S-exp-ii Math Devoir S1 11
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ﻤﺩﺓ ﺍﻻﻨﺠﺎﺯ :ﺴﺎﻋﺘﺎﻥ ﺍﻝﺴﻨﺔ 05-06ﺍﻝﺩﻭﺭﺓ 1
ﺜﺎﻨﻭﻴﺔ ﻤﻴﺩﺍﻥ ﺍﻝﻔﺭﻭﺴﻴﺔ ﻓﺎﺱ ﺍﻝﺜﺎﻨﻴﺔ ﺒﺎﻙ ﻋﻠﻭﻡ ﺘﺞ 3 .2 .1 ﺍﻷﺴﺘﺎﺫ ﻤﺤﻤﺩ ﺸﺎﺸﻴل ----------------------------------------------------------------------------------)(20-01-2006 ﻓﺭﺽ ﻤﺤﺭﻭﺱ 3
x +1 ﻨﻌﺘﺒﺭ ﺍﻝﺩﺍﻝﺔ uﺍﻝﻤﻌﺭﻓﺔ ﺒـ : x −1
ﺍﻝﺘﻤﺭﻴﻥ ﺍﻷﻭل 3):ﻨﻘﻁ( 0.5
(1 (2
0.5 1
ﺤﺩﺩ D uﻤﺠﻤﻭﻋﺔ ﺘﻌﺭﻴﻑ ﺍﻝﺩﺍﻝﺔ u ' uا ا ا ا u أ -د ' ! D uا ا ا ' u #ـ -أD u ' ! x & u '( x ) $%
ج -أ $%ا ا ا ا hا ( #ـ :
1
= )u ( x
x +1 x −1
h( x) = Arctg
--------------------------------------------------------------------ا ا . - (,- 17 ) :ا ا ا د fا ( . IR / #ـ: 0.5 1
(1 (2
1 1
f ( x) = x 2 − x 3 2 f ( x) = x + 2 x − 2
x<2 x≥2
8#أن ا ا . 2 6( 9 ! f أ – أ $%ا lim f ( x) 8 5;1 ∞x →+
1
(4
) (C
4 − 3x أ 8# -أن 2 2− x )2( x + 1
#ـ 8# -أن
0,5
.
#ـ – د ا ?وع ا =/121 8<5;- أ – أدرس ا 5 Bق / fا x0 = 2 6( 88و ا F Gو= ه58D1 #ـ – أدرس ا 5 Bق / fا 5%8ر ( x0 = 2 6و ا F Gو= ه. 58D1 ' fا ا ا ا IR − {2} / f
2
3. 3 x 2 + 2 x
= )f '( x
#ار ∞ +و ∞ −
[∀x ∈ ]−∞, 2
.
[∞∀x ∈ ]2, +
.
= )f '( x
1
و
f
1,5
(5 (6
ﻀﻊ ﺠﺩﻭل ﺘﻐﻴﺭﺍﺕ . f ﺤﺩﺩ ﻨﻘﻁ ﺘﻘﺎﻁﻊ ) 2! L! ( C fر ا. &8J5(K
2
(7
أ6-ء ا /121
(8
9O g 8ر / fا 5ل [∞[ 2, + أ 8# -أن 5 ! 2- [ 2, +∞[ ! gل Q2 $ J
1
0,5 1 1
ج -أ$%
f
g −1
)3
3
' −1
. -ا ( un )n≥0 8 5ا ( 6 5#
0,5 1
1 #ـ 8# -أن < un ≤ 1 4
1,5
!g −1 /121
.
( g ) (2
أ -أ$%
1
.
) (C
-أ6-ء ( R?- 6ا (C ) 3
#ـ
(9
. xlim )f ( x ∞→−
f
(3
) (C
!341! !5 ! 3 ! 6( f /121
) ( O, i , j
1 4
= u0
و
un +1 = un . 2 − un
& IN ! n
u1
∀n ∈ IN
.
ج -أدرس ر #5ا . ( un )n≥0 8 5 د -ا T 1 Dأن ا 5 ! ( un )n≥0 8 5ر #وا$%
lim un
∞n →+
-------------------------------------------------------------ﺤﻅ ﺴﻌﻴﺩﺴﻴﺅﺨﺫ ﺒﻌﻴﻥ ﺍﻹﻋﺘﺒﺎﺭ ﺍﻝﺩﻗﺔ ﻭ ﺍﻝﻌﻨﺎﻴﺔ ﺃﺜﻨﺎﺀ ﺍﻝﺘﺤﺭﻴﺭ . http://arabmaths.ift.fr
ﺜﺎﻨﻭﻴﺔ ﻤﻴﺩﺍﻥ ﺍﻝﻔﺭﻭﺴﻴﺔ ﻓﺎﺱ ﺍﻝﺜﺎﻨﻴﺔ ﺒﺎﻙ ﻋﻠﻭﻡ ﺘﺞ 3 .2 .1 ﺍﻷﺴﺘﺎﺫ ﻤﺤﻤﺩ ﺸﺎﺸﻴل ----------------------------------------------------------------------------------)(20-01-2006 ﻓﺭﺽ ﻤﺤﺭﻭﺱ 3
x +1 ﻨﻌﺘﺒﺭ ﺍﻝﺩﺍﻝﺔ uﺍﻝﻤﻌﺭﻓﺔ ﺒـ : x −1
ﺍﻝﺘﻤﺭﻴﻥ ﺍﻷﻭل 3):ﻨﻘﻁ( 0.5
(1 (2
0.5 1
ﺤﺩﺩ D uﻤﺠﻤﻭﻋﺔ ﺘﻌﺭﻴﻑ ﺍﻝﺩﺍﻝﺔ u ' uا ا ا ا u أ -د ' ! D uا ا ا ' u #ـ -أD u ' ! x & u '( x ) $%
ج -أ $%ا ا ا ا hا ( #ـ :
1
= )u ( x
x +1 x −1
h( x) = Arctg
--------------------------------------------------------------------ا ا . - (,- 17 ) :ا ا ا د fا ( . IR / #ـ: 0.5 1
(1 (2
1 1
f ( x) = x 2 − x 3 2 f ( x) = x + 2 x − 2
x<2 x≥2
8#أن ا ا . 2 6( 9 ! f أ – أ $%ا lim f ( x) 8 5;1 ∞x →+
1
(4
) (C
4 − 3x أ 8# -أن 2 2− x )2( x + 1
#ـ 8# -أن
0,5
.
#ـ – د ا ?وع ا =/121 8<5;- أ – أدرس ا 5 Bق / fا x0 = 2 6( 88و ا F Gو= ه58D1 #ـ – أدرس ا 5 Bق / fا 5%8ر ( x0 = 2 6و ا F Gو= ه. 58D1 ' fا ا ا ا IR − {2} / f
2
3. 3 x 2 + 2 x
= )f '( x
#ار ∞ +و ∞ −
[∀x ∈ ]−∞, 2
.
[∞∀x ∈ ]2, +
.
= )f '( x
1
و
f
1,5
(5 (6
ﻀﻊ ﺠﺩﻭل ﺘﻐﻴﺭﺍﺕ . f ﺤﺩﺩ ﻨﻘﻁ ﺘﻘﺎﻁﻊ ) 2! L! ( C fر ا. &8J5(K
2
(7
أ6-ء ا /121
(8
9O g 8ر / fا 5ل [∞[ 2, + أ 8# -أن 5 ! 2- [ 2, +∞[ ! gل Q2 $ J
1
0,5 1 1
ج -أ$%
f
g −1
)3
3
' −1
. -ا ( un )n≥0 8 5ا ( 6 5#
0,5 1
1 #ـ 8# -أن < un ≤ 1 4
1,5
!g −1 /121
.
( g ) (2
أ -أ$%
1
.
) (C
-أ6-ء ( R?- 6ا (C ) 3
#ـ
(9
. xlim )f ( x ∞→−
f
(3
) (C
!341! !5 ! 3 ! 6( f /121
) ( O, i , j
1 4
= u0
و
un +1 = un . 2 − un
& IN ! n
u1
∀n ∈ IN
.
ج -أدرس ر #5ا . ( un )n≥0 8 5 د -ا T 1 Dأن ا 5 ! ( un )n≥0 8 5ر #وا$%
lim un
∞n →+
-------------------------------------------------------------ﺤﻅ ﺴﻌﻴﺩﺴﻴﺅﺨﺫ ﺒﻌﻴﻥ ﺍﻹﻋﺘﺒﺎﺭ ﺍﻝﺩﻗﺔ ﻭ ﺍﻝﻌﻨﺎﻴﺔ ﺃﺜﻨﺎﺀ ﺍﻝﺘﺤﺭﻴﺭ . http://arabmaths.ift.fr
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