ﺔﺒﻌﺸﻟا
:
ﺔﻴﺿﺎﻳر مﻮﻠﻋ
ةﺪﻤﻟا
:
4
تﺎﻋﺎﺳ
ﺎﻳرﻮﻟﺎﻜﺒﻟا ةدﺎﻬﺵ ﻞﻴﻨﻟ ﺪﺣﻮﻤﻟا ﻲﻨﻃﻮﻟا نﺎﺤﺘﻡلاا
ﻮﻴﻥﻮﻳ ةرود
2003
ﺔﻴﺏﺮﻐﻤﻟا ﺔﻜﻠﻤﻤﻟا
ﺒﺸﻟا و ﺔﻴﻨﻃﻮﻟا ﺔﻴﺏﺮﺘﻟا ةرازو
بﺎ
ﻦﻳﺮﻤﺕ
1
ﻲﻓ ﺮﺒﺘﻌﻥ
2
*`
ﺔﻴﻟﺎﺘﻟا ﺔﻟدﺎﻌﻤﻟا
:
(
)
(
)
(
)
2
2
:
7
2
7
E
x x
y
x
+
=
+
ﻦﻜﻴﻟ
(
)
2
*
;x y ∈`
ﻦﻜﻴﻟو
δ
ﻦﻳدﺪﻌﻠﻟ ﺮﺒآلأا كﺮﺘﺸﻤﻟا ﻢﺳﺎﻘﻟا
x
و
y
.
ﻊﻀﻥ
x
a
δ
=
و
y
b
δ
=
1
-
نأ ضﺮﺘﻔﻨﻟ
(
)
;x y
ﺔﻟدﺎﻌﻤﻠﻟ ﻞﺣ
(
)
E
.
أ
(
نأ ﻖﻘﺤﺕ
:
(
)
(
)
2
2 2
7
2
a
a
b a b
δ
+
=
+
ب
(
ﻪﻥأ ﺞﺘﻨﺘﺳا
:
ﻲﻌﻴﺒﻃ ﺢﻴﺤﺻ دﺪﻋ ﺪﺟﻮﻳ
k
ﺚﻴﺣ
2 2
7
a
kb
δ
+ =
و
2
2a b ka
+ =
ت
(
نأ ﻦﻴﺏ
1
a =
.
ث
(
نأ ﺞﺘﻨﺘﺳا
(
)2
2
1
8
b
δ
+
=
+
2
-
ﻲﻓ ﻞﺣ
2
*`
ﺔﻟدﺎﻌﻤﻟا
(
)
E
.
ﺕ
ﻦﻳﺮﻤ
2
ﻢﻈﻨﻤﻡ ﺪﻡﺎﻌﺘﻡ ﻢﻠﻌﻡ ﻰﻟإ بﻮﺴﻨﻡ ىﻮﺘﺴﻤﻟا
(
)
; ;
O i j
G G
.
ﻰﻨﺤﻨﻤﻟا ﺮﺒﺘﻌﻥ
(
)
E
ﻪﺘﻟدﺎﻌﻡ يﺬﻟا
2
3 16
4
y
x
=
−
1
-
أ
(
نأ ﻦﻴﺏ
(
)
E
ﻩﺪﻳﺪﺤﺕ ﻢﺘﻳ ﺞﻴﻠها ﻦﻡ ءﺰﺟ
.
ب
(
ﻰﻨﺤﻨﻤﻟا ﻢﺳرأ
(
)
E
.
2
-
ﻦﻜﺘﻟ
(
)
4;0
A
و
(
)
0;3
B
ﻦﻴﺘﻄﻘﻥ
.
ﺔﻄﻘﻨﻟا ﺮﺒﺘﻌﻥ
1M
ﻦﻡ
(
)
E
ﺎﻬﻟﻮﺼﻓأ ﻲﺘﻟا
1x
ﺚﻴﺣ
[
]
1
0;4
x ∈
.
ﻊﻀﻥ
1
1
4cos
x
t
=
ﺚﻴﺣ
1
0
2
t
π
≤ ≤
.
ﻲﺕلآا ﻞﻡﺎﻜﺘﻟا ﺮﺒﺘﻌﻥ و
:
(
)
1
4
2
1
3
16
4 x
I x
x dx
=
−
∫
.
أ
(
ﻊﺿﻮﺏ ﻚﻟذ و ﺮﻴﻐﺘﻤﻟا ﺮﻴﻴﻐﺘﺏ ﺔﻠﻡﺎﻜﻡ لﺎﻤﻌﺘﺳﺎﺏ
4cos
x
t
=
ﺚﻴﺣ
0
2
t π
≤ ≤
نأ ﻦﻴﺏ ،
:
(
)
(
)
1
1
1
6
3sin 2
I x
t
t
=
−
03pts
0,50
0,50
0,50
0,75
0,75
3pts
0,50
0,50
1,25
ب
(
ﻦﻜﺘﻟ
(
)
1
S x
ﻦﻴﻤﻴﻘﺘﺴﻤﻟا ﻦﻴﺏ رﻮﺼﺤﻤﻟا ﺢﻄﺴﻟا ﺔﺣﺎﺴﻡ
(
)
OA
و
(
)
1
OM
ﻰﻨﺤﻨﻤﻟاو
(
)
E
.
ﻦﻜﺘﻟو
S
ﻦﻴﻤﻴﻘﺘﺴﻤﻟا ﻦﻴﺏ رﻮﺼﺤﻤﻟا ﺢﻄﺴﻟا ﺔﺣﺎﺴﻡ
(
)
OA
و
(
)
OB
ﻰﻨﺤﻨﻤﻟاو
(
)
E
.
•
ﺔﻄﻘﻨﻟا بﻮﺕرأ نأ ﻖﻘﺤﺕ
1M
ﻮه
1
3sin t
•
ﺐﺴﺣأ
(
)
1
S x
ﺔﻟلاﺪﺏ
1
t
.
•
ﺔﻤﻴﻗ ﺞﺘﻨﺘﺳا
S
.
3
-
*
نأ ﻦﻴﺏ
(
)
1
1
1
2
4
S x
S
t
π
= ⇔ =
.
*
ﻲﺘﻴﺛاﺪﺣإ دﺪﺣ
1M
ﻢﻠﻌﻨﻟا ﻲﻓ
(
)
;
;
O OA OB
JJJG JJJG
ﺔﻟﺎﺣ ﻲﻓ
1
4
t
π
=
.
ﻦﻳﺮﻤﺕ
3
I
-
ﻞﻜﻟ
(
)
;a b
ﻦﻡ
2\
ﺔﻓﻮﻔﺼﻤﻟا ﺮﺒﺘﻌﻥ ،
(
)
;a b
a b
b
M
b
a
+
−
=
ﻲﻓ
(
)
2M \
ﻦﻜﺘﻟ،
(
)
E
ﺔﻴﺕلاا تﺎﻓﻮﻔﺼﻤﻟا ﺔﻋﻮﻤﺠﻡ
:
(
)
(
) (
)
{
}
2
;
/
;
a b
E
M
a b
=
∈\
.