Zbirka Zadataka-matematika I

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    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,

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    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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    lv

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    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*

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    ,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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    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=

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    \S^rx

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    ^,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-

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

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

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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,

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

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

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

    6,

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

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

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    v

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    2,RfuM+,A)^

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    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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    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 .

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    6x3

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    I t6',

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    f c*1{r*1=

    fr*t={r"t=

    *3X,*+

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    t x=2

    , X=8

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

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    x= 64

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    fr*;=

    52x -x

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

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    2-48229,

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

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

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

    h(xno+40) -1

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    261,lul= xorfffi \u1='-r

    2267.fr"1= ,

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

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    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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    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

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    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,[email protected],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-- *

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    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

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    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..

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    ,^ , 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 - '

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    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

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    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,

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    h

    nw x 1Qna, X >O

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

    za,x+Ob za/ x=o

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    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.

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    {

    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"[email protected]+.

    4t6,{r*t=

    x +'l2x+13x+1

    x

  • 8/8/2019 Zbirka Zadataka-matematika I

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

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    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,'[email protected] \; 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,

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    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,

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    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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    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*

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    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 [email protected] '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

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    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

  • 8/8/2019 Zbirka Zadataka-matematika I

    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

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    ^)-r le

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

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

    x

    a.t

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    pl

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    ffith o

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

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    Ary t=3x'2,

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    , l- Y= fa 1

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    xa 5 *" *7*

    2x-x'

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

    W787,

    7u, Y-

    x=\J=

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    x-13

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

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

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    gg+, ) N,;,'("

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    17,

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    645.\-("-*i;

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    6,3.t2,14,16,

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    ABCDEF

  • 8/8/2019 Zbirka Zadataka-matematika I

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    66,t [6s

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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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    31600

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

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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

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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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    L86

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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"

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    x-4

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    J.evnww

    x0?.wa,NTJ{w

    xl l ,w3 5,3tt,

    'N^1","N^f

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

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    xI1

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

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