Math Devoir 12

pbïšbî‹€€€€€€€€€€€€€€€€€ÜaZò†b€€€€€€€€€€€€€€€€€€€€€€€€€€€¾a p@Ë@l@‘2@ó€åÜaZõín€€€€€€€€€€€€€€€€€€€€€€¾a

ò‹Ñïå‚@óibïä

‘ì‹«@‹Ð

ðäbîÜa@âŽbÕÜa@ðic@óîíäbq

2HZŒb−fia@ò‡€€€€€€€€€€€€€€€€€€à

.3

x + 2 + 3 1 − x = 3 3 ، Arc tan2 ( x ) −

π 4

Zßìÿa@æî‹ánÜa

Arc tan ( x ) = 0 :‫ ﺍﻝﻤﻌﺎﺩﻝﺘﻴﻥ ﺍﻝﺘﺎﻝﻴﺘﻴﻥ‬ℝ ‫ ﺤل ﻓﻲ‬-1

 π 2  4  ‫ ﺘﻘﺒل ﻋﻠﻰ ﺍﻷﻗل ﺤﻼ ﻓﻲ ﺍﻝﻤﺠﺎل‬tan ( x ) + 2 sin ( x ) − 1 = 0 ‫ ﺒﻴﻥ ﺃﻥ ﺍﻝﻤﻌﺎﺩﻝﺔ‬-2

. 0,

ZðäbrÜa@æî‹ánÜa 3

lim

x →+∞

 x3 +1 x2 + x − 3 x3 +1 x +1 ، lim ، lim Arc tan  3  :‫أ ا ت ا‬ x →1 3 x x 2 −1 x →+∞ x +4 x −3 +

. lim

x →3 3

.f

x2 −1 −2

ZsÜbrÜa@æî‹ánÜa

( x ) = x 3 − 6 x 2 + 12 x

− 8 :  ‫ ا‬f ‫ اا اد‬ .+(& ,  J ‫*ل‬# '( ℝ "# $%& f ‫ " أن‬-1 . ( x − 2 ) -‫ أ‬:‫ أ‬-2 3

. J "#

x $1 f

−1

(x )

/ 0‫ا‬:‫ب‬

@ZÊia‹Üa@æî‹ánÜa . ℕ "#

u = 2u n − n + 1; ∀n ∈ ℕ n $1v n = u n − n 23  n +1 :  ‫( ا‬u n ) ‫ ا‬ u0 = 1  .v 0 ‫ول‬6‫ ود ه ا‬2 00‫ أ‬0 ‫ ه‬# (v n ) ‫ " أن‬-1 . n 7 u n / 0‫ ا‬89 n 7 v n ‫د‬:‫ أ‬-2 . n 7 S n ‫ أ‬S n = v 0 + v 1 + ⋅ ⋅ ⋅ + v n 23:‫ب‬ . n 7 T n ‫أ‬T n = u 1 + u 2 + ⋅ ⋅ ⋅ + u n 23 :‫ج‬ Z÷àb©a@æî‹ánÜa

u = u 2 + 2; ∀n ∈ ℕ n :  ‫( ا‬u n ) ‫ ا‬  n +1 = 2 u  0 . ℕ "# n $1 u n ≥ 2 :‫ " أن‬-1 2 . ℕ "# n $1 v n = u n 23 -2 .v 0 ‫ول‬6‫  و ه ا‬00‫(دا أ‬#  # . n 7

(v n ) ‫ " أن‬:‫أ‬

u n / 0‫ ا‬89 n 7 v n ‫ د‬:‫ب‬ . n 7 S n ‫ أ‬S n = v 1 + ⋅ ⋅ ⋅ + v n 23 :‫ج‬ [email protected]