Matematica M3 si M4 - Subiectul I cu 100 variante din 2009

8/11/2019 Matematica M3 si M4 - Subiectul I cu 100 variante din 2009

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www.cxfkcbdcnflfjfurcft.njh`spht .rh

Qfrefbtc

996-699


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Kebestcruj Cdulfece, Lcrlctree e EbhvreeLcbtruj Bfehbfj pcbtru Lurrelujuk e Cvfjufrc b bvkbtuj Yrcubevcrsetfr

NFLFJFS^CFT >995-KFTCKFTELYrhnf D, KT995Yrhnslresjf KFTCKFTEL Yrhnf D

Aejecrf vhlfehbfj, prhaejuj pcdf`h`el, spclefjezfrcf bvthr-cdulfthfrc. Thftc sunecltcjc subt hnje`fthree. Tekpuj cacltev dc julru cstc dc < hrc. \c flhrd69 publtc deb haeleu. Jf thftc sunecltcjc sc lcr rczhjvre lhkpjctc.

> \SNECLTSJ E (

3p 6.\sc rczhjvc b kujekcf bukcrcjhr rcfjc clufef > 6 6x ; .3p >.\sc frftc lvclthruj v f n l; + +

, ubdc , < , >f e g n e g l e g; ; + ; +

cstc lhjebefr lu vclthruj

4 1d e g; +

3p 4 = ... > 69> >> 3 > 9x x x x+ + ; , ubdc 6 >,x x subt shjueejc clufece

>< 9x x f + ; .

3p 1.\sc dckhbstrczc rcjfef > >lhs lhs 6N L+ ; b treub`meuj FNLdrcptub`mel b F.


4/101



Aejecrf vhlfehbfj, prhaejuj pcdf`h`el, spclefjezfrcf bvthr-cdulfthfrc. Thftc sunecltcjc subt hnje`fthree. Tekpuj cacltev dc julru cstc dc < hrc. \c flhrd69 publtc deb haeleu. Jf thftc sunecltcjc sc lcr rczhjvre lhkpjctc.< \SNECLTSJ E (> < jh`

bb + .

3p >.Aec publtcjc ( ... lhs605+ + + , teebd lhs 59 9; .

3p 1.\sc rczhjvc b kujekcf bukcrcjhr rcfjc clufef( )

> 3

4,4>>

xx

;

.


5/101



Aejecrf vhlfehbfj, prhaejuj pcdf`h`el, spclefjezfrcf bvthr-cdulfthfrc. Thftc sunecltcjc subt hnje`fthree. Tekpuj cacltev dc julru cstc dc < hrc. \c flhrd69 publtc deb haeleu. Jf thftc sunecltcjc sc lcr rczhjvre lhkpjctc.4 \SNECLTSJ E (.\sc rcprczebtc `rfael aublef 7 , ( ) 4a a x x ; .

3p >6 >x x+ , teebd l 6x e >x subt shjueejc clufece>

> 6 9x x ; .

3p 4.\sc rczhjvc b kujekcf bukcrcjhr rcfjc clufef >j` ( 63 ) >x x ; .

3p 3.\sc dctcrkebc vfjhfrcf bukrujue rcfj fteebd lpubltuj (4, )L f sc fajpc drcfptf dctcrkebftdcpubltcjc ( 3, >)F e ( (seb 43 seb6


6/101



Aejecrf vhlfehbfj, prhaejuj pcdf`h`el, spclefjezfrcf bvthr-cdulfthfrc. Thftc sunecltcjc subt hnje`fthree. Tekpuj cacltev dc julru cstc dc < hrc. \c flhrd69 publtc deb haeleu. Jf thftc sunecltcjc sc lcr rczhjvre lhkpjctc.3 \SNECLTSJ E ( 6a a x x ; .

3p >.\sc dctcrkebc x pcbtru lfrc3

> 6x

.

3p >6 >C x x; + , ubdc 6x e >x subt shjueejc clufece>

> < < 9x x ; .

3p 4.\sc rczhjvc b kujekcf bukcrcjhr rcfjc clufef >3jh` (> 6) 6x x ; .

3p 3.\sc dctcrkebc clufef drcptce lfrc trclc preb publtcjc ()N .

3p 1.Treub`meuj FNLfrc 69FN FL; ; e ( ) 6>9k F ; . \sc lfjlujczc jub`ekcf jfturee NL.


7/101



Aejecrf vhlfehbfj, prhaejuj pcdf`h`el, spclefjezfrcf bvthr-cdulfthfrc. Thftc sunecltcjc subt hnje`fthree. Tekpuj cacltev dc julru cstc dc < hrc. \c flhrd69 publtc deb haeleu. Jf thftc sunecltcjc sc lcr rczhjvre lhkpjctc.1 \SNECLTSJ E (v fe g; +

e > .\sc rczhjvc b kujekcf bukcrcjhr bfturfjc ebclufef > < 3x : .

3p 6

> 6

b b

bC

++ +

;

+

cstc bukr bfturfj, hrelfrc fr ae b .

3p 4.\sc dctcrkebc clufef drcptce lfrc trclc preb publtuj (6, 6)F e cstc pcrpcbdelujfrpc drcfptf dcclufec 6 9x y+ + ; .

3p 3.Treub`meuj FNLfrc 9k FLN ; . \sc lfjlujczc jub`ekcf jfturee FN .

3p 1.\sc rczhjvc b kujekcf bukcrcjhr rcfjc clufef 6> (9,>3)x x ; .


8/101



Aejecrf vhlfehbfj, prhaejuj pcdf`h`el, spclefjezfrcf bvthr-cdulfthfrc. Thftc sunecltcjc subt hnje`fthree. Tekpuj cacltev dc julru cstc dc < hrc. \c flhrd69 publtc deb haeleu. Jf thftc sunecltcjc sc lcr rczhjvre lhkpjctc.0 \SNECLTSJ E (( 6) , 4 >v f e g v e g; + ; +

subt lhjebefre.

3p 5\ ; + + + + + .

3p 4.Treub`meuj drcptub`mel FNLfrc ( ) 59 , 0F x x; + e { }1

Z 6 |6

N xx

;

. \sc dctcrkebc F N .

3p 1.\sc frftc lvrauj pfrfnhjce fshleftc aublece >7 , ( ) >( 6) >a a x kx k x k ; + + + + , lu 9k sc fajpc drcfptf dc clufec 6y x; + .


9/101



Aejecrf vhlfehbfj, prhaejuj pcdf`h`el, spclefjezfrcf bvthr-cdulfthfrc. Thftc sunecltcjc subt hnje`fthree. Tekpuj cacltev dc julru cstc dc < hrc. \c flhrd69 publtc deb haeleu. Jf thftc sunecltcjc sc lcr rczhjvre lhkpjctc.= \SNECLTSJ E ( > ) 7 > > >C ; + .

3p >.\sc dctcrkebc bukcrcjc rcfjcxey deb prh`rcsef fretkctel ,6, ,3,0,5,66,....x y .

3p )N . \sc dctcrkebc clufef kcdefthfrce sc`kcbtujueFN .

3p 4.\sc rczhjvc b kujekcf bukcrcjhr bfturfjc clufef ( )( )6 > >69b b b+ + ; .

3p 3.\sc dctcrkebc ebtcrvfjcjc dc khbhthbec fjc aublece >7 , ( ) < 4a a x x x ; + + .

3p 1.\sc rczhjvc b kujekcf bukcrcjhr rcfjc clufef 6 < >x x+ + ; .


10/101



Aejecrf vhlfehbfj, prhaejuj pcdf`h`el, spclefjezfrcf bvthr-cdulfthfrc. Thftc sunecltcjc subt hnje`fthree. Tekpuj cacltev dc julru cstc dc < hrc. \c flhrd69 publtc deb haeleu. Jf thftc sunecltcjc sc lcr rczhjvre lhkpjctc.5 \SNECLTSJ E (.\sc frftc l < 60 jh` 4

>6=

>

xx

+ ;

.

3p 1.\sc lfjlujczc jub`ekcf jfturee FLf treub`meujue FNL, teebd l 6>, ( ) 19 , ( ) 03NL k F k N; ; ; .


11/101



Aejecrf vhlfehbfj, prhaejuj pcdf`h`el, spclefjezfrcf bvthr-cdulfthfrc. Thftc sunecltcjc subt hnje`fthree. Tekpuj cacltev dc julru cstc dc < hrc. \c flhrd69 publtc deb haeleu. Jf thftc sunecltcjc sc lcr rczhjvre lhkpjctc.69 \SNECLTSJ E (3% deb >99=.

3p >.\sc rczhjvc sestckuj < 6

x y

x y

+ ;

;, ,x y .

3p )F e ( 6,6)N .

3p 4.\sc lfjlujczc seb 43 lhs6> 1 > = 9x x + ; .

3p 1.\sc lfjlujczc vfjhfrcf cxprcsece 6 >

> 6

,x x

Cx x

; + ubdc 6 >,x x subt shjueejc clufece>

1 1 9x x + ; .


12/101



Aejecrf vhlfehbfj, prhaejuj pcdf`h`el, spclefjezfrcf bvthr-cdulfthfrc. Thftc sunecltcjc subt hnje`fthree. Tekpuj cacltev dc julru cstc dc < hrc. \c flhrd69 publtc deb haeleu. Jf thftc sunecltcjc sc lcr rczhjvre lhkpjctc.66 \SNECLTSJ E (,.\sc rczhjvc b kujekcf bukcrcjhr rcfjc ebclufef > 6 < ) 6x x ; .

3p 1.\sc dctcrkebc lhhrdhbftcjc publtujue dc kebek fj aublece 7a , >( ) 1 =a x x x; + .


13/101



Aejecrf vhlfehbfj, prhaejuj pcdf`h`el, spclefjezfrcf bvthr-cdulfthfrc. Thftc sunecltcjc subt hnje`fthree. Tekpuj cacltev dc julru cstc dc < hrc. \c flhrd69 publtc deb haeleu. Jf thftc sunecltcjc sc lcr rczhjvre lhkpjctc.6> \SNECLTSJ E (

3p 6.\sc dctcrkebc k teebd lvclthree >f e g; +

e ( >) >n k e g; +

vcreaelc`fjetftcf >f n;

.

3p >.\sc dctcrkebc aublef 7 , ( )a a x fx n ; + teebd lpubltcjc (6,>), ( 6,1)F N fpfreb `rfaelujueaublece a.

3p 14bb : .3p 4.Treub`meuj FNLfrc jfturejc 3, 6FL NL FN; ; ; . \sc lfjlujczc seb sebN L+ .3p 3.\sc rczhjvc b kujekcf bukcrcjhr rcfjc ebclufef > 1 3 9x x + .3p 1.\sc rczhjvc b kujekcf bukcrcjhr rcfjc clufef j` ( 6) >j`( 6) 6x x+ ; .


14/101



Aejecrf vhlfehbfj, prhaejuj pcdf`h`el, spclefjezfrcf bvthr-cdulfthfrc. Thftc sunecltcjc subt hnje`fthree. Tekpuj cacltev dc julru cstc dc < hrc. \c flhrd69 publtc deb haeleu. Jf thftc sunecltcjc sc lcr rczhjvre lhkpjctc.6< \SNECLTSJ E (

x y

x y

+ ; + ;

, ,x y .

3p >.\sc dctcrkebc f pcbtru lfrc drcptcjc 6d 7 > 1 9x y+ ; e > 7d > 3 9x fy+ + ; subtpcrpcbdelujfrc.

3p

< 4x ; .

3p 4.Treub`meuj FNLfrc ( ) 59k F ; , 5FN ; e 6>FL ; . \sc lfjlujczc lhs lhsN L+ .

3p 3.\sc rczhjvc b kujekcf bukcrcjhr rcfjc clufef < < 6 6x x ; .

3p 1.\sc dctcrkebc vfjhrejc }Z 6k fstacj blt clufef >( 6) 6 9k x kx k + + ; sfenshjuee rcfjc.


15/101



Aejecrf vhlfehbfj, prhaejuj pcdf`h`el, spclefjezfrcf bvthr-cdulfthfrc. Thftc sunecltcjc subt hnje`fthree. Tekpuj cacltev dc julru cstc dc < hrc. \c flhrd69 publtc deb haeleu. Jf thftc sunecltcjc sc lcr rczhjvre lhkpjctc.64 \SNECLTSJ E (, 6 6x .

3p

66 6

(9,6>3)4

xx

;

.

3p 1.\sc dctcrkebc f fstacj blt vrauj pfrfnhjce fshleftc aublece 7a , >( ) 6 9x y+ ; .


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63 \SNECLTSJ E ( 9< > 0

x y

x y

;+ ;

, ,x y .

3p >.Aec publtcjc ( 1,4), (6,9)F N e ( 6,3)L . \sc lfjlujczc lhhrdhbftcjc lcbtrujue dc `rcutftc fj treub`meujueFNL.

3p

> >995x

.

3p 4.\sc lfjlujczc seb6>9 lhs639\ ; + .3p 3.\sc rczhjvc b kujekcf bukcrcjhr rcfjc clufef >6 > 6 >,x x subt shjueejc clufece>

< 3 9x x ; .


17/101



Aejecrf vhlfehbfj, prhaejuj pcdf`h`el, spclefjezfrcf bvthr-cdulfthfrc. Thftc sunecltcjc subt hnje`fthree. Tekpuj cacltev dc julru cstc dc < hrc. \c flhrd69 publtc deb haeleu. Jf thftc sunecltcjc sc lcr rczhjvre lhkpjctc.61 \SNECLTSJ E ( 6 .\sc lfjlujczc6 6

6> 6 >

+ +

.

3p > < 3 9x x .

3p 1.\sc rczhjvc b kujekcf bukcrcjhr rcfjc clufef >3jh` ( 6) 9x x+ + ; .


18/101



Aejecrf vhlfehbfj, prhaejuj pcdf`h`el, spclefjezfrcf bvthr-cdulfthfrc. Thftc sunecltcjc subt hnje`fthree. Tekpuj cacltev dc julru cstc dc < hrc. \c flhrd69 publtc deb haeleu. Jf thftc sunecltcjc sc lcr rczhjvre lhkpjctc.60 \SNECLTSJ E ()F N fpfreb`rfaelujue aublece.

3p >.\sc lfjlujczc 4 >v f n l; +

, ubdc 3 0 , > < , 3 3f e g n e g l e g; ; + ; +

.

3p 6

x xC

x x; + , ubdc 6 >,x x subt shjueejc clufece

>1 4 9x x + ; .

3p 3.\sc rczhjvc b kujekcf bukcrcjhr rcfjc clufef j` (> 4 4) 6x x+ + ; .

3p 1.\sc lfjlujczc > < > < > > + .


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Aejecrf vhlfehbfj, prhaejuj pcdf`h`el, spclefjezfrcf bvthr-cdulfthfrc. Thftc sunecltcjc subt hnje`fthree. Tekpuj cacltev dc julru cstc dc < hrc. \c flhrd69 publtc deb haeleu. Jf thftc sunecltcjc sc lcr rczhjvre lhkpjctc.6= \SNECLTSJ E (


20/101



Aejecrf vhlfehbfj, prhaejuj pcdf`h`el, spclefjezfrcf bvthr-cdulfthfrc. Thftc sunecltcjc subt hnje`fthree. Tekpuj cacltev dc julru cstc dc < hrc. \c flhrd69 publtc deb haeleu. Jf thftc sunecltcjc sc lcr rczhjvre lhkpjctc.65 \SNECLTSJ E ( 6. \sc dctcrkebc fstacj blt vclthree 6 >( v e g v e g ; + + + ; +

saec lhjebefre.

3p n ; e 3

FN FL; ; e ( ) x x+ ; .

3p 1.\sc rczhjvc sestckuj>

y x

y x x

; +

; +, ,x y .


21/101



Aejecrf vhlfehbfj, prhaejuj pcdf`h`el, spclefjezfrcf bvthr-cdulfthfrc. Thftc sunecltcjc subt hnje`fthree. Tekpuj cacltev dc julru cstc dc < hrc. \c flhrd69 publtc deb haeleu. Jf thftc sunecltcjc sc lcr rczhjvre lhkpjctc.>9 \SNECLTSJ E (9

3p 6.\sc dctcrkebc publtcjc dc ebtcrsclec fjc `rfaelujue aublece >7 , ( ) 1 3a a x x x ; + lu fxcjcdc lhhrdhbftc.

3p >.\sc dctcrkebc jub`ekcf jfturee NLf treub`meujue FNLteebd l 4FN FL; ; e ( ) 6>9k F ; .

3p 1>x x x x x x+ + + + + ; .

3p 4.\sc dctcrkebc rfef e prekuj tcrkcb fj ubce prh`rcsee fretkctelc 6( )b bf teebd l6 > < 4

>6

4>

f f f

f f f

+ + ;

+ + ;.

3p 3.\sc rczhjvc b kujekcf bukcrcjhr rcfjc clufef 6 6 6< (9,(


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3p 6.\sc rczhjvc b kujekcf bukcrcjhr bfturfjc bcbujc clufef ( )( )6 > >4b b b+ + ; .

3p >.\sc rczhjvc b kujekcf bukcrcjhr rcfjc clufef >6

69699

x; .

3p 6, >, =x x x + + subt tcrkcbe lhbscluteve fe ubce

prh`rcsee `chkctrelc.

3p 1.\sc dctcrkebc k teebd lclufef > (


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Aejecrf vhlfehbfj, prhaejuj pcdf`hèl, spclefjezfrcf bvthr-cdulfthfrc. Thftc sunecltcjc subt hnje`fthree. Tekpuj cacltev dc julru cstc dc < hrc. \c flhrd69 publtc deb haeleu. Jf thftc sunecltcjc sc lcr rczhjvre lhkpjctc.>> \SNECLTSJ E (>

3p 6.\sc dctcrkebc f fstacj blt drcptcjc 6d 7 > > 9fx y+ + ; e > 7< 6 9d x y + ; saec pfrfjcjc.

3p >.\sc lfjlujczc vfjhfrcf cxprcsece C ; 6 >

> 6

x x

x x+ , ubdc 6 >,x x subt shjueejc clufece

>3 3 9x x + ; .

3p

4

x

+ ;

.

3p 4.\sc dctcrkebc prekuj tcrkcb e rfef ubce prh`rcsee `chkctrelc 6( )b bn , teebd l> 4

6 9

n n

n n

+ ;

+ ;.

3p 3.\sc rczhjvc b kujekcf bukcrcjhr btrcè ebclufef > >9x .

3p 1.Treub`meuj FNLfrc >, 4FL FN; ; e ( ) 19k F ; . \sc lfjlujczc jubèkcf jfturee NL.


24/101



Aejecrf vhlfehbfj, prhaejuj pcdf`h`el, spclefjezfrcf bvthr-cdulfthfrc. Thftc sunecltcjc subt hnje`fthree. Tekpuj cacltev dc julru cstc dc < hrc. \c flhrd69 publtc deb haeleu.

Jf thftc sunecltcjc sc lcr rczhjvre lhkpjctc.

>< \SNECLTSJ E ( < (> )(6,3)

(4 ) 1 .

3p >.\sc lfjlujczc pcrekctruj treub`meujue FNLb lfrc ( ) 59 , >9k F NL ; ; e ( ) )N . \sc dctcrkebc lhhrdhbftcjc publtujue N , teebd l F cstc kegjhluj

sc`kcbtujue NN .

3p 4.\sc rczhjvc b kujekcf bukcrcjhr rcfjc clufef >jh` (6 6) 6x + ; .

3p 3.\sc dctcrkebc bukruj rcfj xdeb rcjfef dc c`fjetftc > 3 = 66 ... 633x+ + + + + ; .

3p 1.\sc dctcrkebc aublef dc `rfduj fj dhejcf >7 , ( )a a x fx nx f ; + + , 9f teebd lfrcvfjhfrcf kfxekc`fjlu 6> , hnebutb publtuj dc fnsles > .


25/101




3p 6. \sc dctcrkebc f , teebd ldrcptcjc 6 7 > 9d x y+ ; e > 7 > 6 9d x fy + ; subt pcrpcbdelujfrc.

3p >.\sc dctcrkebc kujekcf { }* | 6

6

y x

y x x

;

; +, ,x y .

3p 4.\sc lfjlujczc \ ;< 6

seb6>9 lhs6>9> >

+

.

3p 3.\sc rczhjvc b kujekcf bukcrcjhr rcfjc clufef j` j`( =9x+ + + + + ; .


26/101




3p 6. \sc dctcrkebc clufef drcptce lfrc trclc preb publtcjc (6,9)F e (9,6)N .3p >.\sc rczhjvc b kujekcf bukcrcjhr rcfjc clufef ( )

46 61x ; .

3p < > 9x x + .3p 4.\sc rczhjvc b kujekcf bukcrcjhr rcfjc clufef

f f f

f f f

+ ;

;.

3p 1.Treub`meuj FNL frc ( ) 59 , 1, 6>k F FL NL ; ; ; . \sc lfjlujczc jub`ekcf jfturee FN.


27/101



Aejecrf vhlfehbfj, prhaejuj pcdf`h`el, spclefjezfrcf bvthr-cdulfthfrc. Thftc sunecltcjc subt hnje`fthree. Tekpuj cacltev dc julru cstc dc < hrc. \c flhrd69 publtc deb haeleu. Jf thftc sunecltcjc sc lcr rczhjvre lhkpjctc.>1 \SNECLTSJ E ( 6 9x x+ .3p 4.\sc dctcrkebc clufef drcptce lfrc trclc preb publtcjc ( )6, >F e ( )>, 6N .

3p 3.\sc rczhjvc b clufef 5 4 < < 9x x + ; .

3p 1.Treub`meuj FNL frc ( ) 59k F ; , 1FN ; e < 1NL; . \sc lfjlujczc fref treub`meujue FNL .


28/101




3p 6.\sc rczhjvc b kujekcf bukcrcjhr rcfjc clufef >3 3x ; .

3p >.\sc lfjlujczc seb6>9 . 3p F e ( )>,6 .N

3p 4.\ sc lfjlujczc prhnfnejetftcf lf, fjc`bd ub cjckcbt deb kujekcf { }9, 6, >,

4 < 9x x + ; .

3p 3.\sc dctcrkebc prekuj tcrkcb 6f fj ubce prh`rcsee fretkctelc ( ) 6b bf teebd l6 3

6 >9

f f

f f

+ ;

+ ;.

3p 1.\sc rczhjvc b ebclufef > < > 6x x x+ + 2 .


29/101



Aejecrf vhlfehbfj, prhaejuj pcdf`h`el, spclefjezfrcf bvthr-cdulfthfrc. Thftc sunecltcjc subt hnje`fthree. Tekpuj cacltev dc julru cstc dc < hrc. \c flhrd69 publtc deb haeleu. Jf thftc sunecltcjc sc lcr rczhjvre lhkpjctc.>= \SNECLTSJ E (=

3p 6.\c lhbsedcrvclthree 6 < 4v e g; +

e > 4 v v+

.

3p >.Treub`meuj FNLfrc ( ) NL ; . \sc lfjlujczc jub`ekcf jfturee .FL

3p < 6996 > > > > .\ ; + + + + +

3p 4.\sc rczhjvc b clufef ( )>jh` > 6 9x + ; .

3p 3.teebd l 6 >,x x subt shjueejc clufece>

0 < 9,x x+ + ; ssc lfjlujczc> >6 >

6 6.

x x+

3p 1.\sc dctcrkebc vfjhrejc pfrfkctrujue rcfj k fstacj blt >> 3 9,x x k + 2 pcbtru hrelc .x


30/101




3p 6.\sc rczhjvc b ebclufef > 1 3 9.x x + 3p >.\sc rczhjvc b clufef ( )n e g;

subt lhjebefre.

3p 1.Treub`meuj FNLfrc ( ) 59k F ; , ( ) 19k N ; e 5.FL ; \sc lfjlujczc jub`ekcf bjekee FD

f treub`meujue FNL.


31/101



Aejecrf vhlfehbfj, prhaejuj pcdf`h`el, spclefjezfrcf bvthr-cdulfthfrc. Thftc sunecltcjc subt hnje`fthree. Tekpuj cacltev dc julru cstc dc < hrc. \c flhrd69 publtc deb haeleu. Jf thftc sunecltcjc sc lcr rczhjvre lhkpjctc.x ; .

3p .

3p 4.\sc dctcrkebc vfjhfrcf kebekf aublece ( ) >7 , > > < 55 699

+ + +

+ + +


32/101



Aejecrf vhlfehbfj, prhaejuj pcdf`h`el, spclefjezfrcf bvthr-cdulfthfrc. Thftc sunecltcjc subt hnje`fthree. Tekpuj cacltev dc julru cstc dc < hrc. \c flhrd69 publtc deb haeleu. Jf thftc sunecltcjc sc lcr rczhjvre lhkpjctc.x + ; .

3p 3.\sc dctcrkebc rfef ubce prh`rcsee fretkctelc ( )6b b

f

teebd l> 3

< 5

>1

,> , 6,> .F N L


33/101



Aejecrf vhlfehbfj, prhaejuj pcdf`h`el, spclefjezfrcf bvthr-cdulfthfrc. Thftc sunecltcjc subt hnje`fthree. Tekpuj cacltev dc julru cstc dc < hrc. \c flhrd69 publtc deb haeleu. Jf thftc sunecltcjc sc lcr rczhjvre lhkpjctc. \SNECLTSJ E ( > > > 6jh` jh` < jh` 4 jh` .\sc lfjlujczc fj leblejcf tcrkcb fj ubce prh`rcsee `chkctrelc ( ) 6b bn teebd l 66

, 4FL FN; ; e ( ) 19k F ; . \sc lfjlujczc jub`ekcf jfturee .NL


34/101



Aejecrf vhlfehbfj, prhaejuj pcdf`h`el, spclefjezfrcf bvthr-cdulfthfrc. Thftc sunecltcjc subt hnje`fthree. Tekpuj cacltev dc julru cstc dc < hrc. \c flhrd69 publtc deb haeleu. Jf thftc sunecltcjc sc lcr rczhjvre lhkpjctc. = 9x x ; .3p ,NL ; ( ) 43k F ; e ( ) 19 .k N ; \sc lfjlujczc jub`ekcf jfturee .FL

3p 4.\c lhbsedcrvclthree 4

f n +

3p 3.\sc rczhjvc b clufef ( )6>

jh` > >

6 < < 3

< < 3

B ; +

cstc bfturfj.


35/101



Aejecrf vhlfehbfj, prhaejuj pcdf`h`el, spclefjezfrcf bvthr-cdulfthfrc. Thftc sunecltcjc subt hnje`fthree. Tekpuj cacltev dc julru cstc dc < hrc. \c flhrd69 publtc deb haeleu. Jf thftc sunecltcjc sc lcr rczhjvre lhkpjctc. .f n

3p >.\sc frftc l

jh` 61 cstc bukr bfturfj.

3p > 6

>6

lhs lhs lhs>

fn L nl F lf N f n l + + ; + + ,

ubdc , ,f n l subt jub`ekejc jfturejhr ,NL FL, rcspcltev .FN


36/101



Aejecrf vhlfehbfj, prhaejuj pcdf`h`el, spclefjezfrcf bvthr-cdulfthfrc. Thftc sunecltcjc subt hnje`fthree. Tekpuj cacltev dc julru cstc dc < hrc. \c flhrd69 publtc deb haeleu. Jf thftc sunecltcjc sc lcr rczhjvre lhkpjctc. 1.a ;

3p jh` < > >6 > 6C x x; + , ubdc 6x e >x subt shjueejc clufece>

3 6 9.x x + ;

3p 3. \sc dctcrkebc jub`ekcf jfturee FN f treub`meujue FNLteebd l =, ( ) 43NL k F; ; e

( ) 693 .k N ;

3p 1.Aec treub`meuj FNLhfrclfrc e H ub publt frnetrfr deb pjfb. \sc dckhbstrczc l

.FN FL HN HL ;


37/101



Aejecrf vhlfehbfj, prhaejuj pcdf`h`el, spclefjezfrcf bvthr-cdulfthfrc. Thftc sunecltcjc subt hnje`fthree. Tekpuj cacltev dc julru cstc dc < hrc. \c flhrd69 publtc deb haeleu. Jf thftc sunecltcjc sc lcr rczhjvre lhkpjctc. >, 4NL FL; ; e ( ) j` 1j` 3 9.x x + ;

3p 1.\sc dctcrkebc x W pcbtru lfrc ( )( )> >6 3 9.x x+


38/101



Aejecrf vhlfehbfj, prhaejuj pcdf`h`el, spclefjezfrcf bvthr-cdulfthfrc. Thftc sunecltcjc subt hnje`fthree. Tekpuj cacltev dc julru cstc dc < hrc. \c flhrd69 publtc deb haeleu. Jf thftc sunecltcjc sc lcr rczhjvre lhkpjctc. < < 4+ +

+ + +

.

3p 1.Clufef > < 9x x ; frc shjueejc 6 >,x x . \sc lfjlujczc6 >

> 6

x x

x x+ .


39/101



Aejecrf vhlfehbfj, prhaejuj pcdf`h`el, spclefjezfrcf bvthr-cdulfthfrc. Thftc sunecltcjc subt hnje`fthree. Tekpuj cacltev dc julru cstc dc < hrc. \c flhrd69 publtc deb haeleu. Jf thftc sunecltcjc sc lcr rczhjvre lhkpjctc. 4 9,x x k+ + 2 hrelfrc fr ae x .

3p 3.\sc dctcrkebc aublef ( )7 ,a a x fx n ; + , lu ,f n ,fstacj blt publtcjc6 6

,> >

F

e

( )9,


40/101



Aejecrf vhlfehbfj, prhaejuj pcdf`h`el, spclefjezfrcf bvthr-cdulfthfrc. Thftc sunecltcjc subt hnje`fthree. Tekpuj cacltev dc julru cstc dc < hrc. \c flhrd69 publtc deb haeleu. Jf thftc sunecltcjc sc lcr rczhjvre lhkpjctc. ,6x .

3p 3.\sc rczhjvc b ebclufef6

6.> > 6 9k x x + 2 , hrelfrc fr ae .x


41/101



Aejecrf vhlfehbfj, prhaejuj pcdf`h`el, spclefjezfrcf bvthr-cdulfthfrc. Thftc sunecltcjc subt hnje`fthree. Tekpuj cacltev dc julru cstc dc < hrc. \c flhrd69 publtc deb haeleu. Jf thftc sunecltcjc sc lcr rczhjvre lhkpjctc.49 \SNECLTSJ E ( < 0+ + cstc bfturfj.

3p 7 , < 6a a x x kx ; + + strcflpreb

publtuj ( ), 3 .F k

3p 1.\sc rczhjvc b ebclufef>

6.6

x

x

+2

+


42/101



Aejecrf vhlfehbfj, prhaejuj pcdf`h`el, spclefjezfrcf bvthr-cdulfthfrc. Thftc sunecltcjc subt hnje`fthree. Tekpuj cacltev dc julru cstc dc < hrc. \c flhrd69 publtc deb haeleu. Jf thftc sunecltcjc sc lcr rczhjvre lhkpjctc.46 \SNECLTSJ E (9 jce rcprczebt >3% debtr-h sukdc nfbe. \sc dctcrkebc sukf dc nfbe.3p >.Aec vclthree < 3f e g; +

e >n e g; +

. \sc lfjlujczc

6 6.

< >f n +

3p .x x+ ;

3p 3.\sc rczhjvc b ebclufef> 6

>.7 , > 6, .a a x x kx k ; + + \sc dctcrkebc k fstacj blt shjueejc 6 >,x x fjc

clufece ( ) 9a x ; svcreaelc rcjfef > >6 > 64x x+ 2 .


43/101




3p 6.\sc lfjlujczc fref treub`meujue FNL, teebd l ( ) 59k F ; , 6>NL ; e 1FL ; .

3p >.\sc lfjlujczc < 6 < < 6 . +

3p > 0 5 9x x ; .3p 4.\sc dctcrkebc aublef ( )7 ,a a x fx n ; + , lu ,f n , fstacj blt `rfaeluj ce sebtcrscltczc

fxf Hx b publtuj ( )>,9F e fxf Hy b publtuj ( )9, 4 .N

3p 3.\sc rczhjvc b ebclufef>

69.

< >x x:

+ +

3p 1. Aec treub`meuj FNL lu vraurejc ( ) ( ) ( )6,< , 9, < , 6,> .F N L \ sc slrec clufef kcdefbce ,FK

ubdc K cstc kegjhluj jfturee .NL


44/101



Aejecrf vhlfehbfj, prhaejuj pcdf`h`el, spclefjezfrcf bvthr-cdulfthfrc. Thftc sunecltcjc subt hnje`fthree. Tekpuj cacltev dc julru cstc dc < hrc. \c flhrd69 publtc deb haeleu. Jf thftc sunecltcjc sc lcr rczhjvre lhkpjctc.4< \SNECLTSJ E (>jh` ( 4) FN NL LF o FN+ + ;

.

3p 4.\sc rczhjvc b clufef ( )>>

66 .x ;

3p 3.\sc dctcrkebc pfrfkctruj rcfj k fstacj blt clufef >> 9x kx k + ; sfenshjuee rcfjc c`fjc.

3p 1.\sc lfjlujczc sukf > 556 < < < .+ + + +


45/101



Aejecrf vhlfehbfj, prhaejuj pcdf`h`el, spclefjezfrcf bvthr-cdulfthfrc. Thftc sunecltcjc subt hnje`fthree. Tekpuj cacltev dc julru cstc dc < hrc. \c flhrd69 publtc deb haeleu. Jf thftc sunecltcjc sc lcr rczhjvre lhkpjctc.44 \SNECLTSJ E ( > >FN NL LD DF o FN+ + + ;

.3p >.\sc rczhjvc b clufef 0 4.x ; 3p 9 seb6>9 .+ 3p 4.\sc dctcrkebc vfjhfrcf kfxekf aublece ( ) >7 , 3.a a x x ; +

3p 3.Aec aublef ( )7 , < >.a a x x ; \sc dctcrkebc lhhrdhbftcjc ubue publt dc pc `rfaeluj aublecea

pcbtru lfrc fnslesf cstc c`fjlu hrdhbftf.

3p 1.Duplc Furcj f lmcjtuet >9% debtr-h sukdc nfbe e bl


46/101



Aejecrf vhlfehbfj, prhaejuj pcdf`h`el, spclefjezfrcf bvthr-cdulfthfrc. Thftc sunecltcjc subt hnje`fthree. Tekpuj cacltev dc julru cstc dc < hrc. \c flhrd69 publtc deb haeleu. Jf thftc sunecltcjc sc lcr rczhjvre lhkpjctc.43 \SNECLTSJ E (% deb 6999. 3p >.\sc rczhjvc b clufef < 6 9.x + ;

3p 9 , 4KB KY k BKY BY; ; ; . \ sc lfjlujczc jub`ekcf

bjekee ( )K^ ^ BY f treub`meujue .KBY

3p 4.\sc dctcrkebc *f fstacj blt drcptcjc ' 7 > 3 9d x y + ; e '' 7 4 6 9d fx y + ; saecpcrpcbdelujfrc.

3p 3.\sc rczhjvc b ebclufef>995

9.>99=x

:

3p 1.Aec aublef ( ) ( )> >7 , 6 4, .a a x k x kx k ; + + \sc dctcrkebc k fstacj blt ( 6) 6a ;


47/101



Aejecrf vhlfehbfj, prhaejuj pcdf`h`el, spclefjezfrcf bvthr-cdulfthfrc. Thftc sunecltcjc subt hnje`fthree. Tekpuj cacltev dc julru cstc dc < hrc. \c flhrd69 publtc deb haeleu. Jf thftc sunecltcjc sc lcr rczhjvre lhkpjctc.41 \SNECLTSJ E (9% , prcuj ubce kfebe dc spjft cstc ==9 jce. Lfrc f ahst prcuj bfebtc dcrcdulcrc8

3p >.\sc dctcrkebc tcrkcbuj 6=f fj ubce prh`rcsee fretkctelc ( ) 6b bf teebd l> =

< 69

>4.

4=

f f

f f

+ ;

+ ;

3p < 4 6 9x x+ ; , lu shjueejc 6 >,x x . \sc lfjlujczc > >6 >

6 6.

x x+

3p 4.Trfpczuj eshslcj ( )FNLD FD NL; frc 69 e ( ) 19 .FD k FDL; ; \sc lfjlujczc destfbf dc jfpubltuj F jf drcfptf LD .

3p 3.\sc dctcrkebc f fstacj blt publtuj ( )6, 6K sfpfrebdrcptce 7 > < 9d fx y+ + ; .

3p 1.\sc rczhjvc b clufef 6 6x x+ ; .


48/101



Aejecrf vhlfehbfj, prhaejuj pcdf`h`el, spclefjezfrcf bvthr-cdulfthfrc. Thftc sunecltcjc subt hnje`fthree. Tekpuj cacltev dc julru cstc dc < hrc. \c flhrd69 publtc deb haeleu. Jf thftc sunecltcjc sc lcr rczhjvre lhkpjctc.40 \SNECLTSJ E (.\sc lfjlujczc destfbf debtrc publtcjc ( )6,6F e ( )>, > .N

3p a a x kx ; + s trcflpreb publtuj

( )4,1 .F

3p 4.Drcptub`meuj FNLD frc 6> e ( ) > < 9kx kx+ ; sfenshjuee rcfjc c`fjc.

3p 1.\sc rczhjvc b clufef 4 4 3 > .x x+ ;


49/101



Aejecrf vhlfehbfj, prhaejuj pcdf`h`el, spclefjezfrcf bvthr-cdulfthfrc. Thftc sunecltcjc subt hnje`fthree. Tekpuj cacltev dc julru cstc dc < hrc. \c flhrd69 publtc deb haeleu. Jf thftc sunecltcjc sc lcr rczhjvre lhkpjctc.4= \SNECLTSJ E (,

4 < 9.x x + ;

3p >.\sc lfjlujczc sukf 6 > < 49.+ + + +

3p 4 6 9x kx + ; sfenshjuee rcfjc.3p 4.\sc lfjlujczc destfbf dc jf publtuj ( )6,>F jf drcfptf 7 6 9.d x y+ + ;

3p 3.\sc rczhjvc b clufef >0 = 0 0 9.x x + ;

3p 1.\sc lfjlujczc6

lhs6


50/101


51/101



Aejecrf vhlfehbfj, prhaejuj pcdf`h`el, spclefjezfrcf bvthr-cdulfthfrc. Thftc sunecltcjc subt hnje`fthree. Tekpuj cacltev dc julru cstc dc < hrc. \c flhrd69 publtc deb haeleu. Jf thftc sunecltcjc sc lcr rczhjvre lhkpjctc.39 \SNECLTSJ E (99 6>=b+ ; + .

3p >.\sc dctcrkebc k fstacj blt clufef > 6 9x k x k ; sfenshjuee rcfjc c`fjc.

3p F , N , .

3p 3. \ sc dctcrkebc x fstacj blt bukcrcjc > < >, 1 3x , x x s aec tcrkcbe lhbscluteve fe ubceprh`rcsee fretkctelc.

3p 1.\sc rczhjvc b kujekcf bukcrcjhr rcfjc clufef >j` 3j` 1 9x x ; .


52/101



Aejecrf vhlfehbfj, prhaejuj pcdf`h`el, spclefjezfrcf bvthr-cdulfthfrc. Thftc sunecltcjc subt hnje`fthree. Tekpuj cacltev dc julru cstc dc < hrc. \c flhrd69 publtc deb haeleu. Jf thftc sunecltcjc sc lcr rczhjvre lhkpjctc.36 \SNECLTSJ E (f fj ubce prh`rcsee fretkctelc ( ) 6b bf teebd l 69 69f ; e 63 63f ; .

3p >.\sc rczhjvc b kujekcf bukcrcjhr rcfjc clufef> \SNECLTSJ E (

3p 6.\sc rczhjvc b clufef >64

jh` >x ; .

3p >. \sc rczhjvc b ebclufef >< 5 9x .3p 6a ; e ( )< 6a ; .

3p 4. \sc dctcrkebc kujekcf { 6 6F x x; .3p 3. Aec publtuj K kegjhluj sc`kcbtujue FN , efr H ub publt hfrclfrc deb pjfb. \sc dckhbstrczc l

6( )

>HK HF HN; +

.

3p 1. Treub`meuj FNLfrc h( ) 59k F ; , h( )


54/101




3< \SNECLTSJ E (7 , ( ) < 3 6a a x x x ; + .

3p F x x; + : .

3p 4. \sc dctcrkebc k teebd l`rfaeluj aublece>

7 , ( )< 3

ka a x x ; , lhbebc publtuj

F k

.

3p 3. \sc rczhjvc b kujekcf bukcrcjhr rcfjc clufef > 6 > > > > > =51x x x + + ; .3p 1. \sc frftc l, dflb treub`meuj FNLfrc jhl c`fjetftcf seb >seb lhsF N L; , ftuble _ [ _ [FN FL .


55/101



Aejecrf vhlfehbfj, prhaejuj pcdf`h`el, spclefjezfrcf bvthr-cdulfthfrc. Thftc sunecltcjc subt hnje`fthree. Tekpuj cacltev dc julru cstc dc < hrc. \c flhrd69 publtc deb haeleu. Jf thftc sunecltcjc sc lcr rczhjvre lhkpjctc.34 \SNECLTSJ E ( 3 9x .3p >. \sc rczhjvc b kujekcf bukcrcjhr rcfjc clufef ( )>6

>

jh` 6 6x + ; .

3p < >9956 > > > ... >\ ; + + + + + jf < sc hnebc rcstuj 9.3p 4. \sc slrec clufef drcptce lfrc lhbebc publtcjc ( )F e ( )6,3N .

3p 3. \sc rczhjvc sestckuj dc clufee6

>< 6

y x

y x x

;

; +, ,x y .

3p 1. Treub`meuj FNLfrc h( ) 59k F ; , NL; 69 e lhs 9,1L ; . \sc lfjlujczc pcrekctruj treub`meujue FNL.


56/101



Aejecrf vhlfehbfj, prhaejuj pcdf`h`el, spclefjezfrcf bvthr-cdulfthfrc. Thftc sunecltcjc subt hnje`fthree. Tekpuj cacltev dc julru cstc dc < hrc. \c flhrd69 publtc deb haeleu. Jf thftc sunecltcjc sc lcr rczhjvre lhkpjctc.33 \SNECLTSJ E (+ .

3p >. \sc dctcrkebc fj dhejcf tcrkcb fj prh`rcsece `chkctrelc ( )6b b

n

lfrc frc rfef >q ; e = ;>31n .

3p ,x x fjc clufece ( )> 3 < 9x k x k+ + ; , teebd l 6 > 4x x+ ; .

3p 4. \sc rczhjvc b clufef 6< < 69=x x+ + ; .3p 3. \c lhbsedcrpubltcjc ( )3,=F , ( )>,N f e ( , >)L n . \sc dctcrkebc ,f n pcbtru lfrc publtuj N

cstc kegjhluj sc`kcbtujue FL.

3p 1. \sc lfjlujczch h

h h

seb6


57/101



Aejecrf vhlfehbfj, prhaejuj pcdf`h`el, spclefjezfrcf bvthr-cdulfthfrc. Thftc sunecltcjc subt hnje`fthree. Tekpuj cacltev dc julru cstc dc < hrc. \c flhrd69 publtc deb haeleu. Jf thftc sunecltcjc sc lcr rczhjvre lhkpjctc.31 \SNECLTSJ E (

b b ; .

3p >. \sc lfjlujczc sukf prekejhr 69 tcrkcbe fe ubce prh`rcsee fretkctelc 6( )b bf teebd l 3 64f; e 63 44f ; .

3p x; saec shjuec f clufece ( )> >6 > < 9k x kx+ ; .3p 4. \sc rczhjvc b kujekcf bukcrcjhr rcfjc clufef 6 < 6x x; .3p 3. Treub`meuj FNLfrc < 3FL , FN ; e 19k( F) ; . \sc dctcrkebc jub`ekcf jftureeNL.

3p 1. Aec publtcjc 6 >F , e 6 4N , . \sc slrec clufef kcdefthfrce sc`kcbtujue FN .


58/101



Aejecrf vhlfehbfj, prhaejuj pcdf`h`el, spclefjezfrcf bvthr-cdulfthfrc. Thftc sunecltcjc subt hnje`fthree. Tekpuj cacltev dc julru cstc dc < hrc. \c flhrd69 publtc deb haeleu. Jf thftc sunecltcjc sc lcr rczhjvre lhkpjctc.30 \SNECLTSJ E ( > > < 9x kx k + + ; frc dhushjuee rcfjc c`fjc.3p >. \sc lfjlujczc sukf prekejhr 1 tcrkcbe fe ubce prh`rcsee `chkctrelc ( )

6b bn

, lfrc frc tcrkcbe phzeteve,

6; = 9x x + ; .3p 4.\sc dckhbstrczc lb hrelc treub`me FNL lu h( ) 59k F ; frc jhl c`fjetftcf > >seb seb 6N L+ ; .

3p 3. \sc lfjlujczc6 6 6 6 6

...6 > > < < 4 665 6>9 6>9 6>6

+ + + + +

+ + + + +

.

3p 1. Aec FNLD ub pfrfjcjh`rfk dc lcbtru H e Y ub publt hfrclfrc deb pjfbuj pfrfjcjh`rfkujue . \sc

dckhbstrczc l 4YF YN YL YD YH+ + + ;

.


59/101



Aejecrf vhlfehbfj, prhaejuj pcdf`h`el, spclefjezfrcf bvthr-cdulfthfrc. Thftc sunecltcjc subt hnje`fthree. Tekpuj cacltev dc julru cstc dc < hrc. \c flhrd69 publtc deb haeleu. Jf thftc sunecltcjc sc lcr rczhjvre lhkpjctc.3= \SNECLTSJ E (> 0 5 9x x+ : .3p >.Aec aublef 7 , ( ) < ... >9a a a a+ + + + .

3p >

n l

f

, ubdc f, n, lsubt

jub`ekejc jfturejhrNL,FL, rcspcltevFN.

3p 4. \sc rczhjvc b kujekcf bukcrcjhr rcfjc clufef 61 4x x+ ; .3p 3. Aec publtcjc ( )>, > < >990 >99=

...> < < 4 >99= >995

+ + + .


60/101



Aejecrf vhlfehbfj, prhaejuj pcdf`h`el, spclefjezfrcf bvthr-cdulfthfrc. Thftc sunecltcjc subt hnje`fthree. Tekpuj cacltev dc julru cstc dc < hrc. \c flhrd69 publtc deb haeleu. Jf thftc sunecltcjc sc lcr rczhjvre lhkpjctc.35 \SNECLTSJ E (.\sc dctcrkebc kujekcfF ;{ }, 64 9N x x nx f; + + ; e{ },3F N ; .

3p 1. Aec treub`meujFNL. Yubltcjc , ,K B Y subt kegjhflcjc jfturejhr treub`meujue e H cstc ub publthfrclfrc deb pjfbuj treub`meujue. \sc dckhbstrczc lHF HN HL HY HK HB + + ; + +

.


61/101



Aejecrf vhlfehbfj, prhaejuj pcdf`h`el, spclefjezfrcf bvthr-cdulfthfrc. Thftc sunecltcjc subt hnje`fthree. Tekpuj cacltev dc julru cstc dc < hrc. \c flhrd69 publtc deb haeleu. Jf thftc sunecltcjc sc lcr rczhjvre lhkpjctc.19 \SNECLTSJ E ( 6. \sc rczhjvc b kujekcf bukcrcjhr rcfjc clufef >3 3 >x x+ ; .

3p > 9x x k+ ; sfenshjuee rcfjc.3p 4. Aec aublef 7 , ( ) < >a a x x ; . \sc dctcrkebc lhhrdhbftcjc publtujue dc pc rcprczcbtfrcf

`rfaelf aublece a pcbtru lfrc fnslesf cstc c`fjlu hrdhbftf.

3p 3. Aec FNLD ub pfrfjcjh`rfk, efr H ub publt hfrclfrc deb pjfbuj pfrfjcjh`rfkujue. \sc frftc l

HF HL HN HD+ ; +

.

3p 1. \sc dckhbstrczc lbtr-ub treub`me hfrclfrc FNLfrc jhl rcjfef lhs lhsf L l F n+ ; , ubdc f, n, l

subt jub`ekejc jfturejhrNL,FL, rcspcltevFN.


62/101



Aejecrf vhlfehbfj, prhaejuj pcdf`h`el, spclefjezfrcf bvthr-cdulfthfrc. Thftc sunecltcjc subt hnje`fthree. Tekpuj cacltev dc julru cstc dc < hrc. \c flhrd69 publtc deb haeleu. Jf thftc sunecltcjc sc lcr rczhjvre lhkpjctc.16 \SNECLTSJ E ( < 6b b+ + ; .

3p >.\sc rczhjvc b kujekcf bukcrcjhr rcfjc clufef ( )>x + ; .3p >seb seb sebN L F+ ; cstc drcptub`mel.

3p 3. \sc dctcrkebc ,f n teebd l { }> < 9F x x fx; + + ; , { }> 6 9N x x nx f; + + + ; e{ }6,


63/101




3p 6. \sc rczhjvc b kujekcf bukcrcjhr rcfjc clufef ( )>4jh` 6 9x + ; .3p >. Clufef ( ) ( )>6 > 9k x k x k ; lu { }6k frc shjueejc 6 >,x x . \sc dctcrkebc { }6k

fstacj blt 6 > 6 > >x x x x+ ; .

3p

kF

fpfrebc `rfaelujue aublece 7 , ( )a a x x k ; + .

3p 4. teebd lFNLcstc ub treub`me drcptub`mel lu h( ) 59k F ; , ssc dckhbstrczc l

( ) ( )> >

seb seb lhs lhsN L N L+ + cstc bukr btrc`.

3p 3. Aec pftrujftcruj lhbvcxFNLD . Dflpubltcjc ,K B subt kegjhflcjc jfturejhr FN , rcspcltev LD , ssc

dckhbstrczc l ( )6>

KB FD NL; + .

3p 1.\sc dctcrkebc *b pcbtru lfrc6 6 6

... 6 < > 6b b

+ + + ;

+ + +

.


64/101



Aejecrf vhlfehbfj, prhaejuj pcdf`hèl, spclefjezfrcf bvthr-cdulfthfrc. Thftc sunecltcjc subt hnje`fthree. Tekpuj cacltev dc julru cstc dc < hrc. \c flhrd69 publtc deb haeleu. Jf thftc sunecltcjc sc lcr rczhjvre lhkpjctc.1< \SNECLTSJ E (. \sc rczhjvc b kujekcf bukcrcjhr rcfjc ebclufef> 4 3

< 5 6=x

+ .

3p 6 9x x k+ + ; sfenshjuee rcfjc destebltc.

3p 4. \sc rczhjvc b kujekcf bukcrcjhr rcfjc clufef ( )>6x x + ; .

3p 3. Yubltcjc ( )>,9F , ( )4,9N e (9,1)L subt vraurejc ubue treub`me. \sc dctcrkebc jubèkcf kcdefbce

lhrcspubzthfrc jftureeNL.

3p 1. \sc dckhbstrczc lb hrelc treub`me FNLcstc fdcvrftc`fjetftcf lhs lhsf N n F l + ; , ubdc f,

n, lsubt jubèkejc jfturejhrNL,FL, rcspcltevFN.


65/101



Aejecrf vhlfehbfj, prhaejuj pcdf`h`el, spclefjezfrcf bvthr-cdulfthfrc. Thftc sunecltcjc subt hnje`fthree. Tekpuj cacltev dc julru cstc dc < hrc. \c flhrd69 publtc deb haeleu. Jf thftc sunecltcjc sc lcr rczhjvre lhkpjctc.14 \SNECLTSJ E (. \sc rczhjvc b kujekcf bukcrcjhr rcfjc clufef > 63 6>3x+ ; .3p > 9x fx f ; lu f , ssc dctcrkebc lcfjfjtshjuec >x .

3p 4. \sc lfjlujczc sukf > < 56 > > > ... >\ ; + + + + + .3p 3. Aec , ,K B Y kegjhflcjc jfturejhr ,NL FL , rcspcltev FN fjc treub`meujue FNL . \sc frftc l

9FK NB LY+ + ;

.

3p 1.\sc lfjlujczc vfjhfrcf cxprcseceseb6>9 seb639

lhs6>9 lhs639C

;

+

.


66/101



Aejecrf vhlfehbfj, prhaejuj pcdf`h`el, spclefjezfrcf bvthr-cdulfthfrc. Thftc sunecltcjc subt hnje`fthree. Tekpuj cacltev dc julru cstc dc < hrc. \c flhrd69 publtc deb haeleu. Jf thftc sunecltcjc sc lcr rczhjvre lhkpjctc.13 \SNECLTSJ E (9b b+ + ; .

3p >.\sc rczhjvc b kujekcf bukcrcjhr rcfjc clufef>

> 6x x

; .

3p 1 r e g; + +

, > ,x x fjc clufece ( ) ( )> > 4 > 9kx k x k+ + + ;

svcreaelc rcjfef6 >

6 6>

x x+ ; .

3p 1.\sc frftc l b hrelc treub`me FNL, lfrc frc ( ) 59k F ; , frc jhl c`fjetftcf

( )( ) >seb seb lhs lhs > seb sebl N n L l N n L f N L + + ; , ubdc f, n, lsubt jub`ekejc jfturejhrNL,FL,rcspcltevFN.


67/101



Aejecrf vhlfehbfj, prhaejuj pcdf`h`el, spclefjezfrcf bvthr-cdulfthfrc. Thftc sunecltcjc subt hnje`fthree. Tekpuj cacltev dc julru cstc dc < hrc. \c flhrd69 publtc deb haeleu. Jf thftc sunecltcjc sc lcr rczhjvre lhkpjctc.11 \SNECLTSJ E ( < 4 6> + .

3p >. \c lhbsedcraubleejc ( ) ( )> >, 7 , >, > < 3a ` a x x x ` x x x ; + ; + + . \sc dctcrkebc shjueejc

rcfjc fjc clufece ( ) ( )a x ` x; .

3p 3>, 34n n; ; .

3p 4. \sc rczhjvc b clufef>

>6

< 4

x

x

+

;

+

.

3p 3. \sc lfjlujczc fref ptrftujue FNLD teebd l ( )6,>N e ( )>,


68/101



Aejecrf vhlfehbfj, prhaejuj pcdf`h`el, spclefjezfrcf bvthr-cdulfthfrc. Thftc sunecltcjc subt hnje`fthree. Tekpuj cacltev dc julru cstc dc < hrc. \c flhrd69 publtc deb haeleu. Jf thftc sunecltcjc sc lcr rczhjvre lhkpjctc.10 \SNECLTSJ E (,6995 .3p >. \sc rczhjvc b clufef ( )>jh` < > 9x ; .

3p > > ... > 69> 6 > 9k x k x k+ + ; vcreael

rcjfef ( )6 > 6 >6 3

>

x x x x+ ; .


69/101



Aejecrf vhlfehbfj, prhaejuj pcdf`h`el, spclefjezfrcf bvthr-cdulfthfrc. Thftc sunecltcjc subt hnje`fthree. Tekpuj cacltev dc julru cstc dc < hrc. \c flhrd69 publtc deb haeleu. Jf thftc sunecltcjc sc lcr rczhjvre lhkpjctc.1= \SNECLTSJ E ( 4r e g

; + , < >r e g

; + . \sc dctcrkebc , , fstacj

blt 6 > r r r ;

.

3p >. \sc rczhjvc b kujekcf bukcrcjhr rcfjc clufef > 6 >> < > 6 9x x+ + ; .

3p < 56 < < < ... ,x x fjc clufece ( )

>6 > 9kx k x+ + ; ,

vcreaelrcjfef 6 > 6 > lhsf n L; , ftuble n l; , ubdc fe nsubtjub`ekejc jfturejhr NL, rcspcltev FL.

3p 1. Sb hneclt lhst>399 jce. Hnecltuj s-f ecatebet lu 69% deb prc, fphe s-f ecatebet lu 6>% deb bhuj prc.\sc lfjlujczc vfjhfrcf ujtekujue prc.


70/101



Aejecrf vhlfehbfj, prhaejuj pcdf`hèl, spclefjezfrcf bvthr-cdulfthfrc. Thftc sunecltcjc subt hnje`fthree. Tekpuj cacltev dc julru cstc dc < hrc. \c flhrd69 publtc deb haeleu. Jf thftc sunecltcjc sc lcr rczhjvre lhkpjctc.15 \SNECLTSJ E (49 dc pfèbe, f dhuf ze .\sc rczhjvc b kujekcf bukcrcjhr rcfjc clufef >< > > 6 6 9x k x k ; vcreael

rcjfef 6 > 6 >>

995-KFTCKFTELYrhnf D, KT995Yrhnslresjf KFTCKFTEL Yrhnf D


09 \SNECLTSJ E ( < 4 699

.

3p >.\sc rczhjvc b kujekcf bukcrcjhr rcfjc clufef 3jh`

> 4x

; .

3p 4

>

y x

y x x

; +

; , ,x y .

3p 4. Aec aublef 7 , ( ) < 1 >a a x x k ; + . \sc dctcrkebc k fstacj blt publtuj (4 3, )F k k sfpfreb`rfaelujue aublece a.

3p 3.Sb treub`me FNLfrc ( ) ( ) 19 , ND ; , ssclfjlujczc jubèkcf jfturee FL.

3p 1.\sc lfjlujczc vfjhfrcf cxprcseceseb639 seb6>9

seb639 seb6>9

+

.


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06 \SNECLTSJ E (| 1 0 9F x x x; ; .3p >. \sc dctcrkebc ,f n fstacj blt ( ) ( ) > x ; .3p 3. \sc dctcrkebc k pcbtru lfrc vrauj pfrfnhjce aublece ( ) ( )>7 , > 4 < 1 0a a x x k x k ; + + +

cstc setuft pc fxf Hx .

3p 1. b treub`meuj FNLsc tec l ,FD NL D NL , ( ) ( )19 ,


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\SNECLTSJ E (

3p 6.

\sc rczhjvc b kujekcf bukcrcjhr rcfjc clufef 6x ; .

3p >. Aec aublef 7 , ( ) > 4a a x x ; + . \sc dctcrkebc lhhrdhbftcjc ubue publt fj `rfaelujue aublece apcbtru lfrc hrdhbftf cstc c`fjlu dunjuj fnslesce.

3p > >1 < 6 > 9k x k x k+ ; .

3p 4. Sbuj deb ub`meurejc ubue trfpcz eshslcj cstc dc 43 , efr bjekcf trfpczujue frc jub ekcf > . \scdctcrkebc sukf jub`ekejhr jfturejhr bcpfrfjcjc fjc trfpczujue.

3p 3. H pcrshfbf lmcjtuet >9% debtr-h suke bl619 jce deb cf. \sc dctcrkebc sukf ebeefj, teebd le-f rkfs 03% deb flcfstf.

3p 1. Aec publtcjc ( )6,3F e ( )>,>N . \sc dctcrkebc clufef kcdefthfrce sc`kcbtujue FN .


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Aejecrf vhlfehbfj, prhaejuj pcdf`hèl, spclefjezfrcf bvthr-cdulfthfrc. Thftc sunecltcjc subt hnje`fthree. Tekpuj cacltev dc julru cstc dc < hrc. \c flhrd69 publtc deb haeleu. Jf thftc sunecltcjc sc lcr rczhjvre lhkpjctc.0< \SNECLTSJ E (jh` < > >x+ ; .3p >. \sc lfjlujczc sukf prekcjhr 69 bukcrc bfturfjc ekpfrc.

3p 4 63 9x x ; lu shjueejc 6 >,x x . \sc lfjlujczc> >6 >x x+ .

3p 4. H pcrshfbfrc ub sfjfreu dc 6999 jce. Lfrc vf ae sfjfreuj pcrshfbce duph kelhrfrc lu 3%, urkftdch krerc lu 3%8

3p 3. \sc dctcrkebc lhhrdhbftcjc publtujue b lfrc drcfptf dctcrkebftdc publtcjc ( )F e ( )>,=N

ebtcrscltcfzfxf Hy .

3p 1. b treub`meuj drcptub`mel FNL ( )( )59k F ; kcdefbf lhrcspubzthfrc ephtcbuzce frc jubèkcf dc3 lk, efr lftctf FN cstc dc 3 lk. \sc lfjlujczc jubèkcf jfturee FL.


75/101



Aejecrf vhlfehbfj, prhaejuj pcdf`h`el, spclefjezfrcf bvthr-cdulfthfrc. Thftc sunecltcjc subt hnje`fthree. Tekpuj cacltev dc julru cstc dc < hrc. \c flhrd69 publtc deb haeleu. Jf thftc sunecltcjc sc lcr rczhjvre lhkpjctc.04 \SNECLTSJ E (x x ; .

3p 7 , ( ) >a a x x x ; + .

3p 4. Aec aublef 7 , ( ) < >a a x x ; + . \sc lfjlujczc ( ) ( ) ( ) ( )6 > < ... 69a a a a+ + + + .

3p 3. teebd lclufef drcptce dctcrkebftdc publtcjc (>,>)F e (


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77/101



Aejecrf vhlfehbfj, prhaejuj pcdf`hèl, spclefjezfrcf bvthr-cdulfthfrc. Thftc sunecltcjc subt hnje`fthree. Tekpuj cacltev dc julru cstc dc < hrc. \c flhrd69 publtc deb haeleu. Jf thftc sunecltcjc sc lcr rczhjvre lhkpjctc.01 \SNECLTSJ E (x + ; .

3p < 3 , 6 >6 >

6 6C x x


>0 9x x ; .

3p 1.\sc lfjlujczc>

seb6>9 > lhs6>9 > seb 43 > lhs19

995-KFTCKFTELYrhnf D, KT995Yrhnslresjf KFTCKFTEL Yrhnf D

Aejecrf vhlfehbfj, prhaejuj pcdf`hèl, spclefjezfrcf bvthr-cdulfthfrc. Thftc sunecltcjc subt hnje`fthree. Tekpuj cacltev dc julru cstc dc < hrc. \c flhrd69 publtc deb haeleu. Jf thftc sunecltcjc sc lcr rczhjvre lhkpjctc.00 \SNECLTSJ E (f; e rfef >q; . \sc dctcrkebc sukf 1 =f f .3p >.\sc lfjlujczc prcuj ubue prhdus duph slukperc lu 3% , teebd lprcuj ebeefj crf dc 6>9 jce.3p > 3 > 9x x+ 2 .3p 4.Treub`meuj FNLfrc 59k( F ) ; , 3 69FN , NL; . \sc lfjlujczc fref treub`meujue FNL.

3p 3.b treub`meuj FNL, publtcjc K , B, Ysubt kegjhflcjc jfturejhr NL, FL, rcspcltev FN. \sc frftc l

> > > 9FK NB LY + + ; .

3p 1.\sc rczhjvc b clufef>

4> 5 6995-KFTCKFTELYrhnf D, KT995Yrhnslresjf KFTCKFTEL Yrhnf D

Aejecrf vhlfehbfj, prhaejuj pcdf`hèl, spclefjezfrcf bvthr-cdulfthfrc. Thftc sunecltcjc subt hnje`fthree. Tekpuj cacltev dc julru cstc dc < hrc. \c flhrd69 publtc deb haeleu. Jf thftc sunecltcjc sc lcr rczhjvre lhkpjctc.0= \SNECLTSJ E ( jh` 6

0+ + .

3p >.Aec 6( )b bf h prh`rcsec fretkctellu 0 6661, >9.f f; ; \sc dctcrkebc sukf prekejhr >9 dc tcrkcbefe prh`rcsece fretkctelc.

3p ( ) 3 4a x x x; + .

3p 4.\c lhbsedcrtreub`meuj FNL, lu vclthree dc phzeec < 4 , 3 , >F N Lr e g r e r g; + ; ;

. \sc

dctcrkebc vclthruj dc phzeec fj lcbtrujue dc `rcutftc fj treub`meujue FNL.

3p 3.\sc rczhjvc b clufef 6 >< < < 660x x x+ ++ + ; .

3p 1.Treub`meuj FNLfrc 0, =, 6>FN NL FL; ; ; . \sc lfjlujczclhs

lhs

F

N

.


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81/101


82/101



Aejecrf vhlfehbfj, prhaejuj pcdf`h`el, spclefjezfrcf bvthr-cdulfthfrc. Thftc sunecltcjc subt hnje`fthree. Tekpuj cacltev dc julru cstc dc < hrc. \c flhrd69 publtc deb haeleu. Jf thftc sunecltcjc sc lcr rczhjvre lhkpjctc.=6 \SNECLTSJ E (( ) 7"> < 0 3, "p x x x x x+ ; + . \sc dctcrkebc vfjhfrcf dc fdcvr fprhphzeece ( .\sc slrec rcjfeejc jue Qetc pcbtru clufef >> 0 9x x ; .3p >6f r+ .

3p 4.b treub`meuj FNLsc lubhsl 3v e g; +

dupvclthree f e g; +

e >


83/101



Aejecrf vhlfehbfj, prhaejuj pcdf`h`el, spclefjezfrcf bvthr-cdulfthfrc. Thftc sunecltcjc subt hnje`fthree. Tekpuj cacltev dc julru cstc dc < hrc. \c flhrd69 publtc deb haeleu. Jf thftc sunecltcjc sc lcr rczhjvre lhkpjctc.=> \SNECLTSJ E (

3p 6.\sc dctcrkebc clufef drcptce lfrc trclc preb publtcjc (.\sc lfjlujczc pcrekctruj treub`meujueFNL lfrc frc ( ) 59 , ( ) 43k F k N; ; e 3 >NL; .

3p


84/101



Aejecrf vhlfehbfj, prhaejuj pcdf`h`el, spclefjezfrcf bvthr-cdulfthfrc. Thftc sunecltcjc subt hnje`fthree. Tekpuj cacltev dc julru cstc dc < hrc. \c flhrd69 publtc deb haeleu. Jf thftc sunecltcjc sc lcr rczhjvre lhkpjctc.=< \SNECLTSJ E (> , > , > , > , > .3p >.\sc lfjlujczc destfbf debtrc publtcjc ( )F e (9,3)N .

3p 3

, ,4 6

x yx y

x y

;

+ ; .

3p 4.\sc lfjlujczc vfjhfrcf cxprcsece 6 > 6 >>C x x x x; + , ubdc 6 >,x x subt shjueejc clufece>

> < 6 9x x ; .

3p 3.\sc rczhjvc b clufef >0) lhs639 seb 43 lhs43> >

+ .


85/101



Aejecrf vhlfehbfj, prhaejuj pcdf`h`el, spclefjezfrcf bvthr-cdulfthfrc. Thftc sunecltcjc subt hnje`fthree. Tekpuj cacltev dc julru cstc dc < hrc. \c flhrd69 publtc deb haeleu. Jf thftc sunecltcjc sc lcr rczhjvre lhkpjctc.=4 \SNECLTSJ E ( 963 3 36>3

.

3p >.Aec ( ) 6b bf h prh`rcsec fretkctellu 6 3f ; e rfef >r ; . \sc lfjlujczc ( )>

6 0f f+ .

3p

6 6C


>< > 0 9x x + ; .

3p 4.\sc rczhjvc b clufef > Nr e g; +

e

>Lr g;

. \sc dctcrkebc vclthruj dc phzeec fj lcbtrujue dc `rcutftc fj treub`meujue FNL.

3p 1.b treub`meuj FNLsc lubhsl =,


86/101



Aejecrf vhlfehbfj, prhaejuj pcdf`h`el, spclefjezfrcf bvthr-cdulfthfrc. Thftc sunecltcjc subt hnje`fthree. Tekpuj cacltev dc julru cstc dc < hrc. \c flhrd69 publtc deb haeleu. Jf thftc sunecltcjc sc lcr rczhjvre lhkpjctc.=3 \SNECLTSJ E ( > >x ; .

3p >.\sc slrec clufef drcptce lfrc trclc preb publtuj ( )6,4F e frc pfbtf6

>k ; .

3p < 1

, ,> 4

x yx y

x y

;

+ ; .

3p 4.\sc studeczc sckbuj aublece 7a , >( ) > 3 >a x x x; + .

3p 3.\sc rczhjvc b clufef> 1 6

>61

x x ; .

3p 1.Aec treub`meuj FNL. teebd l seb seb seb 9f F n N l L ; , ssc frftc ltreub`meuj FNLcstcdrcptub`mel, ubdc f, n, lsubt jub`ekejc jfturejhrNL,FL, rcspcltevFN.


87/101



Aejecrf vhlfehbfj, prhaejuj pcdf`h`el, spclefjezfrcf bvthr-cdulfthfrc. Thftc sunecltcjc subt hnje`fthree. Tekpuj cacltev dc julru cstc dc < hrc. \c flhrd69 publtc deb haeleu. Jf thftc sunecltcjc sc lcr rczhjvre lhkpjctc.=1 \SNECLTSJ E ( 4 6

16 6> > 7 > >0 >

+

.

3p >.Aec ( ) 6b bn h prh`rcsec `chkctrel, lu 3 >0n ; e lu rfef6

< 6a x x x; .

3p 4.\sc rczhjvc b clufef ( )3jh` > >x ; .

3p 3.\c lhbsedcrpubltcjc ,F N lfrc fu lf vclthre dc phzeec 4 , > 3F Nr e g r e g; + ; +

. \sc dctcrkebc

vclthruj dc phzeec fj publtujue _ [K FN , teebd l >FK

KN; .

3p 1.b treub`meuj FNLsc lubhsl 4,


88/101



Aejecrf vhlfehbfj, prhaejuj pcdf`h`el, spclefjezfrcf bvthr-cdulfthfrc. Thftc sunecltcjc subt hnje`fthree. Tekpuj cacltev dc julru cstc dc < hrc. \c flhrd69 publtc deb haeleu. Jf thftc sunecltcjc sc lcr rczhjvre lhkpjctc.=0 \SNECLTSJ E (.\sc lfjlujczc 3 3 36

jh` >3 jh` 3 jh`6>3

+ .

3p 6

x yx y

x y

+ ;

; .

3p 4.Aec ( )6b b

f

h prh`rcsec fretkctellu 6 4f ; e rfef 6y x; + .

3p 1.\sc rczhjvc b clufef < < 4 6x x+ ; .


89/101



Aejecrf vhlfehbfj, prhaejuj pcdf`h`el, spclefjezfrcf bvthr-cdulfthfrc. Thftc sunecltcjc subt hnje`fthree. Tekpuj cacltev dc julru cstc dc < hrc. \c flhrd69 publtc deb haeleu. Jf thftc sunecltcjc sc lcr rczhjvre lhkpjctc.== \SNECLTSJ E (.\sc rcprczebtc `rfael aublef 7a , ( ) > 1a x x; + .

3p ( ) >a x x kx; + + , ubdc kcstc ub bukr rcfj. \sc dctcrkebc kteebd lvfjhfrcf kebekf aublecea cstc c`fjlu >.

3p 4.\sc rczhjvc b clufef6 6

> < 6 94 >

x x

+ ;

.

3p 3.\sc dctcrkebc bukcrcjc rcfjc fe nteebd lpubltcjc ( ),6F f e ( )6,N f n+ fpfreb drcptce dc clufec

> 4 9x y+ + ; .

3p 1.\sc lfjlujczc fref treub`meujueFNLteebd l >, 4FN FL; ; e ( )


90/101



Aejecrf vhlfehbfj, prhaejuj pcdf`h`el, spclefjezfrcf bvthr-cdulfthfrc. Thftc sunecltcjc subt hnje`fthree. Tekpuj cacltev dc julru cstc dc < hrc. \c flhrd69 publtc deb haeleu. Jf thftc sunecltcjc sc lcr rczhjvre lhkpjctc.=5 \SNECLTSJ E ( 3 1 9x x + ; .3p >.\c lhbsedcrvclthree > , < , 3u e g v e w g; + ; ;

. \sc lfjlujczc vclthruj >u v w

.

3p q ; . \sc dctcrkebc sukf prekejhr 1 tcrkcbe fe

prh`rcsece `chkctrelc.

3p 4.\sc rczhjvc b ebclufef > 1 9x + .

3p 3.\sc lfjlujczcseb6


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92/101


93/101




3p 6.b rcpcruj lfrtczefb xHy , ssc lfjlujczc destfbf debtrc publtcjc ( )>,3F e ( )4,9N .3p >.\sc lfjlujczc prhnfnejetftcf lf, fjc`bd ub cjckcbt deb kujekcf {9,>,4,1,=,69}F ; , flcstf saec

shjuec f clufece > 1 = 9x x + ; .

3p 6a x x; .

3p 4.\sc dcf cxckpju dc h aublec ( )7 ,a a x fx n ; + , lu ,f n , lrcslthfrc, f lrce

rcprczcbtfrc `rfaelstrcflpreb publtuj ( )>,9K .

3p 3.\c lhbsedcrtreub`meuj FNLlu 0, =, 5FN NL FL; ; ; . \sc lfjlujczc6 6 6

lhs lhs lhsF N Lf n l

+ , ubdc f, n, lsubt jubèkejc jfturejhrNL,FL, rcspcltevFN.

3p 1.\sc rczhjvc b clufef 6 > < 49< < < 995-KFTCKFTELYrhnf D, KT995Yrhnslresjf KFTCKFTEL Yrhnf D

Aejecrf vhlfehbfj, prhaejuj pcdf`hèl, spclefjezfrcf bvthr-cdulfthfrc. Thftc sunecltcjc subt hnje`fthree. Tekpuj cacltev dc julru cstc dc < hrc. \c flhrd69 publtc deb haeleu. Jf thftc sunecltcjc sc lcr rczhjvre lhkpjctc.5< \SNECLTSJ E (.\sc studeczc sckbuj aublece 7a , ( ) < 1a x x; .

3p

6jh` =jh` = >> 45 .

3p 4.\sc rczhjvc b clufef < 3 > >x ; .3p 3.b rcpcruj lfrtczefb xHy sc lhbsedcrpubltcjc ( ) ( ) ( )1,9 , 9, < , >,3F N L . \sc lfjlujczc fref

treub`meujue FNL.3p 1.\sc frftc ldflb treub`meuj FNLfvck lhs lhs lhsn N l L f F + ; , ftuble treub`meuj cstc

drcptub`mel, ubdc f, n, lsubt jubèkejc jfturejhrNL,FL, rcspcltevFN.


95/101



Aejecrf vhlfehbfj, prhaejuj pcdf`h`el, spclefjezfrcf bvthr-cdulfthfrc. Thftc sunecltcjc subt hnje`fthree. Tekpuj cacltev dc julru cstc dc < hrc. \c flhrd69 publtc deb haeleu. Jf thftc sunecltcjc sc lcr rczhjvre lhkpjctc.54 \SNECLTSJ E (.Jfturejc treub`meujue FNLsubt 1, 0, =NL FL FN; ; ; . \sc lfjlujczc lhs lhsN L .3p a x x; +

lu fxcjc dc lhhrdhbftc Hxe Hy.

3p 4.\sc dctcrkebc clufef drcptce lfrc trclc preb publtuj ( )>,

> 6, ,

< 3

x yx y

x x y

+ ;

+ ; .

3p 1.\sc rczhjvc b clufef >5 >


96/101


97/101



Aejecrf vhlfehbfj, prhaejuj pcdf`h`el, spclefjezfrcf bvthr-cdulfthfrc. Thftc sunecltcjc subt hnje`fthree. Tekpuj cacltev dc julru cstc dc < hrc. \c flhrd69 publtc deb haeleu. Jf thftc sunecltcjc sc lcr rczhjvre lhkpjctc.51 \SNECLTSJ E (

x yx y

x y

; + ;

.

3p >.Treub`meuj FNLfrc ( ) 59 , 1, 1 > 6x x .

3p 1.b rcpcruj lfrtczefb xHy sc lhbsedcrpubltcjc (


98/101



Aejecrf vhlfehbfj, prhaejuj pcdf`h`el, spclefjezfrcf bvthr-cdulfthfrc. Thftc sunecltcjc subt hnje`fthree. Tekpuj cacltev dc julru cstc dc < hrc. \c flhrd69 publtc deb haeleu. Jf thftc sunecltcjc sc lcr rczhjvre lhkpjctc.50 \SNECLTSJ E (.\sc slrec rcjfeejc jue Qetc pcbtru clufef >4 (< ) 1 > 9x k x k + + ; , ubdc k .

3p 4x x ; .3p 3.\sc dctcrkebc aublef 7a , ( )a x fx n; + , , , 9f n f teebd l`rfaeluj su lhbebc

publtcjc (>, seb69 > < seb 19 > seb


99/101



Aejecrf vhlfehbfj, prhaejuj pcdf`h`el, spclefjezfrcf bvthr-cdulfthfrc. Thftc sunecltcjc subt hnje`fthree. Tekpuj cacltev dc julru cstc dc < hrc. \c flhrd69 publtc deb haeleu. Jf thftc sunecltcjc sc lcr rczhjvre lhkpjctc.5= \SNECLTSJ E (, 3 9b b .

3p >.\sc rcprczebtc `rfael aublef 7a , ( ) > > 6a x x x; + + .

3p 0x +

trclc preb publtuj ( ) >seb 6>9 lhs 639+ .

3p 1.\sc rczhjvc b clufef >> >> jh` 3 jh` > 9x x + ; .


100/101



Aejecrf vhlfehbfj, prhaejuj pcdf`h`el, spclefjezfrcf bvthr-cdulfthfrc. Thftc sunecltcjc subt hnje`fthree. Tekpuj cacltev dc julru cstc dc < hrc. \c flhrd69 publtc deb haeleu. Jf thftc sunecltcjc sc lcr rczhjvre lhkpjctc.55 \SNECLTSJ E (.\sc dctcrkebc publtcjc dc ebtcrsclec fjc rcprczcbtree `rfaelc f aublece 7a ,

( ) > 3 4a x x x; + lu fxf Hx .

3p , 4), ( 6,9), (4,9)F N L . \sc lfjlujczc pcrekctrujtreub`meujue FNL.

3p 3.\sc rczhjvc b ebclufef < < 6x x .

3p 1.\sc rczhjvc b clufef < < >> > 0 6x x x x + + ; + .


101/101


C]FKCBSJ DC NFLFJFS^CFT >995Yrhnslresjf KFTCKFTEL Yrhnf D

Aejecrf vhlfehbfj, prhaejuj pcdf`h`el, spclefjezfrcf bvthr-cdulfthfrc. Thftc sunecltcjc subt hnje`fthree. Tekpuj cacltev dc julru cstc dc < hrc. \c flhrd69 publtc deb haeleu. Jf thftc sunecltcjc sc lcr rczhjvre lhkpjctc.699 \SNECLTSJ E (.\sc lfjlujczc 0 jh` jh` < jh` 65

+ .

3p 33

x x+

;

.

3p 3.\sc rczhjvc sestckuj

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Matematica M3 si M4 - Subiectul I cu 100 variante din 2009

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