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ﺔﺒﻗﺮﻟا ﺪﻤﺤﻣ
ﺔﻴﺒﻳﺮﺠﺗ مﻮﻠﻋ يﻮﻧﺎﺛ ﻰﻟوﻷا 2007
/ 2008
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ﻦﻳﺮﻤﺗ 1 :
ﺔﻟاﺪﻟا قﺎﻘﺘﺷا ﺔﻴﻠﺑﺎﻗ سردأ f
0 ﻲﻓ ﺔﻴﻟﺎﺘﻟا تﻻﺎﺤﻟا ﻲﻓ x :
1 (
( )
3 2f x = x +x
0 0
x =
2
( )
2 1 ( f x = x− −x0
1 x = 2
3 (
( )
11 f x x
x
= − +
0 0
x =
( )
g
ﻦﻳﺮﻤﺗ 2 :
ﻦﻜﻴﻟ
( )
ﻤﻤﻟا ﻰﻨﺤﻨﻤﻟا ﺔﻟاﺪﻠﻟ ﻞﺜ
f م م ﻦﻣ
(
o i j, ,)
ﻰﻨﺤﻨﻤﻠﻟ سﺎﻤﻤﻟا ﺔﻟدﺎﻌﻣ دﺪﺣ
( )
0 ﻲﻓ ﺔﻴﻟﺎﺘﻟا تﻻﺎﺤﻟا ﻲﻓ x :
1
( )
3 2 2 ( f x =x − x0 0
x =
2
( )
3 2 2 ( f x =x − x0 1
x =
3
( )
cos 2 (f x = x
0 2
x =π
ﻦﻳﺮﻤﺗ 3 :
ﺔﻴﻟﺎﺘﻟا لاوﺪﻟا تاﺮﻴﻐﺗ سردأ :
1 (
( )
1 2f x = − +x x
2 (
( )
3 3 2f x =x − x
3
( )
33 ( 1 1 f x xx
= − +
4
( )
2 1 ( 1 f x xx
= − +
5 ( π x π
− ≺ ≺ ,
( )
tan 22 f x = ⎛ ⎞⎜ ⎟⎝ ⎠x +
ﻦﻳﺮﻤﺗ 3 :
ﺔﻟاﺪﻟا ﺮﺒﺘﻌﻧ f
ب ﺔﻓﺮﻌﻤﻟا :
( )
2 3 61
x x
f x x
− +
= −
1 ( اﺪﻟا ﻰﻨﺤﻨﻣ نأ ﻦﻴﺑ ﺔﻟ
ﺔﻟدﺎﻌﻤﻟا وذ ﻢﻴﻘﺘﺴﻤﻠﻟ ﻦﻴﻳزاﻮﻣ ﻦﻴﺳﺎﻤﻣ ﻞﺒﻘﻳf y=3x
2 ( ﻴﺳﺎﻤﻤﻟا ﻦﻳﺬه ﻲﺘﻟدﺎﻌﻣ ﺐﺘآأ ﻦ
.
ﻦﻳﺮﻤﺗ 5 :
ﺎﻬﻤﺠﺣ ءﺎﻄﻏ نوﺪﺑ ﻞﻜﺸﻟا ﺔﻴﻧاﻮﻄﺳا ﺐﻠﻋ ﻊﻨﺻ ﺪﻳ ﺮﻧ 1l
نﺪﻌﻤﻟا ﻦﻣ ﻦﻜﻤﻳ ﺎﻣ ﻞﻗأ لﺎﻤﻌﺘﺳﺎﺑ ﻚﻟذ و
ﺔﺒﻠﻌﻟا ﻩﺬه عﺎﻔﺗرا ﻮه ﺎﻣ ﻲﻜﻟ
نﻮﻜﺗ ب ﺔﻔﻠﻜﺗ ﻞﻗأ .
ﻦﻳﺮﻤﺗ 6 :
ﺣﺎﺴﻣ ﺎﻳﻮﻧد ﻪﻄﻴﺤﻣ نﻮﻜﻳ ﻲﻜﻟ ﻞﻴﻄﺘﺴﻤﻟا اﺬه يﺪﻌﺑ دﺪﺣ ﻲه ﻞﻴﻄﺘﺴﻣ ﺔ .
ﻦﻳﺮﻤﺗ 7 :
ﻪﺘﺣﺎﺴﻣ يﺬﻟا ﻞﻴﻄﺘﺴﻤﻟا ﻮهﺎﻣ ﻂﻴﺤﻤﻟا ﺲﻔﻧ ﺎﻬﻟ ﻲﺘﻟا تﻼﻴﻄﺘﺴﻤﻟا ﻦﻴﺑ ﻦﻣ ﺔﻳﻮﺼﻗ
) ﺔﻳﻮﻧد (
ﻦﻳﺮﻤﺗ 8 :
ﺔﻳدﺪﻌﻟا ﺔﻟاﺪﻟا ﺮﺒﺘﻌﻧ f
ﻲﻠﻳ ﺎﻤﺑ ﺔﻓﺮﻌﻤﻟا :
( )
2 3 24 2 2 12 4 2
x x x
f x x x
− + +
= − +
1 ( دﺪﺣ ﻮﻤﺠﻣD ﺔﻟاﺪﻟا ﻒﻳﺮﻌﺗ ﺔﻋ .f
تاﺪﺤﻣ ﺪﻨﻋ تﺎﻳﺎﻬﻨﻟا ﺐﺴﺣا ﻢﺛ Df
2 ( ﻦﻳدﺪﻌﻟا ﻲﺘﻤﻴﻗ ﺐﺴﺣأ a
و b ﺚﻴﺤﺑ
( )
2(
1)
2f x ax b x
= + −
f : x D
∀ ∈
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www.0et1.com ذﺎﺘــــﺳﻷا
ﺔﺒﻗﺮﻟا ﺪﻤﺤﻣ
ﺮﺠﺗ مﻮﻠﻋ يﻮﻧﺎﺛ ﻰﻟوﻷا ﺔﻴﺒﻳ
2007 / 2008
3 ( لاﺆﺴﻟا ﻦﻣ ﺞﺘﻨﺘﺳا )
2 ( نأ : ﻞﻜﻟ x
f ﻦﻣ D ,
( ) ( )
( )
3 3
1 1
'
1 f x x
x
− −
= −
تاﺮﻴﻐﺗ لوﺪﺟ ﻂﻋأ ﻢﺛ f
ﻦﻳﺮﻤﺗ 9 :
ﻦﻜﺘﻟ f ﻰﻠﻋ ﺔﻓﺮﻌﻤﻟا ﺔﻳدﺪﻌﻟا ﺔﻟاﺪﻟا ﻲﻠﻳ ﺎﻤﺑ
:
( ) ( )
2 sin 2 sin 4
; 0
0 0
x x
f x x
f
− α
⎧ = ≠
⎪⎨
⎪ =
⎩
1 ( نأ ﻦﻴﺑ
( )
sin2 : ' 4 sin 2 . xf x x
= x
; x *
∀ ∈
2 ( قﺎﻘﺘﺷا ﺔﻴﻠﺑﺎﻗ سردأ f
ﻲﻓ 0
ﻦﻳﺮﻤﺗ 10 :
ﺔﻳدﺪﻌﻟا ﺔﻟاﺪﻟا ﺮﺒﺘﻌﻧ f
ﻲﻠﻳ ﺎﻤﺑ ﺔﻓﺮﻌﻤﻟا
( )
4 2 : f x = −x −x1 ( ﻒﻳﺮﻌﺗ ﺰﻴﺣ دﺪﺣ
ﺔﻟاﺪﻟا :f D
2 ( ﺐﺴﺣأ
( )
0f
( )
2 و f −3 ( ﻲﻓ ﻞﺣ ﺔﻟدﺎﻌﻤﻟاD
:
( )
2 2f x = −
4 ( ﺔﻟاﺪﻠﻟ ﺔﻘﻠﻄﻤﻟا ﺎﻴﻧﺪﻟا ﺔﻤﻴﻘﻟا نأ ﻦﻴﺑ f
ﻰﻠﻋ ﻲهD
−2 2
ﻦﻳﺮﻤﺗ 11 :
1 ( ﺮﺸﻧأ
(
a+1)(
b+ −1)
4:ﺚﻴﺣ a و نﺎﻴﻘﻴﻘﺣ نادﺪﻋ b .
2 ( ﺮﺒﺘﻌﻧ f ﻲﻘﻴﻘﺤﻟا ﺮﻴﻐﺘﻤﻠﻟ ﺔﻳدﺪﻌﻟا ﺔﻟاﺪﻟا ﻲﻠﻳ ﺎﻤﺑ ﺔﻓﺮﻌﻤﻟا x
( )
2 3 : 1 f x xx
= + +
ﺔﻟاﺪﻟا ﺔﺑﺎﺗر سردأ ﺔﻴﻟﺎﺘﻟا تﻻﺎﺠﻤﻟا ﻦﻣ ﻞآ ﻰﻠﻋf
]
−∞, 3]
: ;]
− −3, 1[
;
] [
−1,1;
]
1,+∞[
ﺔﻟاﺪﻟا تاﺮﻴﻐﺘﻟا لوﺪﺟ ﻂﻋأ دﺪﺣ ﻢﺛ f
ﺎﻬﻔﻳرﺎﻄﻣ .
ﻦﻳﺮﻤﺗ 13 :
ﻦﻜﺘﻟ f ﻲﻠﻳ ﺎﻤﺑ ﻰﻠﻋ ﺔﻓﺮﻌﻤﻟا ﺔﻳدﺪﻌﻟا ﺔﻟاﺪﻟا
( )
2 : 2 f x xx
= − +
1 ( دﺪﺣ Df
ﺔﻟاﺪﻟا ﻒﻳﺮﻌﺗ ﺰﻴﺣ .f
2 ( أ - ﻦﻳدﺪﻌﻟا ﺐﺴﺣأ a
و ﻞﻜﻟ ﺚﻴﺤﺑ b x
f ﻦﻣ : D
( )
2f x a b
= + x +
ب - نأ ﻦﻴﺑ : ﻞﻜﻟ x
f ﻦﻣ D
( )
: 1 f x 1− ≤ ≺
3 ( نأ ﻦﻴﺑ f ﻰﻠﻋ ﺔﻳﺪﻳاﺰﺗ Df .