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ﻧﻴﺎﺑﺔ ﻛﻠﻤﻴﻢ ﺑﺎﺏ ﺍﻟﺼﺤﺮﺍء ﺛﺎﻧﻮﻳﺔ ﺍﻟﺨﻮﺍﺭﺯﻣﻲ ﻓﺮﺽ ﻣﺤﺮﻭﺱ ﺭﻗﻢ2- 1ﺑﺎﻙ -1 ﺫ :ﺍﻟﺰﻏﺪﺍﻧﻲ ﺍﻟﺘﻤﺮﻳﻦ ﺍﻷﻭﻝ:
ﺃﺣﺴﺐ ﺍﻟﻨﻬﺎﻳﺎﺕ ﺍﻟﺘﺎﻟﻴﺔ:
1 x3 4 x
3
x x 1 x x 2 7 2
lim
x
,
lim
ﺍﻟﺘﻤﺮﻳﻦ ﺍﻟﺜﺎﻧﻲ: ﻧﻌﺘﺒﺮ ﺍﻟﻤﺘﺘﺎﻟﻴﺘﻴﻦ (Un) ﻭ) (Vnﺍﻟﻤﻌﺮﻓﺘﻴﻦ ﻛﻤﺎ ﻳﻠﻲ
U n 1 U n 32 V n V n 1 U n 3 V n 4
(1ﻧﻀﻊ n1 Vn Unﺑﺮﻫﻦ ﺃﻥ) ( nﻫﻨﺪﺳﻴﺔ ﻭﺣﺪﺩ ﺣﺪﻫﺎ ﺍﻷﻭﻝ ﻭ ﺃﺳﺎﺳﻬﺎ: (2ﺍﻋﻂ ﺻﻴﻐﺔ nﺑﺪﻻﻟﺔ nﺛﻢ ﺍﺳﺘﻨﺘﺞ ﺃﻧﻪn : Vn U n 0 (3ﺑﺮﻫﻦ ﺃﻥ ﺍﻟﻤﺘﺘﺎﻟﻴﺔ) (Unﺗﺰﺍﻳﺪﻳﺔ ﻭﺃﻥ (Vn) ﺗﻨﺎﻗﺼﻴﺔ.
(4ﺑﺮﻫﻦ ﺃﻧﻪn : U0 Un Vn V0 (5ﺃﺳﺘﻨﺘﺞ ﺃﻥ ﺍﻟﻤﺘﺘﺎﻟﻴﺘﺎﻥ (Un) ﻭ) (Vnﻣﺘﻘﺎﺭﺑﺘﺎﻥ.
(6ﺃﺳﺘﻨﺘﺞ ﺣﺴﺐ ﻣﺎ ﺳﺒﻖ ﺃﻥ l i m V n : n
n
- l i nm Uﻧﺮﻣﺰ ﻟﻬﺪﻩ ﺍﻟﻨﻬﺎﻳﺔ ﺏL
(7ﻧﻌﺘﺒﺮ ﺍﻟﻤﺘﺘﺎﻟﻴﺔ) (tnﺍﻟﻤﻌﺮﻓﺔ ﻛﻤﺎ ﻳﻠﻲ :
n : t n 3U n 8V n
ﺃ( ﺑﺮﻫﻦ ﺃﻧﻪ n : t n 1 t n ﺛﻢ ﺃﺳﺘﻨﺘﺞ ﺃﻧﻪ: ﺏ( ﺃﺳﺘﻨﺘﺞ ﻗﻴﻤﺔ L :
n : tn 99
ﺍﻟﺘﻤﺮﻳﻦ ﺍﻟﺜﺎﻟﺚ:
( f : x A rcT a n
ﻧﻌﺘﺒﺮ ﺍﻟﺪﺍﻟﺔ ﺍﻟﻌﺪﺩﻳﺔ2 x 3 )
(1ﺑﺮﻫﻦ ﺃﻥ ﻣﺠﻤﻮﻋﺔ ﺗﻌﺮﻳﻒ ﺍﻟﺪﺍﻟﺔ f ﻫﻲ fﺗﺰﺍﻳﺪﻳﺔ ﻗﻄﻌﺎ ﻋﻠﻰ D
3 D ; : 2
ﺛﻢ ﺃﺣﺴﺐlim f ( x )
(2ﺑﻴﻦ ﺃﻥ (3ﺑﻴﻦ ﺃﻥ f ﻣﺘﺼﻠﺔ ﻋﻠﻰ. D (4 ﺃ( ﺑﻴﻦ ﺃﻥ f ﺗﻘﺎﺑﻞ ﻣﻦ D ﻧﺤﻮ ﻣﺠﺎﻝ Jﻳﺠﺐ ﺗﺤﺪﻳﺪﻩ. .
ﺏ( ﺃﺣﺴﺐ f 1 ( y ) ﻟﻜﻞ yﻣﻦ. J
x
U01 V012