S-exp-ii Math Devoir S1 5
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ﻓﻮج B
ﻓﺮض ﻣﺤﺮوس رﻗﻢ 1
اﻟﺜﺎﻧﯿﺔ ﻣﻦ ﺳﻠﻚ اﻟﺒﻜﺎﻟﻮرﯾﺎ ﻋﻠﻮم ﺗﺠﺮﯾﺒﯿﺔ
اﻟﺘﻤﺮﯾﻦ اﻻول 6 ) :ﻧﻘﻂ ( ( 1أ ﺣﺴﺐ اﻟﻨﮭﺎ ﯾﺎ ت اﻟﺘﺎ ﻟﯿﺔ : 3
x 2 1 x ( 1) 1 x 2
x 3 8 x
lim
3
)A rc tan(x 1 x 1 x 2 1
lim
lim
x
(2ﺑﯿﻦ أ ن اﻟﻤﻌﺎ دﻟﺔ x 3 3x 3x 2 1 :ﺗﻘﺒﻞ ﺣﻼ وﺣﯿﺪا aﺑﺤﯿﺚ 0
ﻟﺘﻜﻦ fداﻟﺔ ﻋﺪدﯾﺔ ﻟﻠﻤﺘﻐﯿﺮ اﻟﺤﻘﯿﻘﻲ xاﻟﻤﻌﺮﻓﺔ ﺑﻤﺎ ﯾﻠﻲ f (x ) 3 x 2 2x : ) f (x (1ﺣﺪد ﻣﺠﻤﻮﻋﺔ ﺗﻌﺮﯾﻒ اﻟﺪاﻟﺔ fو ا ﺣﺴﺐ ) lim f (xو x 2 x (2ﻟﺘﻜﻦ gﻗﺼﻮر اﻟﺪ اﻟﺔ fﻋﻠﻰ اﻟﻤﺠﺎ ل I 2,
lim
x 2
أ ( ﺗﺤﻘﻖ أ ن x 2 2x (x 1)2 1 :ﺛﻢ ﺑﯿﻦ أ ن ﻟﻜﻞ xو yﻣﻦ : I ب( ﺑﯿﻦ أ ن gﺗﻘﺎ ﺑﻞ ﻣﻦ Iﻧﺤﻮ ﻣﺠﺎ ل Jﯾﺘﻢ ﺗﺤﺪﯾﺪه ﺛﻢ أ ﺣﺴﺐ )g 1 (2 ج ( ﺣﺪد ) g 1 (xﻟﻜﻞ xﻣﻦ J
) x y f (x ) f ( y
اﻟﺘﻤﺮﯾﻦ اﻟﺜﺎﻟﺚ 7 ) :ﻧﻘﻂ (
ﻧﻌﺘﺒﺮ اﻟﻤﺘﺘﺎ ﻟﯿﺔ اﻟﻌﺪدﯾﺔ ) ( Unاﻟﻤﻌﺮﻓﺔ ﺑﻤﺎ ﯾﻠﻲ :
n IN
1 U 0 2 U n 1 2U n 1 U n
(1أ ﺣﺴﺐ U1و U2 n IN (2ﺑﯿﻦ أ ن 0 U n 1 : (3أ درس رﺗﺎ ﺑﺔ اﻟﻤﺘﺘﺎ ﻟﯿﺔ )( Un 1 (4ﻧﻀﻊ : Un
V n 1
n IN
أ ( ﺑﯿﻦ أ ن ) (V nﻣﺘﺘﺎ ﻟﯿﺔ ھﻨﺪﺳﯿﺔ ﻣﺤﺪدا أ ﺳﺎ ﺳﮭﺎ وﺣﺪھﺎ اﻻول v0 2n ب ( ﺣﺪد Vnﺑﺪﻻﻟﺔ nواﺳﺘﻨﺘﺞ أ ن : 2n 1 (5ﻧﻀﻊ S n v 0 v 1 ... v n 1 :أ ﺣﺴﺐ Snﺑﺪﻻﻟﺔ n
Un
اﻻﺳﺘــــــﺄ ذ :ﻣﺤﻤــﺪ ھــﺮ ﺑــﻮز
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ﻓﻮج A
ﻓﺮض ﻣﺤﺮوس رﻗﻢ 1
اﻟﺜﺎﻧﯿﺔ ﻣﻦ ﺳﻠﻚ اﻟﺒﻜﺎﻟﻮرﯾﺎ ﻋﻠﻮم ﺗﺠﺮﯾﺒﯿﺔ
اﻟﺘﻤﺮﯾﻦ اﻻول 6 ) :ﻧﻘﻂ ( ( 1أ ﺣﺴﺐ اﻟﻨﮭﺎ ﯾﺎ ت اﻟﺘﺎ ﻟﯿﺔ : x 25 3 x 7 3
3
lim
lim x 3 8x 3 4x 1
x
x 2
x 2 1 ) x 2 3
(lim Arc tan
x
(2ﺑﯿﻦ أ ن اﻟﻤﻌﺎ دﻟﺔ x 3 2x x 2 :ﺗﻘﺒﻞ ﺣﻼ وﺣﯿﺪا aﺑﺤﯿﺚ -1
(2أ درس ﺗﻐﯿﺮات اﻟﺪاﻟﺔ f (3ﻟﺘﻜﻦ gﻗﺼﻮر اﻟﺪاﻟﺔ fﻋﻠﻰ اﻟﻤﺠﺎ ل I 2, أ ( ﺑﯿﻦ أ ن gﺗﻘﺎ ﺑﻞ ﻣﻦ Iﻧﺤﻮ ﻣﺠﺎ ل Jﯾﺘﻢ ﺗﺤﺪﯾﺪه ب ( ﺣﺪد ) g 1 (xﻟﻜﻞ xﻣﻦ J ج ( ﺣﻞ ﻓﻲ IRاﻟﻤﻌﺎ د ﻟﺔ g 1 (x ) g (x ) : اﻟﺘﻤﺮﯾﻦ اﻟﺜﺎﻟﺚ 7 ) :ﻧﻘﻂ ( 1 U 0 2 ﻧﻌﺘﺒﺮ اﻟﻤﺘﺘﺎ ﻟﯿﺔ اﻟﻌﺪدﯾﺔ ) ( Unاﻟﻤﻌﺮﻓﺔ ﺑﻤﺎ ﯾﻠﻲ : U n 1 2U n 1 n IN Un 2
(1أ ﺣﺴﺐ U1و U2 n IN (2ﺑﯿﻦ أ ن 0 U n 1 : (3أ درس رﺗﺎ ﺑﺔ اﻟﻤﺘﺘﺎ ﻟﯿﺔ )( Un U n 1 (4ﻧﻀﻊ : U n 1
Vn
n IN
أ ( ﺑﯿﻦ أ ن ) (V nﻣﺘﺘﺎ ﻟﯿﺔ ھﻨﺪﺳﯿﺔ ﻣﺤﺪا أ ﺳﺎ ﺳﮭﺎ وﺣﺪھﺎ اﻻول v0 3n 1 1 ب ( ﺣﺪد Vnﺑﺪﻻﻟﺔ nواﺳﺘﻨﺘﺞ أ ن : 3n 1 1 ( 5ﻧﻀﻊ S n v 0 v 1 ... v n 1 :أ ﺣﺴﺐ Snﺑﺪﻻﻟﺔ n
Un
اﻻﺳﺘــــــﺄ ذ :ﻣﺤﻤــﺪ ھــﺮ ﺑــﻮز
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ﻓﺮض ﻣﺤﺮوس رﻗﻢ 1
اﻟﺜﺎﻧﯿﺔ ﻣﻦ ﺳﻠﻚ اﻟﺒﻜﺎﻟﻮرﯾﺎ ﻋﻠﻮم ﺗﺠﺮﯾﺒﯿﺔ
اﻟﺘﻤﺮﯾﻦ اﻻول 6 ) :ﻧﻘﻂ ( ( 1أ ﺣﺴﺐ اﻟﻨﮭﺎ ﯾﺎ ت اﻟﺘﺎ ﻟﯿﺔ : 3
x 2 1 x ( 1) 1 x 2
x 3 8 x
lim
3
)A rc tan(x 1 x 1 x 2 1
lim
lim
x
(2ﺑﯿﻦ أ ن اﻟﻤﻌﺎ دﻟﺔ x 3 3x 3x 2 1 :ﺗﻘﺒﻞ ﺣﻼ وﺣﯿﺪا aﺑﺤﯿﺚ 0
ﻟﺘﻜﻦ fداﻟﺔ ﻋﺪدﯾﺔ ﻟﻠﻤﺘﻐﯿﺮ اﻟﺤﻘﯿﻘﻲ xاﻟﻤﻌﺮﻓﺔ ﺑﻤﺎ ﯾﻠﻲ f (x ) 3 x 2 2x : ) f (x (1ﺣﺪد ﻣﺠﻤﻮﻋﺔ ﺗﻌﺮﯾﻒ اﻟﺪاﻟﺔ fو ا ﺣﺴﺐ ) lim f (xو x 2 x (2ﻟﺘﻜﻦ gﻗﺼﻮر اﻟﺪ اﻟﺔ fﻋﻠﻰ اﻟﻤﺠﺎ ل I 2,
lim
x 2
أ ( ﺗﺤﻘﻖ أ ن x 2 2x (x 1)2 1 :ﺛﻢ ﺑﯿﻦ أ ن ﻟﻜﻞ xو yﻣﻦ : I ب( ﺑﯿﻦ أ ن gﺗﻘﺎ ﺑﻞ ﻣﻦ Iﻧﺤﻮ ﻣﺠﺎ ل Jﯾﺘﻢ ﺗﺤﺪﯾﺪه ﺛﻢ أ ﺣﺴﺐ )g 1 (2 ج ( ﺣﺪد ) g 1 (xﻟﻜﻞ xﻣﻦ J
) x y f (x ) f ( y
اﻟﺘﻤﺮﯾﻦ اﻟﺜﺎﻟﺚ 7 ) :ﻧﻘﻂ (
ﻧﻌﺘﺒﺮ اﻟﻤﺘﺘﺎ ﻟﯿﺔ اﻟﻌﺪدﯾﺔ ) ( Unاﻟﻤﻌﺮﻓﺔ ﺑﻤﺎ ﯾﻠﻲ :
n IN
1 U 0 2 U n 1 2U n 1 U n
(1أ ﺣﺴﺐ U1و U2 n IN (2ﺑﯿﻦ أ ن 0 U n 1 : (3أ درس رﺗﺎ ﺑﺔ اﻟﻤﺘﺘﺎ ﻟﯿﺔ )( Un 1 (4ﻧﻀﻊ : Un
V n 1
n IN
أ ( ﺑﯿﻦ أ ن ) (V nﻣﺘﺘﺎ ﻟﯿﺔ ھﻨﺪﺳﯿﺔ ﻣﺤﺪدا أ ﺳﺎ ﺳﮭﺎ وﺣﺪھﺎ اﻻول v0 2n ب ( ﺣﺪد Vnﺑﺪﻻﻟﺔ nواﺳﺘﻨﺘﺞ أ ن : 2n 1 (5ﻧﻀﻊ S n v 0 v 1 ... v n 1 :أ ﺣﺴﺐ Snﺑﺪﻻﻟﺔ n
Un
اﻻﺳﺘــــــﺄ ذ :ﻣﺤﻤــﺪ ھــﺮ ﺑــﻮز
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ﻓﻮج A
ﻓﺮض ﻣﺤﺮوس رﻗﻢ 1
اﻟﺜﺎﻧﯿﺔ ﻣﻦ ﺳﻠﻚ اﻟﺒﻜﺎﻟﻮرﯾﺎ ﻋﻠﻮم ﺗﺠﺮﯾﺒﯿﺔ
اﻟﺘﻤﺮﯾﻦ اﻻول 6 ) :ﻧﻘﻂ ( ( 1أ ﺣﺴﺐ اﻟﻨﮭﺎ ﯾﺎ ت اﻟﺘﺎ ﻟﯿﺔ : x 25 3 x 7 3
3
lim
lim x 3 8x 3 4x 1
x
x 2
x 2 1 ) x 2 3
(lim Arc tan
x
(2ﺑﯿﻦ أ ن اﻟﻤﻌﺎ دﻟﺔ x 3 2x x 2 :ﺗﻘﺒﻞ ﺣﻼ وﺣﯿﺪا aﺑﺤﯿﺚ -1
(2أ درس ﺗﻐﯿﺮات اﻟﺪاﻟﺔ f (3ﻟﺘﻜﻦ gﻗﺼﻮر اﻟﺪاﻟﺔ fﻋﻠﻰ اﻟﻤﺠﺎ ل I 2, أ ( ﺑﯿﻦ أ ن gﺗﻘﺎ ﺑﻞ ﻣﻦ Iﻧﺤﻮ ﻣﺠﺎ ل Jﯾﺘﻢ ﺗﺤﺪﯾﺪه ب ( ﺣﺪد ) g 1 (xﻟﻜﻞ xﻣﻦ J ج ( ﺣﻞ ﻓﻲ IRاﻟﻤﻌﺎ د ﻟﺔ g 1 (x ) g (x ) : اﻟﺘﻤﺮﯾﻦ اﻟﺜﺎﻟﺚ 7 ) :ﻧﻘﻂ ( 1 U 0 2 ﻧﻌﺘﺒﺮ اﻟﻤﺘﺘﺎ ﻟﯿﺔ اﻟﻌﺪدﯾﺔ ) ( Unاﻟﻤﻌﺮﻓﺔ ﺑﻤﺎ ﯾﻠﻲ : U n 1 2U n 1 n IN Un 2
(1أ ﺣﺴﺐ U1و U2 n IN (2ﺑﯿﻦ أ ن 0 U n 1 : (3أ درس رﺗﺎ ﺑﺔ اﻟﻤﺘﺘﺎ ﻟﯿﺔ )( Un U n 1 (4ﻧﻀﻊ : U n 1
Vn
n IN
أ ( ﺑﯿﻦ أ ن ) (V nﻣﺘﺘﺎ ﻟﯿﺔ ھﻨﺪﺳﯿﺔ ﻣﺤﺪا أ ﺳﺎ ﺳﮭﺎ وﺣﺪھﺎ اﻻول v0 3n 1 1 ب ( ﺣﺪد Vnﺑﺪﻻﻟﺔ nواﺳﺘﻨﺘﺞ أ ن : 3n 1 1 ( 5ﻧﻀﻊ S n v 0 v 1 ... v n 1 :أ ﺣﺴﺐ Snﺑﺪﻻﻟﺔ n
Un
اﻻﺳﺘــــــﺄ ذ :ﻣﺤﻤــﺪ ھــﺮ ﺑــﻮز
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