7/25/2019 2008 Matematic Etapa Locala Subiecte Clasa a XI-A 2

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OLIMPIADA DE MATEMATIC, ETAPA LOCAL, 26.01.2008

CLASA a XI-a

Subiecte:1) ie AM2!R), A"

dc

ba

, daTrA += .

a) S# $e a%ate c# ( ) AxTrAxIxA &et)&et! 22 += , 'e(t%u %ice x R.

b) Dac# ( ) 2&et 2 = IA *i ( ) +&et 2 =+ IA , $# $e cacuee &et A *i ( )22&et IA .

2) a) A%#tai c# (u e/i$t# at%ice X, M2!R) a$te 3(c4t X5 - 5X " In.

b) Dac# A, Mn!R), a$te 3(c4t A5-5A", $# $e a%ate c# (u e$te i(7e%$abi#.

) ie ( ) Nnna u( *i% a$te 3(c4t 00 a *i ++

+=+

n

aa

aa

nn

nn ,

1

121 N.

a) S# $e a%ate c# ( ) Nnna e$te $t%ict c%e$c#t% *i (e#%9i(it.

b) S# $e cacuee8

,in

ann

.

+) ie f:R--1,0;R ,

= +1

11

2)! xx eexxf .

S# $e cacuee:a) Liitee ate%ae 3( 'u(ctu x0 " 0.b) Liitee ate%ae 3( 'u(ctu x0 " -1.

c) )!,i xfx

.