ΘΕΜΑΤΑ ΑΛΓΕΒΡΑΣ Β ΛΥΚΕΙΟΥ
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Transcript of ΘΕΜΑΤΑ ΑΛΓΕΒΡΑΣ Β ΛΥΚΕΙΟΥ
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1
f 3( ) 1xf x e
] f .
B] [3, )x 2ln9 ln 27( )f x f e .
] 5 5ln 1 ln 1
ln2
x xe ef x
2
f ln( ) xf x x , 0x .
] 0x
2(ln )( ) xf x e .
] 4
5ln
( )x
f xe
e
.
] ( )f x e .
3
2x
x
e 1 f(x) ln
e 5
-
] f .
] f(x) = 2ln2
] f(x) > 0 .
4
f(x) = ln(e2x-2ex+3) g(x) = ln3+ln(ex-1). ] f(x) g(x).
] f(x) = g(x).
] f(x) > 2g(x).
5
Q(t) ( ), t
.
300.000 , 6
.
ln Q(t) = t + , t 0 , R .
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:
] Q(t) = 3 4t, t 0
] 1/16
.
]
1/9 .
6
] N : x 1 x
2.4 2.2 1 0
]
3 2P x 2x x x 3 .
P x x 2 3. : i) ,
ii) P x
7
f xf x 5 ) N f
) 2 xf x 5 ) f
8
f x
f xe
, 0 e .
]
;
] 0,e : 2f x f 4x .
] 1 : 1
6f x 5f x
9
3 2( ) (ln ) 6 2lnP x a x x x a ,
, >0 .x P(x) 2-1 -1 :
A] 2a e .
] : (ln ) 1P x .
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:
10
f x ln x g x ln x ] f g .
] : f x g x
] : g xe f e
22008 2 2007
] :
22008 2g x 2007 1h x e f e
f x g x
11
2 2(1 ) .
] 2(1 ) , .
] : 0 4
] : 1 .
12
3 2( ) 14 3
( ) ( ) 2 3Q , .
() -1 3
Q() 2 .
] (2) 7 .
] =3 =11 .
] P() 3-2.
] ( ) 5 .
13
f 3x 2x xf (x) ln e e 6e ] f A ln 2, . ] x A :
x xf (x) x ln(e 2) ln(e 3)
] x A f
y x ln 2 2ln 2 3 .