lim


ر ا ى او م إز اذ ا quot amp ا ر ا ا ز Chorfimouhsineyahoofr ا رات ا 3 ب ت ا وال ا ود و ا وال ا -ر و ا وال ا -ر 3 ب ت ا وال ا 5 ا 7 85 9ل ا وال ا56د ا ت 7ل ا gt5quot quot رlt 1 أن 59 2 lim 3 0 x x x 9quotا ل ا Gح ا E ا -ي quotآ11 0 B- 2 K و x lt 3 4 إذن 2 3 4 lt lt x نJ lt lt 1 1 x أن 7 و x x x x 3 3 2 x x x lt 3 4 lim 4 أن 7 و x 0 x Jن 2 lim 3 0 x x x 2 5L ا M 3 2 lim 3 0 x x x أن O 7 57 2 2 2 lim 0 x 3 x x quot رlt 2 lim 3 أن 59 2 x f x 1 1 x f x x 3 5L ا P98 ف R ا- 1 1 3 3 2 4 2 2 2 3 3 2 1 1 1 1 1 x x x x x x f x x x x x x 3 5 ا ل ا ا ي آ 2 2 2 أن 3 5 2 2 x ن 3 5 2 2 x gt gt و 1 3 1 2 2 x gt gt و quot 1 1 2 x gt إذن 1 2 x 1 lt 2 و 2 2 1 x x x lt f x x 3 2 lt إذن و amp أن 2 lim 2 0 x x إذن 2 lim 3 x f x 1 lim 3 2 1 x x x أن O 7 57 2 1 lim 4 3 2 x x x quot رlt 3 4 أن lim 0 2 5 x x 4 4 4 2 2 2 x x 5 5 x lt ن 2 2 x gt 5 x 2 - ا 01 amp و 4 lim 0 x 2 x 4 و ن lim 0 2 5 x x 4 lim 0 2 5 x x أن O 7 57 2 lim 0 x 1 x x quot رlt 4 lim 2 أن x f x 2 2 2 1 4 x f x x 2 2 2 2 2 2 2 2 1 2 1 2 8 9 9 2 2 4 4 4 4 x x x f x x x x x و 2 2 9 9 x x 4 lt 2 و 9 lim 0 x x إذن 01 ا 2 2 2 2 1 lim 2 x 4 x x Chorfimouhsineyahoofr
2 2 2 1 lim 2 x 4 x x أن O 7 57 2 2 3 1 lim 3 x 2 x x quot رlt 5 lim 1 أن x f x 1 x f x x lim 1 أن ف45 2 ا 67 x f x 1 1 1 1 1 1 x x x f x x x x x و ان 1 lim 0 x x lim 1 ن x f x lim 1 و x f x 1 lim 1 x x x quot رlt 6 أن 2 2 lim 1 x x x 2 2 2 1 1 x x x ن 2 quot1 د9 1 1 x 2 و 1 limx x إذن 2 2 1 limx x x 2 2 1 limx x x أن O 7 57 2 4 1 limx x x quot رlt 7 أن 2 1 3 lim 1 x x lt 2 3 1 f x x 2 و 0lt أن 3 f h 1 h 2 و 1 0 0 1 lim lim 1 lim x h h f x f h h 2 1 3 lim 1 x x quot رlt 8 4 أن lim 2 x x x 4 3 quot و x gt1 أن ضB ار4 ا أن و x x x x 2 2 3 و x gt 2 1 4 3 x x x x x gt 2 2 وamp أن lim x x 4 إذن lim 2 x x x 4 lim 2 x x x Chorfimouhsineyahoofr
ا ت 87quot ا Y ا وال ا ود 1 ا د 53 ه Lر7 K ا 2 lim3 2 4 x x x 2 2 lim3 2 4 3 0 2 0 4 4 x x x 2 2 lim 4 1 x x x 2 2 2 lim 4 1 4 2 2 1 16 2 1 13 x x x 1 ا أو ه ا ا -ي K أآ9quotأس 2 lim 2 5 x x x 2 2 lim 2 5 lim 2 x x x x x 5 2 lim 3 2 5 x x x x 5 2 5 lim 3 2 5 lim 3 x x x x x x 4 lim 2 3 2 x x x 4 4 lim 2 3 2 lim 2 x x x x x ا وال ا -ر 1 دا -ر د 53 ض ا ل 7 ا د 2 1 2 3 limx x x 2 2 1 2 3 5 2 1 3 lim 5 x 1 1 x x 2 2 2 3 lim 2 x x x 2 2 2 2 3 4 3 1 lim 0 x 2 0 x x 1 3 1 lim x 1 x x 1 3 1 4 lim x 1 0 x x د quot5 O 58 أن Y ا 2 2 1 1 limx 1 x x 2 1 1 0 limx 1 0 x x د quot5 O 2 1 1 1 1 1 1 lim lim lim 1 2 x x x 1 1 x x x x x x 3 ا أو ه aرج ا اآ9quotأس 2 2 3 2 limx 2 5 x x x 2 2 2 2 3 2 3 3 3 lim lim lim x x x 2 5 2 2 2 x x x x x 5 2 2 3 2 limx 2 5 x x x x Chorfimouhsineyahoofr
5 2 5 3 2 2 3 2 3 3 lim lim lim x x x 2 5 2 2 x x x x x x x ا وال ا -ر 1 دا -ر د 53 ض ا ل 7 ا د 2 2 1 limx 1 x x 2 2 1 3 1 lim 1 3 3 x x x 2 2 1 lim x 2 x x 2 2 1 3 lim x 2 0 x x 2 2 4 lim x 2 x x 2 2 4 0 lim x 2 0 x x د quot5 O 2 2 2 2 2 2 2 2 2 4 2 4 2 4 2 4 lim lim lim lim 2 2 2 4 0 4 x x x x x x x x x x x x x x x 2 ا أو ا -ر 2 lim 2 x x 2 lim 2 x x 2 lim 2 2 x x x Y ا 2 lim 2 2 x x x د quot5 O O5 ا quot 2 2 2 2 2 lim 2 2 lim 1 2 lim 1 2 x x x x x x x x x x نC 2 2 2 x x 2 1 x 2 و 2 lim 1 2 1 0 2 1 2 1 x x و lim x x 2 و 2 lim 1 2 x x x 2 إذن lim 2 2 x x x 2 2 limx x x ا Y 2 2 limx x x د quot5 O ا O5 2 2 2 2 1 2 2 lim lim lim 1 1 0 1 x x x x x x x x x 2 lim 1 x x x Chorfimouhsineyahoofr
Y ا 2 lim 1 x x x د quot5 O O5 ا 2 2 2 1 1 lim 1 lim 1 lim 1 1 0 x x x x x x x x x x د quot5 O ا quotاP 2 2 2 2 2 2 2 1 1 2 1 1 1 1 1 1 lim 1 lim lim lim 0 x x x x x x x x x x x x x x x x x x ا وال ا 5 آFا Eamp9 ا ت ا sin lim 1 x x x و tan lim 1 x x x 2 و 1 cos 1 limx 2 x x sin limx 4 x x 0 0 sin 1 sin 1 1 lim lim 1 x x 4 4 4 4 x x x x sin limx sin 5 x x 0 0 sin sin 5 1 1 lim lim 1 1 x x sin 5 5 sin 5 5 5 x x x x x x x x 2 1 cos 2 limx x x 2 2 2 0 0 0 1 cos 2 1 cos 2 1 cos 2 1 lim lim 4 4 lim 4 2 x x x 2 2 2 x x x x x x 4 2 2 limx cos 1 x x 2 2 2 2 4 2 2 2 0 0 0 2 2 lim lim 2lim 2 2 4 cos 1 1 cos 1 cos x x x x x x x x x sin 2 limx x x 0 0 0 sin 2 sin 2 sin 2 lim lim 2 2 lim 2 1 2 x x x 2 2 x x x x x x 2 2 sin limx x x 2 2 2 2 0 0 sin sin lim lim 1 1 x x x x x x sin 3 limx 4 x x 0 0 sin 3 sin 3 3 4 3 3 lim lim 1 1 x x sin 4 3 4 sin 4 4 4 x x x x x x x x 2 1 cos 2 limx x x 2 2 0 0 1 cos 2 1 1 cos 2 lim lim 4 4 2 x x 2 2 x x x x 2 2 cos lim x x x Chorfimouhsineyahoofr
cd و x quot5b ا quot55b7 م 2 t x 0 0 2 2 2 cos cos sin lim lim lim 1 t t x t x x t t t 5 2 limx x x 5 5 2 2 lim lim lim 0 x x x x x x x 2 1 2 limx 1 1 x x x 2 1 2 0 limx 1 1 0 x x x د quot5 O 2 2 2 1 1 1 1 1 2 2 2 2 lim lim lim lim lim 1 x x x x x 1 1 1 1 2 2 x x x x x x x x x x x x x 2 2 2 1 1 1 1 1 2 2 2 2 lim lim lim lim lim 2 1 x x x x x 1 1 1 1 x x x x x x x x x x x x x إذن 2 1 2 lim 1 x 1 1 x x x lim 1 1 x x x lim 1 1 x x x د quot5 O 1 1 1 1 1 1 2 2 lim 1 1 lim lim lim 0 1 1 1 1 1 1 x x x x x x x x x x x x x x x x x x 1 3 1 2 limx 1 x x 1 3 1 2 0 limx 1 0 x x د quot5 O 1 1 1 1 1 1 3 1 2 3 1 4 3 3 3 3 3 1 2 3 1 2 3 1 lim lim lim lim lim lim x x x x x x 1 1 3 1 2 1 3 1 2 1 3 1 2 1 3 1 2 3 1 2 4 x x x x x x x x x x x x x x x x 1 lim 1 tan x 2 x x 1 0 0 0 0 0 2 2 2 2 lim 1 tan lim tan 1 lim tan lim lim lim 2 2 2 2 tan tan tan 2 2 2 2 x t t t t t t t t x x t t t t t t t 2 limx x x x x 2 0 0 0 1 1 lim lim lim 1 1 1 x x x x x x x x x x x x x x x ر إ5e 1د ا ت ا Chorfimouhsineyahoofr
2 3 2 2 2 2 1 lim5 7 2 3 2 1 lim 1 2 lim 1 x x x x x x x x x x x sin 3 lim 7 sin 2 lim tan 2 1 1 lim x x x x x x x x x 2 2 2 3 1 2 lim 2 9 lim 3 2 1 lim 1 x x x x x x x x x 2 4 5 lim 5 4 1 lim 1 x x x x x x x 2 2 5 1 lim 4 5 2 1 lim 2 x x x x x x x x ا 7 ت gt5quot quot رlt 1 9quot ا ا f ا quot ا O 2 1 1 x f x x 1 57 أن 1 2 x O f x x R 2 ذا g ا O x 1 R 2 2 2 2 2 2 2 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 x x x x x x f x x x x x x x x و 7 ان x R 2 إذن 1 1 x 2 و 1 1 2 x 2 1 1 1 1 x 2 و quot 2 1 1 1 2 x x x 1 و 2 x f x x R 2 أن 1 2 و f x x lim 0 x x ن lim 0 x f x quot رlt 2 9 2quot ا ا f ا quot ا O f x x x 1 1 57 أن 1 2 f x x x O R lim g ا amp 2 x f x ا O x 5 1 R 2 2 2 2 2 2 2 2 1 1 1 1 1 1 1 1 x x x x x x f x x x x x x x x x R ن و أن x 2 2 و 1 gt x x 2 إذن 1 gt x x 2 quot و 1 2 gt x x x 2 1 1 1 x x 2x lt 1 إذن 2 f x x lt Chorfimouhsineyahoofr 2 ان 1 2 f x x x lt lt R و 1 lim 0 x 2x lim 0 ن x f x quot8 ا hG 7 Mأ
quot رlt 3 9quot ا ا f ا quot ا O 2 2 2 6 3 x x f x x 1 57 أن 1 f x 2 x x O R lim g ا amp 2 x f x و lim x f x quot رlt 4 f x x x x sin 2 O ا quot ا f ا ا quot9 x O f x x gt أن 57 1 R lim g ا amp 2 x f x Chorfimouhsineyahoofr
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