alnhaiat-oalatsal-tmarin-ghir-mhlola-4-4

ýa@ì@pbîbéåÜa
ßb—m
@ @
ﺱﺩﺎﺴﻟﺍ ﻦﻳﺮﻤﺘﻟﺍ
ﺔﻴﻟﺎﺘﻟا تﺎﻳﺎﻬﻨﻟا دﺪﺣ :
(
)
0
sin
limtan 4
π
→
x
x
x
،
2
3
lim cos
3 4
π
→+∞
+
+
x
x
x
(
)
2
lim sin
π
→− ∞
+ +
x
x x x
ﻊﺑﺎﺴﻟﺍ ﻦﻳﺮﻤﺘﻟﺍ
1 ( ﺔﻳدﺪﻌﻟا ﺔﻟاﺪﻟا ﺮﺒﺘﻌﻧ
f
ب ﺔﻓﺮﻌﻤﻟا :
( )
3
1
4 3
2
f x x x
= − −
ﺐﺴﺣأ
(
)
1
f
−
و
1
2
f
−
و
(
)
0
f
و
(
)
1
f
ﺔﻟدﺎﻌﻤﻟا نأ ﺞﺘﻨﺘﺳا ﻢﺛ
(
)
0
f x
=
لﻮﻠﺣ ﺔﺛﻼﺛ ﻞﺒﻘﺗ
2 ( ﺔﻟدﺎﻌﻤﻟا نأ ﻦﻴﺑ
3
1 0
x x
+ − =
ﺒﻘﺗ اﺪﻴﺣو ﻼﺣ ﻞ
α
ﻲﻓ
+
ℝ
ﺚﻴﺤﺑ:
1 3
2 4
α
< <
ﻦﻣﺎﺜﻟﺍ ﻦﻳﺮﻤﺘﻟﺍ
ﻦﻜﺘﻟ
f
ب ﺔﻓﺮﻌﻣ ﺔﻳدﺪﻋ ﺔﻟاد :
( )
2
3
2
x
f x
x
−
=
+
1- ﺔﻘﺘﺸﻤﻟا ﺔﻟاﺪﻟا ﺐﺴﺣأ
(
)
'
f x
ﺿ ﻢﺛ تاﺮﻴﻐﺗ لوﺪﺟ ﻊ
ﺔﻟاﺪﻟا
2- ﻦﻜﺘﻟ
g
لﺎﺠﻤﻟا ﻰﻠﻋ ﺔﻓﺮﻌﻤﻟا ﺔﻟاﺪﻟا
]
]
2, 1
− −
ﻲﻠﻳ ﺎﻤﺑ :
(
)
(
)
=
g x f x
أ - نأ ﻦﻴﺑ
g
ﺔﻴﺴﻜﻋ ﺔﻟاد ﻞﺒﻘﺗ
1
g
−
ﻰﻠﻋ ﺔﻓﺮﻌﻣ
لﺎﺠﻣ
I
هﺪﻳﺪﺤﺗ ﻢﺘﻳ
ب - ﺔﻴﺴﻜﻌﻟا ﺔﻟاﺪﻟا فﺮﻋ
1
g
−
ﻊﺳﺎﺘﻟﺍ ﻦﻳﺮﻤﺘﻟﺍ
ﺔﻟاﺪﻟا ﺮﺒﺘﻌﻧ
f
ﺚﻴﺤﺑ :
( )
2 1
x
f x
x
=
−
1- دﺪﺣ
f
D
تﺎﻳﺎﻬﻧ ﺐﺴﺣأ و
f
ﺎﻬﺗاﺪﺤﻣ ﺪﻨﻋ
2- ﻴﺑنأ ﻦ
( )
( )
2
1
'
2 1
x
f x
x
−
=− تاﺮﻴﻐﺘﻟا لوﺪﺟ ﻊﺿ ﻢﺛ
3- ﻦﻜﺘﻟ
g
لﺎﺠﻤﻟا ﻰﻠﻋ ﺔﻓﺮﻌﻤﻟا ﺔﻟاﺪﻟا
[
[
1,I
= +∞
ﻲﻠﻳ ﺎﻤﺑ :
( )
2 1
=
−
x
g x x
أ - نأ ﻦﻴﺑ
g
ﺔﻴﺴﻜﻋ ﺔﻟاد ﻞﺒﻘﺗ
1
g
−
لﺎﺠﻣ ﻰﻠﻋ ﺔﻓﺮﻌﻣ
J
هﺪﻳﺪﺤﺗ ﻢﺘﻳ
ب- ﺔﻴﺴﻜﻌﻟا ﺔﻟاﺪﻟا فﺮﻋ
1
g
−
ﻝﻭﻷﺍ ﻦﻳﺮﻤﺘﻟﺍ
ﻦﻜﺘﻟ
f
ﻲﻠﻳ ﺎﻤﺑ ﺔﻓﺮﻌﻤﻟا ﺔﻟاﺪﻟا :
(
)
( )
4
4 3
8
lim 4
4
→
=
−
= ≠
−
x
f
x x
f x x
x
ردأ لﺎﺼﺗا س
f
ﺔﻄﻘﻨﻟا ﻲﻓ
4
=
a
ﻲﻧﺎﺜﻟﺍ ﻦﻳﺮﻤﺘﻟﺍ
ﺔﻟاﺪﻟا ﺮﺒﺘﻌﻧ
f
ﺚﻴﺤﺑ :
( )
( )
( )
3
2
2
2
4 2
lim 2
2
1
232
2
2 8
→
−
= >
−
=
−
= <
+ −
x
x
f x x
x
f
x x
f x x
x x
أ (نأ ﻦﻴﺑ
f
رﺎﺴﻳ ﻰﻠﻋ ﺔﻠﺼﺘﻣ ﺔﻄﻘﻨﻟا
2
=
a
ب ( ﺔﻟاﺪﻟا ﻞﻫ
f
ﺔﻄﻘﻨﻟا ﻲﻓ ﺔﻠﺼﺘﻣ
2
=
a
ﺚﻟﺎﺜﻟﺍ ﻦﻳﺮﻤﺘﻟﺍ
ﺔﻟاﺪﻟا ﺮﺒﺘﻌﻧ
f
ﺚﻴﺤﺑ :
( )
( )
2
3 2
2
3
1
− +
= ≥ 2
+
+
= < 2
−
x x
f x x
x
ax
f x x
x
دﺪﻌﻟا دﺪﺣ
a
نﻮﻜﺗ ﻲﻛ
f
ﺔﻄﻘﻨﻟا ﻲﻓ ﺔﻠﺼﺘﻣ
2
α
=
ﻊﺑﺍﺮﻟﺍ ﻦﻳﺮﻤﺘﻟﺍ
ﺔﻟاﺪﻟا ﺮﺒﺘﻌﻧ
f
ﺚﻴﺤﺑ :
( )
( )
( )
2
2
1
1
1
1
+ +
= <1
+
=
−
= >1
−
x x b
f x x
x
f a
x x
f x x
x
1- ﺔﻳﺎﻬﻨﻟا ﺐﺴﺣأ
(
)
1
1
lim
→
>
x
x
f x
2- ﻦﻳدﺪﻌﻟا دﺪﺣ
,
b a
نﻮﻜﺗ ﻲﻛ
f
ﺔﻄﻘﻨﻟا ﻲﻓ ﺔﻠﺼﺘﻣ
1
α
=
ﺲﻣﺎﳋﺍ ﻦﻳﺮﻤﺘﻟﺍ
ﺔﻟاﺪﻟا لﺎﺼﺗا سردأ
f
ﻰﻠﻋ
D
ﺔﻴﻟﺎﺘﻟا تﻻﺎﺤﻟا ﻦﻣ ﻞﻛ ﻲﻓ
1 (
( )
2
2
2sin
4
−
=+
x x
f x
x
و
=
ℝ
D
2 (
( )
(
)
sin 2 = +
f x x
و
+
=
ℝ
D
3 (
( )
( )
2
3
1 sin = − f x x
x
و
]
[
, 1
= −∞ −
D