ﺔﻴﻨﻁﻭﻟﺍ ﺔﻴﺒﺭﺘﻟﺍ ﺓﺭﺍﺯﻭ
ﺩﻌﺒ ﻥﻋ ﻥﻴﻭﻜﺘﻟﺍﻭ ﻡﻴﻠﻌﺘﻠﻟ ﻲﻨﻁﻭﻟﺍ ﻥﺍﻭﻴﺩﻟﺍ
ﻟﺍ لﺤ ةدﺎﻤﻟا 2
: تﺎﻴﺿﺎﻳﺮﻟا
ﻯﻭﺘﺴﻤﻟﺍ :
ﻱﻭﻨﺎﺜ 3 ﺔﺒﻌﺸﻟا
ﻉ : . ﺩ
لﻭﻷﺍ ﻥﻴﺭﻤﺘﻟﺍ :
) ﻁﻘﻨ 04 ( .
/1 ﻲﻓ لﺤ ﺔﻟﺩﺎﻌﻤﻟﺍ م
: ﺹ –2
) 3 +1 ﺕ ( ﺹ + ﺕ 4
= 0
=∆ ﺕ2
………
)...
ﻥ0,5 (
ﺹ
0
= + 1 ﺕ
………
....
………
)...
ﻥ0,75 (
ﺹ = 1
+ 2 ﺕ 2 )...
ﻥ0,75 (
-2 ) ا ﺕ ( ﺏ ، ) + 1 ﺕ ( ، ) ج + 2 ﺕ 2 ( .
لﻭﺤﻴ ﻱﺫﻟﺍ ﺭﺸﺎﺒﻤﻟﺍ ﻪﺒﺎﺸﺘﻟﺍ ﺎﺘ ﻥﻜﻴﻟ ﻰﻟﺇ ﺏ لﻭﺤﻴﻭ ﺏ ﻰﻟﺇ ا
ج
ًﺹ لﻜﺸﻟﺍ ﻥﻤ ﻪﺘﺭﺎﺒﻋ =
ﺹ α + β
ﺎﻨﻴﺩﻟ
:
=
⇔ = +
= +
+
+
= +
ﺎﺘ (ﺏ)
ﺎﺘ ) ( ﺏ 2
2 ﺕ 1)α
(ﺕ β
1 ﺕ (ﺕ)α
β
ج )... ا
ﻥ0,5 (
ﺩﺠﻨﻭ = α
+ 1 ، ﺕ = β ... 2 )...
ﻥ1 (
ﻱﻭﺎﺴﺘ ﻪﺒﺎﺸﺘﻟﺍ ﺔﺒﺴﻨ ﻥﺫﺇ 2ق
ﻪﺘﻴﻭﺍﺯﻭ 4
ﻩﺯﻜﺭﻤﻭ π ) ω
، 0 ( 2 )...
ﻥ0,5 (
ﻲﻨﺎﺜﻟﺍ ﻥﻴﺭﻤﺘﻟﺍ :
) ﻁﻘﻨ 04 ( .
ﺎﻨﻴﺩﻟ :
≥
〉
≥
〉
= + +
= + +
0 0،5
5
7 49
1 5 25
α β
β α
α β
ن ن ...
)...
ﻥ1 (
ﻰﻠﻋ لﺼﺤﻨﻭ
≥
〉
≥
〉
−
=
0 0،5 α
5 β
β12 24 α
)...
ﻥ1 (
ﺩﺠﻨ ﻪﻨﻤﻭ :
0 α βﻭ
2= =
)...
ﻥ1,5 (
ﻥﻭﻜﻴﻭ :
= ن )...51 ﻥ0,5
(
لﺤ ﺔﻟﺄﺴﻤﻟﺍ : ) ﺔﻁﻘﻨ 12 (.
/ I ﺎﻫ ) ﺱ = ( ﺱ + 2
– 2 ﺱﻭﻟ 2 .
(1 ﺔﺴﺍﺭﺩ ﺔﻟﺍﺩﻟﺍ ﺕﺍﺭﻴﻐﺘ ﻫ
ﺎ .
ﻑﻴﺭﻌﺘﻟﺍ ﺔﻋﻭﻤﺠﻤ :
ﻑ
= [
،0 + ] ∞ ...
)....
ﻥ0,5 (
ﺕﺎﻴﺎﻬﻨﻟﺍ
ﺱ :
0 ﺎـﻬﻨ ﺎـﻫ
(ﺱ) ←
=
∞+ π
)...
ﻥ0,5 (
/1 4
ﺔﻴﻨﻁﻭﻟﺍ ﺔﻴﺒﺭﺘﻟﺍ ﺓﺭﺍﺯﻭ
ﺩﻌﺒ ﻥﻋ ﻥﻴﻭﻜﺘﻟﺍﻭ ﻡﻴﻠﻌﺘﻠﻟ ﻲﻨﻁﻭﻟﺍ ﻥﺍﻭﻴﺩﻟﺍ
ﻟﺍ لﺤ ةدﺎﻤﻟا 2
: تﺎﻴﺿﺎﻳﺮﻟا
ﻯﻭﺘﺴﻤﻟﺍ :
ﻱﻭﻨﺎﺜ 3 ﺔﺒﻌﺸﻟا
ﻉ : . ﺩ
ﺱ ﺱ (ﺱ)ﺎﺘ ﺎـﻬﻨ ﺎـﻬﻨ
ﺱ ﺱ2 ﺱ
ﺱ 2 ﺱﻭﻟ
←
∞+
←
∞+ = +
−
= +
∞
)...
ﻥ0,5 (
ﻕﺘﺸﻤﻟﺍ
]
∞+[
∋ ∀ :− =
ﺱ
،0 :
ﹶﺎﻫ ﺱﺱ)2 (ﺱ)
(1 2 )...
ﻥ0,5 (
ﺼﻗﺎﻨﺘﻤ ﺎﻫ ﺔﻟﺍﺩﻟﺍ لﺎﺠﻤﻟﺍ ﻰﻠﻋ ﺔ
[ [
1،0لﺎﺠﻤﻟﺍ ﻰﻠﻋ ﺓﺩﻴﺍﺯﺘﻤﻭ
]
∞+،1]
)...
ﻥ0,5 (
ﺕﺍﺭﻴﻐﺘﻟﺍ لﻭﺩﺠ :
)...
ﻥ0,5 (
0 ﺱ
1
ﺎﻫ
َ) ﺱ ( -
0 +
ﺎﻫ ) ﺱ (
+ ∞
3
ﺎﻫ ) = (1 3
(2 ﺎﻫ ﺓﺭﺎﺸﺇ )
ﺱ ( : ﺱ ∀
[ ∋
،0 + : ] ∞ ﺎﻫ ) ﺱ (
〈
…………0
...
………
)...
ﻥ0,5 (
/ II ﺎﺘ ) ﺱ ﺱ = ( ﺱ 2
ﺱﻭﻟ +
( 1 ﺔﺴﺍﺭﺩ ﺔﻟﺍﺩﻟﺍ ﺕﺍﺭﻴﻐﺘ ﺘ
ﺎ .
ﻑﻴﺭﻌﺘﻟﺍ ﺔﻋﻭﻤﺠﻤ :
ﻑ = [
،0 + ] ∞ )...
ﻥ0,5 (
ﺕﺎﻴﺎﻬﻨﻟﺍ
ﺱ : ﺎـﻬﻨ ﺎﺘ
ﺱ ←
=
∞− ( ) 0 π
……
..
………
)...
ﻥ0,5 (
ﺎـﻬﻨﺱ
ﺎﺘ
ﺱ ∞+←
=
∞+ ( ) ...
)...
ﻥ0,5 (
ﻕﺘﺸﻤﻟﺍ
]
∞+[
∋ ∀ :=(ﺱ )ﹶﺎﺘ : ،0 ﺱ ﺱ
ﺎـﻫ (ﺱ)2
)...
ﻥ0,5 (
ﹶﺎﺘ ﺓﺭﺎﺸﺇ )
ﺱ ( ﺎﻫ ﺓﺭﺎﺸﺇ ﻲﻫ )
ﺱ (.
ﺱ∀ [ ∋
،0 + : ] ∞ ﹶﺎﺘ ) ﺱ (
〈 ... 0
....
)...
ﻥ0,5 (
/2 4
ﺔﻴﻨﻁﻭﻟﺍ ﺔﻴﺒﺭﺘﻟﺍ ﺓﺭﺍﺯﻭ
ﺩﻌﺒ ﻥﻋ ﻥﻴﻭﻜﺘﻟﺍﻭ ﻡﻴﻠﻌﺘﻠﻟ ﻲﻨﻁﻭﻟﺍ ﻥﺍﻭﻴﺩﻟﺍ
ﻟﺍ لﺤ ةدﺎﻤﻟا 2
: تﺎﻴﺿﺎﻳﺮﻟا
ﻯﻭﺘﺴﻤﻟﺍ :
ﻱﻭﻨﺎﺜ 3 ﺔﺒﻌﺸﻟا
ﻉ : . ﺩ
لﻭﺩﺠ ﺕﺍﺭﻴﻐﺘﻟﺍ :
...
. )...
ﻥ0,5 (
ﺱ 0
+
∞
ﹶﺎﺘ ) ﺱ ( +
ﺎﺘ ) ﺱ (
- ∞
(2 ﻰﻨﺤﻨﻤﻠﻟ ﺔﺒﺭﺎﻘﻤﻟﺍ ﺕﺎﻤﻴﻘﺘﺴﻤﻟﺍ )
ﻱ .(
...
)...
ﻥ0,5 (
ﺱ = ﺏﺭﺎﻘﻤ ﻡﻴﻘﺘﺴﻤ ﺔﻟﺩﺎﻌﻤ 0
) (∆ : ﻉ = لﺌﺎﻤ ﺏﺭﺎﻘﻤ ﻡﻴﻘﺘﺴﻤ ﺔﻟﺩﺎﻌﻤ ﺱ
(3 ﻰﻨﺤﻨﻤﻟﺍ ﺔﻴﻌﻀﻭ )
ﻱ ( ﺎﻘﻤﻟﺍ ﻡﻴﻘﺘﺴﻤﻠﻟ ﺔﺒﺴﻨﻟﺎﺒ لﺌﺎﻤﻟﺍ ﺏﺭ
) .(∆ ...
)...
ﻥ1 (
ﺎﺘ ) ﺱ ( – ﺱ 2 = ﺱﻭﻟﺱ
0 ﺱ 1
+ ∞
ﺎﺘ ) ﺱ ( -
ﺱ
- + 0
ﺔﺸﻗﺎﻨﻤﻟﺍ )
ﻱ ( ﺕﺤﺘ ) (∆ )
ﻱ ( ﻕﻭﻓ ) (∆
(4 ﻟﺍ لﺎﺠﻤﻟﺍ ﻰﻠﻋ ﺓﺭﻤﺘﺴﻤ ﺎﺘ ﺔﻟﺍﺩ 2]
،1 [ 1 ﺘ ﻭﺃ 2 ﺎ) (1
× ﺎﺘ ) (1
〉 0
ﻥﺃ ﺞﺘﻨﺘﺴﻨ )
ﻱ ( ﻊﻁﻘﻴ )
َﺱ ﺱ ( ﺎﻬﺘﻠﺼﺎﻓ ﺔﻁﻘﻨ ﻲﻓ ﺱ
ﻕﻘﺤﺘ 0
2: 〉1 ﺱ
〉 0
.1 ...
)...
ﻥ1 (
(5 ﻡﺴﺭ ) ﻱ ... ( ...
)...
ﻥ1,5 (
/3 4
ﺔﻴﻨﻁﻭﻟﺍ ﺔﻴﺒﺭﺘﻟﺍ ﺓﺭﺍﺯﻭ
ﺩﻌﺒ ﻥﻋ ﻥﻴﻭﻜﺘﻟﺍﻭ ﻡﻴﻠﻌﺘﻠﻟ ﻲﻨﻁﻭﻟﺍ ﻥﺍﻭﻴﺩﻟﺍ
ﻟﺍ لﺤ ةدﺎﻤﻟا 2
: تﺎﻴﺿﺎﻳﺮﻟا
ﻯﻭﺘﺴﻤﻟﺍ :
ﻱﻭﻨﺎﺜ 3 ﺔﺒﻌﺸﻟا
ﻉ : . ﺩ
(6 ﻤ ﻡ ﻥﻜﺘﻟ ـﺒ ﺩﺩﺤﻤﻟﺍ ﻱﻭﺘﺴﻤﻟﺍ ﺯﻴﺤﻟﺍ ﺔﺤﺎﺴ
) ﻯ ( ﻡﻴﻘﺘﺴﻤﻟﺍﻭ )
(∆ ﻭ ﻥﻴﻤﻴﻘﺘﺴﻤﻟﺍ ﺱ ﺎﻤﻬﺘﻟﺩﺎﻌﻤ ﻥﻴﺫﻟﺍ
= ﺱ ،1
= . ﻩ
ﻡ ﺎﺘ]
(ﺱ) [ﺱ
ﺱﺎﻔﺘ − 1ﻩ∫ =
1 ﻡ ﺱ 2
ﺱﺎﻔﺘ ﺱﻭﻟ ﻩ∫ =
=
(ﺱﻭﻟ)]
1[2 ﻩ
= ﻡﺴ 1 2
...
)...
ﻥ1,5 (
/4 4
