Math Devoir 11

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pbïšb€€€€€€€€€€€€€€€€€î‹ÜaZò†b€€€€€€€€€€€€€€€€€€€€€€€€€€€¾a

ò‹Ñïå‚@óibïä

‘ì‹«@‹Ð

p@Ë@l@‘2@ó€åÜaZõín€€€€€€€€€€€€€€€€€€€€€€¾a

ðäbîÜa@âŽbÕÜa@ðic@óîíäbq

2HZŒb−fia@ò‡€€€€€€€€€€€€€€€€€€à

Zßìÿa@æî‹ánÜa 3

 1− 3 x  Arc tan ( x − 2 x + 2 ) = 0 (iii  3  + 125 = 0 (ii x 36 + 27 = 0 (i:‫ ﻤﺎﻴﻠﻲ‬ℝ ‫ﺤل ﻓﻲ‬  1+ x  2 . Arc tan ( x − 2 x ) ≺ 0 (iv 2

ZðäbrÜa@æî‹ánÜa :‫ﺃﺤﺴﺏ ﻤﺎﻴﻠﻲ‬ .C =

 3  31π   ، A = Arc tan −   (1  3   3    2 tan ( 3 x ) x . lim ( x sin ( x ) + 2 x ) ‫ ﻭ‬lim ، lim (2 x →0 1 − cos ( 2 x ) x →+∞ x →0 7x

 1 2



 1 3

Arc tan   + Arc tan   ‫ ﻭ‬B = Arc tan  tan  −

3

. lim

x →+∞

3 x +2 x +7 −2 ، lim (3 x − 1 x →1 x − 1

ZsÜbrÜa@æî‹ánÜa

‫ ؟ﺇﺫﺍ ﻜﺎﻥ‬x 0 = 0 ‫ﺘﻘﺒل ﺘﻤﺩﻴﺩﺍ ﺒﺎﻹﺘﺼﺎل ﻓﻲ‬

1   * f ‫ﻫل ﺍﻝﺩﺍﻝﺔ‬. f ( x ) = x sin  3  :‫ ﺒﻤﺎﻴﻠﻲ‬ℝ + ‫ ﺍﻝﺩﺍﻝﺔ ﺍﻝﻤﻌﺭﻓﺔ ﻋﻠﻰ‬f ‫ﻝﺘﻜﻥ‬ 4  x − x  .‫ﺍﻝﺠﻭﺍﺏ ﺒﻨﻌﻡ ﻓﺤﺩﺩ ﻫﺫﺍ ﺍﻝﺘﻤﺩﻴﺩ‬ ZÊia‹Üa@æî‹ánÜa

.f

(c ) =

1

c

‫] ﺒﺤﻴﺙ‬0,1[ ‫ﻤﻥ‬

c ‫[ ﺒﻴﻥ ﺃﻨﻪ ﻴﻭﺠﺩ‬1, 2 ] ‫[ ﻨﺤﻭ‬0,1] ‫ ﺩﺍﻝﺔ ﻤﺘﺼﻠﺔ ﻭﻤﻌﺭﻓﺔ ﻤﻥ‬f ‫ﻝﺘﻜﻥ‬ Z÷àb©a@æî‹ánÜa

.f

2 x  1+ x

( x ) = 2Arc tan 

  :‫ ﺒﻤﺎﻴﻠﻲ‬ℝ ‫ ﺍﻝﺩﺍﻝﺔ ﺍﻝﻤﻌﺭﻓﺔ ﻋﻠﻰ‬f ‫ﻝﺘﻜﻥ‬ 

Arc tan (t ) ‫ ﻭ‬lim f ( x ) :‫ ﻭﺃﺤﺴﺏ ﺍﻝﻨﻬﺎﻴﺎﺕ ﺍﻝﺘﺎﻝﻴﺔ‬D f ‫ﺤﺩﺩ‬:‫(ﺃ‬1 t →0 x →+∞ t f (x ) . lim = +∞ :‫ﺒﻴﻥ ﺃﻥ‬:‫ﺏ‬ x →0 x . I = [1, +∞[ ‫ ﻤﻊ‬I ‫ ﻋﻠﻰ‬f ‫ ﻗﺼﻭﺭ ﺍﻝﺩﺍﻝﺔ‬g ‫(ﻝﺘﻜﻥ‬2 .‫ ﻴﻨﺒﻐﻲ ﺘﺤﺩﻴﺩﻩ‬J ‫ ﻨﺤﻭ ﻤﺠﺎل‬I ‫ ﺘﻘﺎﺒل ﻤﻥ‬g ‫ ﺒﻴﻥ ﺃﻥ‬:‫ﺃ‬ −1 . J ‫ ﻤﻥ‬x ‫ ﻝﻜل‬g ( x ) ‫ ﺤﺩﺩ‬:‫ﺏ‬ π . f ( x ) ≻ ‫ ﻴﺤﻘﻕ ﺍﻝﻤﺘﺭﺍﺠﺤﺔ‬2 ‫( ﺒﻴﻥ ﺃﻥ ﺍﻝﻌﺩﺩ ﺍﻝﺤﻘﻴﻘﻲ‬3

. lim

+

3

Bonne chance [email protected]

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