Matematica.clasa11.Arhimede.2007.05 12
1
&RQFXUVXOQD LRQDOGHPDWHPDWLF $5+,0(’( (WDSDILQDO PDL &ODVDD;,D SD)LH 0 $ ∈ & ’DFD ∈ ∀ ≤ + ] ], $ GHW &FX = ] DWXQFL ∈ ∀ = + ] ] ], $ GHW & ’DQøWHIDQ0DULQHVFX9LRUHO&RUQHD SE&DOFXODWL VLQ VLQ VLQ VLQ VLQ VLQ VLQ VLQ VLQ F ] F \ F [ E ] E \ E [ D ] D \ D [ + + + + + + + + + XQGH[\]DEF ∈ 5 $XUHO’RERœDQ%RW7UDQGDILU SD)LH ≥ Q Q [ XQœLUGHQXPHUHUHDOHFXSURSULHW LOH L ≥ ∀ ≤ + Q [ [ Q Q LL ≥ ∀ > ≥ + + Q D [ [ Q Q $WXQFLœLUXO ≥ Q Q [ HVWHFRQYHUJHQW $GULDQ7URLH SE’HWHUPLQD LIXQF LLOHIJ 5 → 5FDUHVDWLVIDFFRQGL LLOH L 5 ∈ ∀ + = - - + \ [ [ \ J \ I [ I \ [ I LL 5 OLP ∈ = ∞ → D D [ [ I Q ’DQLHO-LQJD,RQHO3RSHVFX SD)LH ≥ Q ,LQWHUYDOœLIJ, → 5GRXDIXQF LLGHQRULGHULYDELO ’DF ≥ [ I N œL ( ) ≥ [ J N SHQWUXRULFH , [ ∈ ‘ ^ Q N ∈ DWXQFL ( ) ≥ N [ J [ I SHQWUXRULFH Q N , [ = ∈ SE6 VHDUDWHF IXQF LD 5 → π I ∈ = π [ [ WJ [ I DUHWRDWH GHULYDWHOHSR]LWLYH 0DULXV5 GXOHVFX SF’DF 5 @ > → I IXQF LHFRQWLQX SH>@GHULYDELO SHV VHDUDWHF H[LVW ∈ F DVWIHOFD F FI F I I I + - = - ’DQ1HGHLDQX S6 VHGHWHUPLQHWRDWHQXPHUHOHQDWXUDOH ≥ Q FXSURSULHWDWHDF HVWHDGHY UDW XUP WRDUHDDILUPD LH & Q 0 % $ ∈ œL Q 2 %$ $% % $ = + = = LPSOLF $%%$ 6RULQ5 GXOHVFX0LKDL3LWLFDUL 1RW 7RDWHVXELHFWHOHVXQWREOLJDWRULL)LHFDUHVXELHFWVHQRWHD] GHODODS )LHFDUHVXELHFWSULPHœWHXQSXQFWGLQRILFLX7LPSGHOXFUXRUH
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Transcript of Matematica.clasa11.Arhimede.2007.05 12
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&RQFXUVXOQD LRQDOGHPDWHPDWLF $5+,0('((WDSDILQDO PDL&ODVDD;,D
SD)LH 0$ & 'DFD + ]],$ GHW &FX =] DWXQFL =+ ]]],$ GHW &
'DQWHIDQ0DULQHVFX9LRUHO&RUQHDSE&DOFXODWL
VLQVLQVLQVLQVLQVLQVLQVLQVLQ
F]F\F[E]E\E[D]D\D[
+++
+++
+++
XQGH[\]DEF 5$XUHO'RERDQ%RW7UDQGDILU
SD)LH QQ[ XQLUGHQXPHUHUHDOHFXSURSULHW LOH
L + Q[[ QQ LL >++ QD[[ QQ $WXQFLLUXO QQ[ HVWHFRQYHUJHQW
$GULDQ7URLHSE'HWHUPLQD LIXQF LLOHIJ55FDUHVDWLVIDFFRQGL LLOHL 5
+
=+ \[[\J\I[I\[I
LL 5OLP =
DD[[I
Q
'DQLHO-LQJD,RQHO3RSHVFX
SD)LH Q ,LQWHUYDOLIJ,5GRXDIXQF LLGHQRULGHULYDELO 'DF [I N L ( ) [J N SHQWUXRULFH ,[ `^ QN DWXQFL ( ) N[J[I SHQWUXRULFH QN,[ =
SE6 VHDUDWHF IXQF LD 5
piI
=
pi[[WJ[I DUHWRDWHGHULYDWHOHSR]LWLYH
0DULXV5 GXOHVFXSF'DF 5@> I IXQF LHFRQWLQX SH>@GHULYDELO SHV VHDUDWHF H[LVW F DVWIHOFD
FFIFIII += 'DQ1HGHLDQX
S6 VHGHWHUPLQHWRDWHQXPHUHOHQDWXUDOH Q FXSURSULHWDWHDF HVWHDGHY UDW XUP WRDUHDDILUPD LH
& Q0%$ L Q2%$$%%$ =+== LPSOLF $% %$
6RULQ5 GXOHVFX0LKDL3LWLFDUL1RW 7RDWHVXELHFWHOHVXQWREOLJDWRULL)LHFDUHVXELHFWVHQRWHD] GHODODS)LHFDUHVXELHFWSULPHWHXQSXQFWGLQRILFLX7LPSGHOXFUXRUH
