اﻟﺪوال اﻷﺻﻠﻴﺔ درس ﺗﻤﺎرﻳﻦ ﻓﻲ ( ) ( )2 ( )2

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‫ﺙ
"ی ا ون اه‬
‫ﺍﳌﺎﺩﺓ‪ :‬ﺍﻟﺮﻳﺎﺿﻴﺎﺕ‬
‫( ' ﻡ&‪$%‬‬
‫ ‬
‫ﺳﻠﺴﻠﺔ ﺭﻗﻢ‪5/‬‬
‫א‪
:‬‬
‫ﻡ*"ى ا*' ا
ك ‪ (,-‬ا‪",‬م ا‪$‬ی(‬
‫• ﻡ*‪" 2‬م اة و ارض‬
‫• ﻡ*‪ 2‬ا‪",‬م ا‪4‬ی‪3‬‬
‫• ﻡ*‪ 2‬ا‪",‬م ا‪4‬را‬
‫ﺕ‪$‬ی‪ 1‬اا ‪ f‬ا [∞‪ [ 0; +‬آ‪:‬‬
‫‪ .1‬د ادی‪ +‬ا"‪+,,‬‬
‫‪b‬‬
‫‪∀x ∈ [ 0; +∞[ f ( x ) = a +‬‬
‫‪2‬‬
‫)‪( x + 1‬‬
‫‪.1‬‬
‫د ﻡ اوال ا ا ‪[ 0; +∞[ f‬‬
‫‪.2‬‬
‫د اا ا ‪ F‬ا ‪ f‬ﺏ"! ‪F (1) = 3‬‬
‫ﺕ‪$‬ی‪ 2‬اا ‪ f‬ا ] ‪ [ 0; π‬آ ‪:‬‬
‫‪f ( x ) = x cos x − sin x‬‬
‫أ‪f ′ ( x ) $%‬‬
‫‪.1‬‬
‫‪5‬‬
‫‪ .2‬د اا ا ‪ F‬ا ‪ f‬ﺏ"!‬
‫‪2‬‬
‫‪1‬‬
‫‪x‬‬
‫‪f ( x ) = 2 x2 + x + 1 +‬‬
‫اﺱ(' ﻡ اوال ا ‪ G‬ا ‪g‬‬
‫‪.2‬‬
‫ا آ ‪g ( x ) = x sin x − cos x :‬‬
‫‪ π‬‬
‫ﺕ‪$‬ی‪ 3‬اا‪ f +‬و ‪ g‬ا‪  0;  +‬آ ‪:‬‬
‫‪ 2‬‬
‫‪x‬‬
‫‪g ( x ) = cos 2‬‬
‫‪ f ( x ) = tan 2 x‬و‬
‫‪2‬‬
‫د ﻡ اوال ا ا‪ f +‬و ‪g‬‬
‫ﺕ‪$‬ی‪ 4‬د ﻡ اوال ا وال ا ‪:‬‬
‫‪x‬‬
‫= )‪f ( x‬‬
‫‪f ( x ) = 5 x 4 + 3x + 1‬‬
‫‪2‬‬
‫‪2‬‬
‫)‪( x − 1‬‬
‫‪x‬‬
‫‪2‬‬
‫‪x +1‬‬
‫‪3‬‬
‫‪x2‬‬
‫= )‪f ( x‬‬
‫‪3‬‬
‫‪8+ x‬‬
‫)‪f ( x ) = ( 2 x − 1‬‬
‫‪f ( x ) = x x2 + 1‬‬
‫)‪f ( x ) = sin ( 4 x − 1‬‬
‫
‬
‫[∞‪ [ 0; +‬آ ‪:‬‬
‫‪2‬‬
‫)‪( x + 1‬‬
‫اذ ‪
:‬‬
‫اا‬
‫ا‬
‫‪f‬‬
‫‬
‫[∞‪ [1; +‬آ‬
‫‪f ( x) = x x −1‬‬
‫‪.1‬ﺏ‪ +‬أن ‪+ x − 1 :‬‬
‫‪3‬‬
‫)‪( x − 1‬‬
‫= )‪f ( x‬‬
‫[∞‪∀x ∈ [1; +‬‬
‫ﺕ‪$‬ی‪ 7‬اا ‪ f‬ا » آ‪:‬‬
‫‪2‬‬
‫‪4‬‬
‫‪5 x + 40 x + 20 x + 80‬‬
‫‪2‬‬
‫)‪+ 4‬‬
‫‪2‬‬
‫‪(x‬‬
‫= )‪f ( x‬‬
‫‪ .1‬د ااد ا"‪ a ,,‬و ‪ b‬و ‪c‬‬
‫‪ax + b‬‬
‫= ) ‪∀x ∈ [ 0; +∞[ f ( x‬‬
‫ﺏ"! ‪+ c :‬‬
‫‪2‬‬
‫‪2‬‬
‫‪x‬‬
‫‪+‬‬
‫‪4‬‬
‫(‬
‫)‬
‫‪ .2‬د اا ا ‪ F‬ا ‪ f‬ﺏ"! ‪F ( 0 ) = c‬‬
‫‪2‬‬
‫‪f ( x ) = ( sin x ) cos x‬‬
‫ﺕ‪$‬ی‪ 5‬اا ‪ f‬ا ‬
‫‪x2 + 2 x‬‬
‫= )‪F (1‬‬
‫ﺕ‪$‬ی‪6‬‬
‫= )‪f ( x‬‬
‫‪f ( x ) = 3x + 1‬‬
‫) ‪f ( x ) = cos ( 2 x + 8‬‬
‫‪a‬‬
‫‪ .2‬د اا ا ‪ F‬ا ‪ f‬ﺏ"! ‪F ( 2 ) = 1‬‬
‫د اا ا ‪ G‬ا ‪ g‬ﺏ"! ‪G (π ) = 0‬‬
‫‪.3‬‬
‫و‬
‫‪b‬‬
‫ﺏ"!‪: :‬‬
‫= )‪f ( x‬‬
‫ ‪ 1‬ﻡ ‪1‬‬
‫‪:‬‬
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