Wi;"'4-'f s"*|y+r=o.

    | -Zl+4x=2""^"*, dJ*dti/t* /r*"r).* r(r. rru^r^^,"\,(/td

    ( t ) [x+31+L=O El -2Y*42=1i rta.'p"-*^l; 4v',ta'.,'tW @ Itl,!"-^,T( z,- s,, ) L Wi',^icir*4{arnJvva'rx -y =Y,, 25 +32 = 2-,

    thlr , **A^4 rL^^t , ,M,vuwuwx-2y=3 L 3'tr- !n=2,kg,9,*--o't^ .,'^"t^;"^'e,W f","(^rr* Lrirlr^r* T,,(o,z, o\ i 1r( l, lrl\ ,a, qo,^r,,rtt*r,+J =l M e k'rftw "L n}o

    t^ 0 , o rv146, !.ro"tuS; ,\r^t;r,^!' k, f^atqr. Wat^x-"" lr',.ul.;6tu Zx+y +r.=4/v 1-u=-6 t awA *; "J-"e,$^h i l " 60",' l 0

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    3,?"-,r"- i ,to.*wir,,* 243^{l5, Y"pa,^,rW

    !rB. ;n X; f"*- # = + =+ 'w '|t'.,,,\,v;n;+31 2r*=01,1+g,\,,*i*U Y-^,--+= ry= i .w^rn^r',a,3y--n-l qa,',LAfurJ"'toito* t,a

    {S3.,0X";; il"*};/t* ,ro^'wL,,l.+', x+3 s y*t - z-z/') -T-= 1 -l .0 , o" x-4 !+4 z'- lttrspl /,t/r4/ tyM^rw -:T= -T-= -O00 |

    tS4.U^dt PW ro^,a\L'\,,ff i ** loL&,*1(t,'2,6\ L-x+4 Y-3 r.+2-T= -T= 1 .

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    244 - f f f\L Ll , Y

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    245ZIIIWt,\il",,,il;.k ^^r*Xr"U fi/ffi/\rva/ tu |

    tFf \il"il;'$- 2x-3Y=3 /'"'a; ''"*'M'^ "U;/*) '|14a)-Aff y$/tn.ut)i

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    2,P*r&^r

    irSo;18 .

    -3x +5xL-Zx + |

    6x3

    246 Zffi ,T^t'e.'i;

    t*i={ ,*y= lEl,{rx;=It+, v1=

    2x2-48x-4 L-? tEL'x -ttxx4+2x3+

    3x3+' l ' lx ' lxa+6x'+92x6-6*# xa- ' ltn)=

    {r^y

    x3+' l ?^ zx"+ZX +X ,{f,5,, ft*y=

    I t6',

    {88,f t*1=

    ffio, x-43

    4s+.\(x)= -l t,X +T{

    f c*1{r*1=

    fr*t={r"t=

    *3X,*+

    t x=Yx-(s+^):6

    t x=2

    , X=8

    , x=-3(+).n'l?- I

    {33.

    * +)**'(fr-'

    ,,9- o ?

    3r r-vx - vx2Lx5+2x34 -x

    x= 64

    x= -l

    x= 10

    2x6* *o- i -1X J -X9Zxt+4x5

    fr*;=

    52x -x

    i f f i ; i r*y q; r hr(x+T) 'Ly

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    4,%A"*WV,W 247{33.r*r=,w./a"{; w ,x=ro,zoo' t t )= a({a"*g)*304a Zkq..44ruzol . Jt ' ) -# '(alox - ba, tx00

    'W-34?A^dfWWy

    0;"1; e L+% (^,^,1;1,*t5k-e*\4

    4

    !.*91.jt*)=sog,f r^)

    n--r t\l A,oA A 1t ,64u (x-,1)- 2*

    X= 5

    x = lo00

    x=2

    x=6

    204.207,

    2t0,

    ft*t=f ,"1=fr*l=tut=

    3r-= rj -2x4

    t= (g-6*) t3x

    ' - Az"-y=4ff^ffi

    0I tx)1,"\ , ,t,"

    {c* t=f r*t=fr*1=

    20t,2o8,241,2t+,

    206,203,212-,ztt,ffil {t"1

    2x-3

    0 tt 4+X220, tx ' t= W g_xz$,l

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    2-48229,

    2-!8,fr*t= x3*4 fl,l l)=tJ-;240,{o) = 2x+Xnxt fftx\= f,;242.f t^t= h" t Jtx)= 0^+5xL4+,lo= h" t f l tx)=,h40

    f , r . t= ^-2 t ?(x) ,( .*k*z)r ,LUl = ext l tx\=1^ , ho1= lx\ft^;4;

    { f"l = az+r.crtx ) olul = N,a' *" , ,9" *) -- 1l' 2x

    a-l'r, f f i l t^,= ' ( ' * ( l+ ' I i +x+ xz)\ri,48,260,Ls2,

    ( t "1=ft"1=fr*1=

    x o^'exv+ (- - +-*t+x)

    Z\lT,f^^"&*fr,1w 22s,lut=E+uF L3o,ir*r=ffi

    0U,;; Al'*",*.,WV ff,y\c.t (7"1\et2gl, { ,^Y= -3 t Jtx\= x'+2

    tgruiu1= t }6\=235, f t*l= 4*t'l frLx)=.,GtL"-.*l,")=^u-^ fl&l=2233. {t^1= rY,nx qrxx, ?(")= a-241,luy={ , ? x) %'* *243,[t"1= ^-'-* t frtx\= -l

    priltr2h6LAY,

    5.W*W232,2.14,236,

    251.{ t*1=253, lu1 =

    f t* ; = 2x-\ t ]1o-1=x' * {x

    fvy=*tJu)--*\t^7 x'*x t ftGl= l

    h(xno+40) -1

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    243LVT.\I(^;; )* ),leovfuwfuv,

    2rS,1r.h#

    @ fin'vtfp"^Ie,&i,uWW f

    G,WW26o.fr^l = x2

    ,3s31,r*l=xt* *26,fr*t= *L6s,{,0 =(4*)'

    |tre,: r^t=3'*-{ {

    261,lul= xorfffi \u1='-r

    2267.fr"1= ,

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    ZTTT.I"o b-:pUJ

    250 T^Iq*

    116,f rx)= 3 211,.a{i,lvt=+ zsz,2.E+.ft*1= i t' l gES,Ltr,{rr1=o'*t - 3 irff , i

    2$.lu)=23s,f r.1= lul=fr'1=$u1

    2Tl, f ,r1=hx+ltC28O, f(x)= x

    n tf:-_fL3,,lt"'f 'l4-2-x286,f c"t 3*-t

    iplr,or^l=^'- 2x+2

    reo.fcx) hr\ *7) Lnl,{ t* t=41."(( l *- l ) ? lot t r t=+3n*(ex+5)212,$t*1=urt, ti^|x ,.13.f t"t=am,wt(4x-{)21t, f rx) Zam.tow$+t\

    3aX - Cx3 --;-, l xL 2x+3

    zXY,10A,103.

    x3+3x'n3x4r=-t/ x"- 8l*(t-2*)

    3o$, (G)"=" z4) x>zo307, ..f,F = tx\ za/ ,t'rtq/oL3o9. ( t.F)t= * za atnlzu xX{{. (( f r) '= * %a, 2.Q3l!, arrO,a,w rttnx\= x za' V{STn{5, 0,"

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    25/83

    TWWW* 251

    { r*1 x'+2xf t"1= x"- tx-2

    )w= *' -2* 1It*1= 2x2+Sx-l

    327, \x)- (x - 1)33es.{cxt#1x*t1"r*- l )a33t.f txt=#(x-t)a(xrz)'(*-g)'

    x-2x+2x- l

    (x-l i \z(x+r\350 (*-r)(x+3)e

    xx+3x-1( x+e)a

    J x-d(x+z)].3xs(x-l)a

    338. a.,u\={txt+l333.Xtrl= t,*l 33s0.gtx\=f(x+l)34{.1tx\ f t*-a)

    ,*gl329,

    J{"-,t*lTW (*326,l

  • 8/8/2019 Zbirka Zadataka-matematika I

    26/83

    252 ZIII .T^,,e*

    3&2,355,t6E,

    Y=Y=Y=Y=Y=Y=

    ww'w36t.3Y0.3Y2,

    ffiy=\r(x-,t)Y=g*-aY= la*xy= *r*x1=a;^(:x-s)

    369. -ffi 3-*=

    3$t,y=*t-13tr7,y=l /*(x+2)350,y=@353,Y= - 3cotx366. Y= rt ir*(x-z\36e.=+c'r(fx+z)

    x2+21x-2)a2*- lVx-2Aily"SxcoA(x tl)

    3$3,5=3-*"

    3&t!.352,.cs5.

    2^-4= 51i36 sy:,+*

    {oozoos= 7,83

    f f i G"Bn' to*Lf4

    5,9$tl^,r"* P^^rttt- j" P^^iltl; y* )/r"W'ei^rr"t*WWp"-qk

    390,hr = t,x2 36f ,('** - -or ZXt62, = 3rl-h f f i %rx=2'48ff i zby*-3)=-4,5'3 365. S{*(**+2) Yn,rc366, I 'Ar(l-rx) = 38 36?. fur(s^-1)='15

    tr

    /*r*0t

    40x= lL45* = 4ooo

    gr+" ,zu^-'=Ll

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    27/83

    3,9't^1^nn;, x'J^X-L 253

    ffi c.ut(2x+7)o,60

    f f i I o

  • 8/8/2019 Zbirka Zadataka-matematika I

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    254 zl I Iwffi+.A)*h ^'^i-- *

  • 8/8/2019 Zbirka Zadataka-matematika I

    29/83

    255

    t,Cya;r,* *p,^AZlX -rt338.

    400,

    /1 ,

    410. U"""x -+ toaml ,U,*'*d x -> +oo

    lrltr, /^r*x->+F

    ffiHl /';,.-i-+"! x++oot{t.. X^i,*X ++oo

    " 4zO.Xto.*x++ea

    x-2hn tX'+JX-vwLnx -x -b;ry+2x-5

    l lx -J5w-1x-12-x-;:=tz-

    L"*x 'r 2/)*,

  • 8/8/2019 Zbirka Zadataka-matematika I

    30/83

    256 7W, q^'r^;,it^tuW ; nufx**,^P*'

    hzz,W(#"-*) l*r?,\,W"&)4zq,h* (c - J?;{ ) +zi,h'* (Pa- C4T)X->+Oo X-)-Oo\Iab.\;,,- (,.-J7;;) +zy,,t;, '*(tf,r+x+1/E)I -*^'*.J x++r x? -0o

    425.,h*430,fu.(*-W)

    +zs.fu,h/1\r 'Yt?:I l / ' 4i45l,l /\^/r'rt :L; "- 1 x+O- {*._r..

    i,+,la;rry" a^o\n* 4gs,u *fu *x+2+ x+2-\,h"1*,4@ Wrtw\teffi,*

    ,^ , o , t f i - | , . 3-W13+./vitw 435, &*"x- '>1 n-4 x- '84 'w-3t- :- - . t o iq-4 r-*-*.r r , f f f i -1i436ftUi',N+:*- l+S2,1tu^,L**:-,..!x-+64 ,[ / -8 t-;;; l x+-2 x+2

    h q-2 n." l r "E-S436. Li^, #-- 435.n,u*x+4 i l2x -2 x-+o x

    ( , , -*)*-q X*on

    *ao1+2,'l^r* (l- **) u i44g /^r* , #qx-+o [. . . " .- . ; l x+l' hh+, *.. (,. *)* 44s. k* 0 - E*-) ."x->tac x+loo - '

  • 8/8/2019 Zbirka Zadataka-matematika I

    31/83

    lL".:tta,i,;W UY=t MtN\6,

    4+6,+60,

    /161.$ = 6x- ' lx+2x4+x+6+, =ffit+2x -3

    ,(^r*x-O/rr*x-ro/rANx-+lf

    XAi'wxt*ux

    Y'-r-rrtrhF,"t^l^-u452,h*x+O

    m " ' l -3xIffi ,UJ*t | -rffilnlr *+O XEffir / t d- fro /.a./awrp-l|F8m xx+o

    aI-t = r(*a

    2: An;*,ti-\t'I

    0, ain4*A rrw --\+o0 , czlx- 4-r

  • 8/8/2019 Zbirka Zadataka-matematika I

    32/83

    2r8 ZIV,W W;,wyxl"t"'**'

    U"d; W/.,f b t'"'td^*W fr*rX,,rA'ry-ft,iniu ,w t ;1,,* xo4'.13.

    476,

    {c^;4t0,

    {c*1=hEz,

    bx-4x2+ b3x-' lx

    h

    nw x 1Qna, X >O

    za, x*Oz,& x=o

    {L{,*t=G+t\z--

    za,x+Ob za/ x=o

    1= t*t v=f tx)5 =-2x+b

    Yy=fx)

    g = xz+b

    g=f lx)

    y= x+t)eIIIIIiIII

    1",^;,^4 ,"+Ar""-f' l* t" t'AnJ* !f^1.'f )rn "A" rw-yJr"r^^tt- *o tohl.l: o=otil7.

    Irxt=

    fr^t=0| (x)=

    {

    3x+4-2x+b

    J.(t +x)*b

    A{"gLxb

    2a/ X

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    4.Ranl;AA xdae& 2[3\4kd' t , *W yW {r"r@48+.

    4t6,{r*t=

    x +'l2x+13x+1

    x

  • 8/8/2019 Zbirka Zadataka-matematika I

    34/83

    260 ZlV.W "n'tA/wi'ni* {*x +tes/-r*(ib- *)"x-t+ F

    nrt+qog;h.AflrofriIcf f i i n.ffiffi| Xrt'r'wErFFq x ++ oo

    n500, tlit'*x *>.f oo

    (*)"

    (#.*).501. /tt^, wrvrax -r loo

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    X.?-Oo

    g02.

    5o7. l lwYhewwll

    s6,0)^*);@Wh**ryL W(x +b)" za, x 13x3*bx zar x>3,(if; *{rehf- * L#J.)xo=3,

    I {.{"=

    +37,

    ffi

    503.50S,

    Aa{wx =74/ X< OZat X =Orat x>O

    n , /t/vw *,-{x +1oo0, xffi ..t3-

    / r \-xl;"- t i/X -+-oo

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    261

    , f \ , , ,1, Uuttnrcr!,4tua

    ( l ) oA,3)"d5 (z) o^5ddL

    i$.XwWW ft"1='-2{7 4 @ fiir,nX,,ii,'-txt@W \; A-ui",,;,L{'ifle* x-ow(,t) oA, Ad t+ (L\ oA h ^d 4ffi U'+^^,W5=f-*r "d;X"J'tt * y W x a'(0 d^nfoxn (2\ 04,xz k *nV ,U /tu&';t^;,L ;r"U ,^' "U ,,^,nit!^rr*|0 t6

    5V.Q)n)i f,rr)-"^^&t,W'd^^;rl"*PwT {t*r(l) '**'e"d'^f1x+a*)- {(xl

    AX

    Y = x +13

    Y=3*513.51,6,

    ( ) oL )dS )'d"^

    avAX

    { (*+o*) - {c*l |at Ax *0, OkAX

    (z\ f,A^^},,i*

    515,Y=^"-15{E, r1= c.c/J

    V = {3J

    ! -Jx+25f4,f t7,

  • 8/8/2019 Zbirka Zadataka-matematika I

    36/83

    "' o;W wyr,1=r*rwYq w,^^^x,u' - /)r,* +! = /,b* t(x+ax) {txlJ axoo ax ax+o a x

    513, Y=7ffiY=J;l

    120.Y=^-7523. Y= 5"

    ir-m -z ,HUW V=X't-ffi |

    52tt. Y = ^r*x

    xo=2xr=3

    I xos{

    528.(x)=t*u-33ff i $t")= x-xz530,fv:r=x3 3^

    ,

    7"*W1 ={t,tf^- f*,, kn"i^ , , , -%Wy, 'yW,'u,,= !J,r* :g = frb* frc'+o') trr*l) at

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    37/83

    Z.\;ty*,,-;y 263

    I xo=3

    t Xo= f,

    ffilL {^^^W {,r,= x'+x "zne".r*J(Wy L ^;+A

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    38/83

    L64 ZV. \-,w"6 ;f,ffig--t- LY,*W ^*,4 l*4"1^l/rr,;,$-Ud/n*yyfu WryXtttL^)*,oJo.d rto ^^5ttp"nf,-',,"r*

    l , - - ' " /^ , A h^ /na,r 4r2w\,I550,?o,*n*A^+'rr^tyL^ ""fui ,$AJ"np fJrL,W Yy/r'r,l I*

  • 8/8/2019 Zbirka Zadataka-matematika I

    39/83

    W g=,toh.

    *g x"- fi1= "-h{ .ty=-5 l ;y3=-4a,*, t inxy= (b-$ l;y = abe/y = t '+4*3- 6 l*"

    W[ 1=(a+g)x

    576, =x3+x578. 1=,i^x+wx -45E0,Y=7x+

    586, ,1= o*bSEt.Y=' l 2x+3d530. ! = a" +b'u'*x- "532, 5= "cdx

    sEl.ft3,5E5.tg7.s83.

    W Y= 2$-x2)an,rl*t'tx

    D-"f^^r,^f WWW Y= sx-4)3 609.ffi

    4.1-,;',r''^^4 /rl';-r'1".("tJ*hf, 265

    Wffi

    W 1=(3*"nh'\(oi-z)516, Y-WY=6oo, uJ

    xt i,tfux + x

    6Xxgxe^- |

    W y=o4; +c* 5iffi '1=xL+t\ ntl**x535. 1= ({+2*'-lL*r) tti,*x

    _^. .53?.Y=+#513. y= tYx-cst=x" l,w*4 - CoL*

    Hfiffil x-'ltf#,,.il"{ .,t = -F-.'rJ " X /hq,x603, Y=* elt**

    .1 (t- a.r**14Y=moe,g= 'f,ffi

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    40/83

    @ y= i,"'(c"dx)Y=Y=

    y= ^, /"ax\o^-r-nh er*(u*rn*J/ ' *(x+ex)

    t^4 brnX.';r*W628, 1= /\^n^,al2x6S0, t = cnto(x- ' t )

    ,zx-46S8; \= Airt -ffi@trr 'l ,,WI T=Van(xL-,a)'a'+

  • 8/8/2019 Zbirka Zadataka-matematika I

    41/83

    638.6h0,6+2,6++,

    Y='/"-Y=h^y = O^ co1,x

    1= */ ,,t'[*L

    Y,\'A^f^* t* .M; xAA,;"t"WiP 26Y631.Y=Xf-1= |

    y= *tr-lanxy =o/ o&Lx

    6hl,6+s,6+6,

    Wts*x y"6h6,ffi

    f f i l ""Jr^", y ' x=-2, u f *t+rI +l=0,6fZ .^ot'r^1 \' ^ y=l , "'llsy x+rL*I=JT.

    ff i x= ,*I,,,S=E661. x=t,et , y=(t- ' l )dW ^=+ht l= /.*'t

    eD^,";4WD;""1W|=frrt"i l^,*@W

    682,6i+.

    65E, '^=\" -3t , ,y=t+3Lf f i a=f. l f , rU=lJE66L,=+, y=#

    r:

    x+y = x313x35+1['= og"v -x+J=01*2-3XY4

    6trT,6hg,6t l .063,

    22.**1 =xYx-Y = Ar,rwrll*y- fiI =ze&x- ufuY =t/ t t

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    42/83

    268 ZV,lz.W;P66+,\,^^.M,tT'* *=f,

    Wl",*"i,^", j' tu y=ztJrtr"]rr ip

    13z,{= L -. ,1 l)2t -3x= + /vt+{

    y = t3- 4L,t+2Y=;;

    667,v =31(-2*",h*666,y= 2 Pinx +SxottxWY=*-5-*6Yo,=^t ry * nt, 671,

    673,67f.W6Y3,681,

    ffi!=JFF-rcax-,ffi67+,y=.lax+rlxi'wx

    cl676,r4=Ax._ I *. 1 Xf 'lW y= tt^*(x")cot(xa)680,Y= 2r"6 {"- l + t

    68+, 1=. ui^2wt Q')682. =,,F n @ f f i J= xe-ur-t**e$

    @o= ;dr+-+3t - qJx 3r -y= {x +, | t , *x

    Xr-X$ = e +qe -bo--,r=b,hx- 7xl*x

    trt-- t7frY='/s ' . l ly = *+o plrl,Ji + a,'relo* ,JVJyWfl*{k*rc)

    6tt, $=4' , l l * ' (e"* l )

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    43/83

    l},T'r:^ra*- a,fr)^r 2636ff i ,y= lx l 6E7,1- l*+zl f f iY=tx l -{683,Y=lx"-3nl 690,1=lni ,*xl 63{, Y=x\xl692, = ('*t*t ffi 5= 'L*xl 69+,Y= |'lnwll

    635. = ** ffit y= **l)hx 5'3?.=(o;nf""

    6115,Y

    701, Y

    n,T'r-4',-*T^ ".,A*

    ffil c/^-,A;Y *w l"'tlwv l.,o=(*-5\'i;,xnw-4' )" ' lno), vyo+,"'ra;4 f "t,t), ^j,rtP $r"1 u'-t - cvt(x-t\ .tas.\2,-^i*,,,,*;,{"(+) "*o i, luy=zG,n L** .

    r^I -xt udl x1o={[ * t z.av xDo

    ( * l^r*t zn y*o=1t o z.a, t=o

    a(I63t, Y=l x z '^ ' tx

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    270 ZV.T"^"*"";.!t

    lat,\""^ir-r, ,,1't* x= 4, ^,tt P "hrJ+,1,(*x =o,ffi \"^";"-r"y11"a,,!= h &" pllO.\aat;'*tay 17"a, j=o , ofu S, x

    ffiJT,r*r4 ,1" a, =zt

    1,zrr";^4 qf"r^41" r,^y)^*,ti (rW I ^tUFW &"Wf""n"\^-r^,[l,brryW/bvX

    Yt8,

    YlL, ,A''*x-+oYl+, 1;,'-x+offfii I;-*\#*f X+O

    722. LJ^x->-472t, /")^,Xr+oo.tr26,./^r^,x->O+

    ^)-r le

    xj =4rh6,=,(.*L; 1=t- '1.

    r=t t+3 i 5=tz+t

    x

    a.t

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    45/83

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    pl

    723. 'r* " /,*xx-> + Da

    {!W-*Bsr-iIJ oo**sh&ftJ

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    ffith o

    a,&x + 3x*in'x +ltx,li*rx +2* + 3^c,r.x+

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    46/83

    2Y2 ZV, \t iu*llfryL,f l11, Jnnogil"a, n Mtrwavf.ol0

    747,0)^d,;"iA,"^)tlj-{ t'r*f^t- ; ^^+-**ltuXrr^"^}rPY* a- *t *h^oifr; * "i':-,"t*;!r""*; l.ffi);rnU La,^rf^XtuW y=*2+x- 6 wP ^;P;v;h,'-NNY'M,74X.0),nd;Wry 1=s* fuly&il- ^ ,,J,J^,h",*,

    Ary t=3x'2,

    iffiU^d;W; *wrrah^,W*u=4', , [= x3+4*hd], i , A

    ffi Urrd;^ t""r*{t^f^- ,'"*,"n't^** t'nZrb a' orJnnroLor'*\= - 2 .ffis, O)^r)i k"r*rfr I* ; *o*-"o,(*/nrww Ay6tii; A

    , l- Y= fa 1

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    47/83

    $. f-&';*p,,'wt 2Y3

    xx=2= (x- ' t ) .

    Ix.

    11,

    763.

    76Y.769,771,T73.775.

    W {c^l= ' 'zx+z\{TTg.$f*l=f f i i r ' t= x-3?;

    $c*tf t"l$,*,f ,"'tf c"tI c*lfo,$t*r

    YYO.772.774.

    W778.ffi782.7$tt.g/rv

    +4 5I *

    7E3, f ",= ,l'l+,lI'

    W?-^.4; W ry y=xa-x.tW ti,t'*A(zr-t),ffit^*"* M ,i-y",-rLrbAG,t\, "^t"U =L*'.rel.\a,*i^4 &"J' ,* ,tfr";tl* W y=xo+l ;ffiI^"*-'1,",& pvWW $=fi iv

    WJ,f^*Wlv)= xu-6x+2f ,"1= 3-5xz+lluy=|c^r=J7;{c*r o ozx?-3xzI t*>= /r-*{c" l = *-nC

    Y64,lrn -- 2x2+hx3766.fr*1= ro-t^uf f i {r*r=#

    / , rq" (x2-2x*5)lz(t'* to1 qx - xaixa- 8f +6xu+t

    = x *f i=t16ff +=oJffi +

    xa 5 *" *7*

    2x-x'

    - ^.R- /eh (4- x")

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    48/83

    274 zv.T-J"*".j.I"

    W787,

    7u, Y-

    x=\J=

    Y=y=

    frxtf ' t

    W f.o=*4-2*"t * '- 2xz+lx{u\=

    It* l=f r" l=

    { t* , -$t"l

    ffi| f r"t= k-r.-.'8ol., t*1=Ur;lo6. $ *t = (x - t)e^

    ffi $r^1 ""7^t*-)W f c*l= n-*^807, ol =Uo (c+x-x")'| . lzto3. W= !r*G4*'*g*-3)

    n.w

    1= *t-3x2+ fy= # x"*xt* x3+2

    786,

    Y92.

    3r-. lx+4x-2.x

    ( * '+ t) e"

    * l - t*"-zxM.TAW

    Wktl" ; r^^"\NW733,7Xg,

    Eol,tog.

    W lut=;+W{r"r=#

    = 3xa-4x3= x3+*'

    JE,+-.5T;.-*

    7X6,YXE,900,

    x-13

    XxL +l

    xr+ 3x

    t lo, fa*t= xL-z.L-x

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    49/83

    275E'l l .f t^1 1-fr**rF

    It {3. f t* t= ^ou

    'J7 t**.*

    ,t5.

    S16, nni,,r'q r-/rA'r/r1'p^-* U*'"tw; A. y = tvi,"- ,w ia,A$i/t t*, UW f

    olrtt.t ,*r' ^1"^,"rW,*'J' /,a iv./* i I*u.L" otat ,itxt^,+L ,ffiU ,W y I.,ih f"*l'"U l=x"-t-i,,*UiA r^",f'*lV*Ub );"*'i l-"',r"1),,+J'*"J""vLP)s^rx ,^XW ye,04y"^W Wry,7=e'8n,WW tnil;"W y="3-3xz-1^.,W ir,-v; o ?,820.,r^r;,r"^^+'no.h&)r.'i' ;,""",ht";,*,(,'^* ""]"^rrW'rh rU'-A-'k* .dt , ,rwW Y =g21.\r^,-W ,-J^"r\r"^""fW 2-y-,utxt1)=o fu

    WAtzz.\",*4WW) x=4-r" , = "u,h"ik^^,W y x=3,mo/^r*w *rA

    Ye-rW

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    rc T,^^X/rr"**{.,""-^l*'1g$)Xrl; fAxu".*"U W'*o=2,

    2Y6 zV,T*i''rani'

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    830'':*tff. m^\t"t=Egt.0)^'-J-f^:W "-4fW *Wy

    {, r t=d r&r Xo=o

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    gg+, ) N,;,'("

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    17,

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    645.\-("-*i;

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    8t2.I 53.

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    , lS,=L6,"f,B*t,

    3,+zE,X=-3a-LE 7,sLFe- ibi ,Ai=LfrrLLt; i=d,Zl t t {3. t=a- l2\- lva

    A

    =4o

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    6,3.t2,14,16,

    fe.= -{ * L(,tiE.t=* i^. fq.4=*(r^.4)

    ABCDEF

  • 8/8/2019 Zbirka Zadataka-matematika I

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    55-.53,6t,63,65.6s.

    lL 66.30"(,1)B(-2, -20) -4)

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    37,39.

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    too, o^,1m, =E ,\= s+'++'a6'l

    66,t [6s

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    { , f4. n(z,-3 ,6),T, 3,-o,

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    {35,J,r0 $6,?"t>^,5r,

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    R.IT, 283l+2,{ l t$.r47112.{5r.,,159.

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    163.

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    31600

    XI

    I 54; l 5x +2J+10x, 6.lSt, 5x + 25-7x+27=Q

    f&t\^f;t ^r"c,t .ra'vn;'"'n\

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    l+8,tt'ii lttg, N2/,et, {fd,A+0 {f {,A=4, =-6x-y-z=2 153. *y +4n =/ax=6 {S6.x=O ,15?,a-6r=Y

    v_,|

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    t6 l , B -8 ,3, L\ f6 '2,B S,- tp)iG+.#X=+ tct ,=+=+t6r .=+=+,i=++=+\4nxYrxVzn=E) 4 =T=E ) 7=a=6-'

    l7a,i= *l't tYl ,+=+ j x=3t,y=2-l- l172,4, l?3. != - 2x+314s-2rb=31?rr . ='15U..=)=6U-{, Y=-5u+2

    (2' t V=- 'x-z\z+175. t) y = (^ lz-L

    175. =3(x+2\ ' '4 ; x=L-z,y=3t '+ l7T, =-f {*- l f*4

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    |W, (1) N,=-(y-, t \ '+2

    x-

    lYg, x=2(X-l f+3; y=t+| , x=zt+3fso.#F- * {8t ' ' * .*182.f+.* 18s,-6+h-f f iI t , i .x*+ -#-* f t r ,Lxz-*-h.W

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    L86

    =lo, l f=[o, t )Df= - *,4\kl= 1'- e,+' to)f-1"14-2*

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    2.9C,1+= - ' . t+ 'o7R+= 1-v, +r)

    23n, Xf= a- o', +oo)Rf=12 ,+oo)

    302. (-oo , +*)[o, + o.;

    Xo6,t{0,3{+.3tg,

    It2'16, Al{.. twutlvln- r ir-2'13,i^l=-Jry' - l o +x2E2- i*)=+ 5-X

    n-l l ,eES.f ,*t=15{tz-x')288,il*r=tu?-4ni, ft,1-L(&-u)134.f-ltf =ta''r'; -32lT" DO=a- o'r+oo)

    kl= (- oo,+c'o)f l*1=Ji-i t

    300.S*= [ 2, +e]k; lo, +oo>i l*1=i|^Q"

    !o3. S+= -o' , o)?1= (-* t o)dlr,1=q Q-e:), tJz

    x-4

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    27E,2 81,281,291,Lna,

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    J.evnww

    x0?.wa,NTJ{w

    xl l ,w3 5,3tt,

    'N^1","N^f

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    i i i

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    324.

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    ( , ut - -Tt"t-^z.Y(x)=-(x+z)+3IAI

    .:4(- i g. r ' i \ , iI : \ '{ ' \r 'i -zrtti\\I

    III

    xI1

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    415.ht3,h2s.+2Y,131,435,433,tr43,qh7.+5f.455,dL-;f*

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    461,x z -2, != 646+,X=-3,x=l1167,=O- rY=2470,x='1,y=o u+o"

    453. y3 ,vrya xs= 24ge. xr= -3 t tz=3

    473. 2IrYT,44El. 4tSX xt=o ) xz=14t5, Xr=I

    474, 74',?6,2

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    (' l , + o")-(2 , + oo;t

    hsl,4r1qss,50eWY,

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    5Og, l) A,x 2 t ay= ra,#= -7 5'{0. l) ax= 3/(e)ax=-{ / ay= l* , * ' -+ (2) ax=-3r

    sfl.V,-Ulr^;Uf i,Ji o* "$* yfu*t * =gl2, (r) f toza,ax*o 6

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    622, SLg,5* U"f

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    'N"YW "t["yW4s3,|nT,501.50$,$06,

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    b=-6, , b=3

    s26:f l ror , t . ro\-- , { ' ( \ t ,@W

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    RV,\ri'n*W 213f cty=4 "J,^-* A* k'/";"^a'vi^ W-f .' k',irLi2 ;rz^,o'tnl'tt)=-+ T"* A^ ,trr.b'* P* W * koi'{,) /rx/-A;4$'cn)o X/r-* A* WW * bni'l* fr* (,tk^;r^;,t-'\, U",;ii ^-f* ,^r)* f"J'*

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    ' (2) Ax= -o,4 ; AY= -T.t t tg; &Y= -ot i

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    68/83

    5+,t {) AX:x-xo,^Y= - , AV V(z) ax=,{n I aY - h , LY= 554G. \(-j ax) *#

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    , L+Q:o,z)=F@;;,* yM @ "-+ A, L+(g;{)=-h(X";L,vyn

  • 8/8/2019 Zbirka Zadataka-matematika I

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    621,626"

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    628, - 2-. tvi,w2-x ctlctrl2x

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    634.636,538.

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    639.

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    o) o

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