كل ما يحتاجه التلميذ في الرياضيات


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3 quotW ampW amp J amp - 4 5 1-2 J quot 6 8 3 4-5 10 6 5 12 9 050 J 8 J 7 quot 13 14 -gt 16 n 18 3lt 20 22 3 24 3 26 28 31 A 5 32 BC 34 36 5 5 38 DEEF
4 4 05 2 K -- 01 a 0 ax b W b a x a amp ax b a ampG a 0 ax bx c 2 W -- 01 x ax bx c 2 W HB W x x 0 x- x amp lt 0 S x x a amp JK 0L 0 2 b S a b a x amp a amp a x 2 2 b x a x a b2 - 4ac gt 0 S x x 1 2 WM 1 2 b x a 2 2 b x a x1 x2 x amp a G amp a amp a x WOPQF 1 2 E x x lt 1 2 x a x x x x O 8Samp 1 x 2 a x ax bx c 0 2 0 W Dx WOTU 1 2 b x x a 1 2 c x x a
5 6 789 4 05 2 K 1 W6 789 b a L 2 2 2 a b a ab b 2 2 2 2 a b a ab b 2 2 2 a b a b a b 3 3 2 2 3 a b a a b ab b 3 3 3 3 2 2 3 a b a a b ab b 3 3 3 3 2 2 a b a b a ab b 3 3 2 2 a b a b a ab b W 4 lt8 1 L Q P WDf 1-2 WD WUx DKVf f x x Df x f x Q x D x Q x f 0 D x x f 0 f x x x f x Q x D x Q x f 0 gt x f x Q x D x x f 0 Q x gt 0 x f x Q x Q x 0 f 0 x D x Q x
6 4 05 2 K gt 1 W187 x x n x x n 4 lim 0 n x x lim 0 x x gt 1 lim 0 n x x 1 lim 0 n x x lim x x 1 lim 0 x x WOTU Un O 8Samp WOTU Xn O 8Samp lim n x x lim n x x 1 lim n x x gt 1 lim n x x lt lim n x x lim n x x 1 lim n x x gt 1 lim n x x lt 4 4 W A P quot Y8 quot D P Z quot Y8 quot quot D 4 W sin lim 1 x x x tan lim 1 x x x 1 cos 1 lim x 2 2 x x x u x W 4 lim x x u x lim x x u x l l 0 gtlt- quotZ 0 PLx 0 P P x
7 WB1C lim lim 0 x x x x f x V x f x V x l l 0 0 lim lim lim x x x x x x u x f x V x u x f x V x l l l lim lim x x x x u x f x f x u x lim lim x x x x u x V x f x V x gtlt- quotZ 0 PLx 0 P P x W D WE l l l lim x x f x l lim x x g x l l lim x x g x f x F WE l l lt 0 l gt 0 0 lim x x f x l lim x x g x l l lim x x g x f x WE GH l l l lt 0 l gt 0 0 lim x x f x l 0 0 lim x x g x l l lim x x g x f x W I gtlt- quotZ 0 PLx 0 P P x
8 4 05 2 K 41J W97 K 41J W1 lim x x f f x f x x0 a4 W D 41J E0 D 41J lim x x f f x f x gt x0 aL4 lim x x f f x f x lt x0 a 4 a L4f 0 x0 a4 f x W4 D 41J a b 3 d48a4 f c 8Sampa b b3 24f O- a b b3 d4 f c 8Sampa b eV3 24 f O- b a 4 a a L4 D 4 W Dk I 3 2L4Lg f I 3 d4kf f g f g 3 LOTUI -5g c 8Samp 1 g f g I 3 dL4 4 8 WLM quot-24Z8 4x x O 4x x cos x x sin O quot-24x x tan 2 k k WE B 41 f I J WMfJ 3 24g I 3 24 f c 8Samp I 3 d4g f WOTU W 8 4 N 0gD4 0g gt 3 2D4 3 2 gt I 3 2 0glt- 4f WNH J f I 3 dlthiAD 3
9 f I 3 d I 3 d I 0g4g -f I 0g-f f b f a f a f b a b lim a b x b f a f x lim x b f x f a lim a b x a f x f b lim x a f b f x lim lim a b x a x b f x f x lim lim x b x a f x f x lim a x f a f x lim x f x f a lim lim a x a x f x f x lim lim x x a f x f x lim a x f x f a lim x f a f x lim lim a x x a f x f x lim lim x a x f x f x x x lim lim f x f x lim lim x x f x f x W9 O7 6P f b f a L 47 DjTUa b 3 24f c 8Samp f WMfa b 3 d Dg W f a f b lt 0 a b 3 24f c 8Samp a b 3 dkampD glt- f x 0 OTU f a f b lt 0 a b 3 2 0glt- 4f c 8Samp a b 3 dkampD lt- f x 0 OTU WQM amp 7R f a f b lt 0 WMfa b 3 2 0glt- 4f a b 3 da f x 0 0 WO 8Samp 2 a b f a f lt 0 WO 8Samp 2 a b f b f lt WOTU 2 a b a jKhlZ lt lt 2 b a 3 d0Z ampm 2 a b a 34n 6PKhl- WOTU 2 a b b jKhlZ lt lt 2 b a 3 d0Z ampm 2 a b b 34n 6PKhl- quotUFjKhl-34oOPkamp0Z ampm Z W I
10 4 05 2 K S7J W K S7J 8T a6 g f Oamp3 0 W quotc 8Sampx 0 0 lim x x f x f x x x quot a f ep- quotZ 0 W j x 0 f x W D ampW J D U0 4 a6 g f 0 x C4UPr0a f nq WDx 0 0 0 y f x x x f x WD 8 Uu 0 0 0 u x f x x x f x C4UPr0a f n s- 0 u f t-D x 0 x W E0 D S7J 8T JE0 D S7J 8T aL6 g f Oamp3 0 quotc 8Sampx lim x x f x f x x x gt quot aL f ep- quotZ 0 W j x 0 f x d a 6 g f Oamp3 0 W quotc 8Sampx lim x x f x f x x x lt quot a f ep- quotZ 0 W j x 0 f x g a6 g f O- 0 a L6 g f c 8Sampx 0 x 0 0 f x f x g d W41J S7J a6 g f c 8Samp 0 a4O- f OTUx 0 x WJ 4 lt8 7X 4 f x f x k k 0 x 1 1 x2 1 x r 1 rx r r 1 x 1 2 x x sinx cos x cos x sinx 2 2 1 1 tan cos x x tanx
11 W 7X JE B 7X -7X 4 D k ku k u u v u v u v u v uv u v uv 1 n n u nu u 1 2 v v v 2 u u v uv v v u v u v v 2 u u u W gtY1 S7J I 3 26 gf I 3 d- f x I f x 0 I 3 d4g - f x I f x 0 I 3 d f x I f x 0 WQZ S7J nDC l quot lt Cf W lim x x f x f x a x x a 0a J a jj A x f x 0 0 lim 0 x x f x f x x x a6 g f x 0a UP J 0 0 A x f x 0 0 lim f x f x a x x x x a 0aLq J14 0 0 A x f x a jj 0 0 lim 0 f x f x x x x x 6 g f Lm 0 x 0 a LDUPq J14 0 0 A x f x 0 0 lim f x f x x x x x Lvq J14 wjA x f x 0 0 0a 0 0 lim f x f x x x x x gK f 6 Lm 0 x Lvq J14 wjA x f x 0 0 0a 0 0 lim f x f x a x x x x a 0a q J14 0 0 A x f x a jj 0 0 lim 0 f x f x x x x x 6 g f x 0a DUPq J14 0 0 A x f x 0 0 lim f x f x x x x x a vq J14 0 0 0 wjA x f x 0 0 lim f x f x x x x x gK f 6 x vq J14 wjA x f x 0 0 0a
12 -0 -0 5 4 05 2 K 9J 97 W-0 5 n x7x a j vZoO Cf WO O hpeySamp 2 f f x D a x D 2 f x D f a x f x W-0 n x8I a b 0O- Cf WO O hpeySamp 2 f f x D a x D 2 2 f x D f a x f x b W9J 97 - 7 O 8Samp3 2nO 3 dZj- JHzcy x I f x 0WO 8Samp nWOTU Cf I 3 dO O 8Samp3 2 7nO 3 dZj- JHz 6U x I f x 0WO 8Samp nWOTU Cf I 3 d 7 O rn0Dn9 00 nZ-KV a- f c 8Samp 0 KV-Hx nOTU Cf C4UP9 00lt 0 x a- f c 8Samp 0 KV-O x nOTU Cf C4UP9 00lt 0 x
13 M amp 2 K 4 05 lim 0 x f x ax b lim x a f x a x lim x f x lim x f x x lim 0 x f x x lim x f x ax b lim x f x ax WltCf Wj x a WltCf U j gt U7 u WltCf U j 7-t u WltCf U jo j vZ y ax u WltCf Wj y ax b u WltCf UP Wj y a u lim x a f x lim x f x a
14 05 2 K 4 WNH I 3 2 0glt- 4 f c 8Samp I 3 dw f I 3 dUlt- f OTU W C 1 f WLM 1 f x y f y x x I y f I 1 x I f f x x 1 y f I f f y y YN W I 3 2 0glt- 4f I 3 d4y f I 3 d4x W D U 5 1 f x y f y x Vgtx 5 y n 1 f x f I x 4 41 W I 3 2 0glt- 4 f c 8Samp OTU 1 f f I 3 d4 S7 W I 3 2 0glt- 4 f f I 3 d4x 0 0 y f x a6 g f c 8Samp 0 x 0 f x 0 OTU 1 f a6 g 0 y W 1 1 f y f x I 3 2 0glt- 4 f I 3 d-5 f p quot I 3 d6 g f c 8Samp OTU 1 f f I 3 d6 g W 1 1 1 x f I f x f f x
15 81 W I 3 2 0glt- 4f 1 f f KV-nG C Q W W6 I n Cf n 1 Cf 1 A a b C f f A b a C lt x a Wj UP lt y a Wj UP lt y b Wj lt x b Wj lt y ax b Wj Wj lt 1 b y x a a Wg g0 yo x ay b Eq J14 PF Jlt Eq J14 PF Jlt UP Eq J14 PF Jlt UP Eq J14 PF Jlt I 3 2 0glt- 4f f LO ltOE 1 f oJ oa o3 14lt O
16 n n 1 4 05 2 K 7 W1 NH n W -gt-Z-gt n Ux x W C n n n x x 2 n n x y x y x y WNH J 2 x x W 3 x 3tZ x WNH 2 n n n n n n n n x y n x x x x x y x y x y x y gt gt 2 2 n n n n m n m n n n n m n m x y m n x y x y x x x x y y y x x W6 I x y x y x y 3 3 3 3 3 3 2 2 x y x y x x y y W WDf 1-2 WD 8Uf n Df 0 f x x n D x x D f u u x 0 f x u x W gtlt- quotZ 0 PLx 0 P P x lim x x u x lim n x x u x l 0 n l
17 W41J n 4x x I 3 2Uu OTUI 3 24 ltu c 8Samp n I 3 d4x u x WS7J n 0 3 d6 gx x W 1 1 0 n n n x x n x I 3 2Uu I 3 26 g 0gltu c 8Samp OTU n I 3 d6 gx u x W 1 n n n u x x I u x n u x a x x a n W D Xn vUn a gt 0 n S a a n n S a S 0 S 0 a 0 a lt 0 S a n S W9T B Q77 7 p r q WMK Z p q p r p q q x x x x WI 1 0 n n x x x WD 8Ux DKV f 1-2 r r f x u x u x gt 0WD D x x D f u 1 1 1 1 n n n u x u x u x u x n y x 4 r r 4 r r r r x x x x x r r r r r r r x x y y r r r x y x y 1 r r x x r r r r x x x
18 4 05 2 K 8 WZ 1- u u r n n 1 q r u q u n n 1 q q u u n p r n p p n n p u u q n p p n 2 1 1 1 n p p n p q u u u q 1 1 1 n p p n p q u u u q q 1 c b a b a c 2 2b a c Y n n I u u n I u M n n I n M lt u n I u m n n I n m V4 n n I u V4 lt n n I u 7 W 81 n n I u u n I u u n n I n n 1 4g - u n I u u n n I n n 1 - u n I u u n n I n n 1
19 W n W Wa lt 0 gt 0 lim n n lim 0 n n n Z Wq Wa q q 1 lt lt 1 1 q q 1 q gt 1 lim n n q lim 1 n n q lim 0 n n q n q quot CG W7 b D lt - 8 D V4 4g - 8 lim lim lim n n n n n n n n n v u w v u v l l l lim lim 0 n n n n n n u v u v l l lim lim n n n n n n u v u v lim lim n n n n n n u v u v Wu f u n1 n Y WD 8U un n n 1 u a u f u I 4a f I I MfI 3 24 f M c 8Samp OTU un f x x W l quot quot
20 4 05 2 K Nc 4 4 Nc W4 D W1 I 3 2U f I 3 d f gtPDF OP3 WO O hpeySamp I 3 d6 gF x I F x f x WNH 3 dZgtPlt-3 248 I 3 2U f WOTUI 3 d f gtPF c 8Samp WD WI U f gt3 Hz x F x k k I 3 2gtPlt- f I 4x 0 4y I 3 d f F gtP- F x y 0 0 WDltpey WQ77 F -E 0d WNc 4 WNH k I 3 2LULLg f WOTUDI 3 dg f LLgtPLG F c 8Samp I 3 d f g gtP F G I 3 dkf gtPkF
21 4 4 Nc gt 4 WJ f x F x a ax k 1 2 2 x x k 1 k x 1 x2 2 x k 1 x 1 1 r x k r r x r -1 sinx cos x k cos x sinx k tanx k 1 1 tan 2 cos 2 x x ln x k 1 x k x e k x e WNc 4 lt8 S7J eN 40 f x F x 2 u x k u x u x 1 k v x 2 v x v x 1 1 r u x k r r u x u x r -1 ln u x k u x u x u x e k u x u x e 1 sin ax b k a a 0 cosax b k 1 cos ax b k a a 0 sinax b
22 4 05 2 K Q W9T D 1 W1 I 3 d f gtPF I 3 24f I 3 d4b a WDb kampa f - b a b f x dx F x F b F a a WNH W9f a f x dx a a b f x dx f x dx b a b b k kf x dx k f x dx a a b b b f x g x dx f x dx g x dx a a a W4 T b c b f x dx f x dx f x dx a a c WB1C x a b f x 0 WO 8Samp 0WOTU b f x dx a x a b f x g x WO 8Samp WOTU b b f x dx g x dx a a W9 07 a b 3 24 f WDD3 d0 1 b f x dx b a a WF c8 I 3 dL4v uLMfI 3 26 L gLv u I 3 d4b a b a b b u x v x dx u x v x u x v x dx a a o i j okamp i Lquot o 0 Du A j 1 u A i j
23 a b 3 24f nL 4 Cf gt U7 W ZL x b x a DW b f x dx u A a a b 3 2L4Lg f LnL 4 Cf Cg 7 W ZL gt U DW x b x a DW b f x g x dx u A a WNH J WDoaDlt DnA- o lt f a b 3 d b f x dx u A a lt f a b 3 d b f x dx u A a ltf a c 3 d lt f c b 3 d c b f x dx f x dx u A a c Cg 6UCf a b 3 d b f x g x dx u A a Cg 6U Cf a c 3 d Cf6U Cg c b 3 d c b f x g x dx g x f x dx u A a c O 73CfnO odo a b 3 2a 8 gt U W 2 b V f x dx u v a Wuv
24 4 05 2 K 0g 4 0g lt W1 ogtDvKlt 1 x x 0 3 d lnW C 1a-r WNH ln 1 0 ln 1 e x y 0 0 ln ln x y x y ln ln x y x y gt gt ln y x y x y x e 0 0 ln ln ln ln ln 1 ln ln ln ln ln r x y xy x y x r x x x x x y y r ln ln WOTU Xn O 8Samp n x x n x W WDf 1-2 WD 8Uf و u x gt 0 f x u x ln D x x D f u 2 f x ln u x f x ln u x و u x 0 D x x D f u WA lim ln x x lim 0 ln n x x x lim ln x x gt lim ln 0 n x x x gt 1 ln lim 1 x 1 x x ln 1 lim 1 x x x n W41J 0 3 d4x x ln I 3 2Uu I 3 d4x u x ln OTUI 3 24 0gltu c 8Samp
25 WS7J 0 6 gx x ln 1 x x 0 ln x I 3 2Uu I 3 26 g 0gltu c 8Samp I 3 d6 gx u x ln WOTU W ln u x x I u x u x WQ Wln x 1 lnx - a 1 Wa a Uh Og W1 W CrDa q o oga l WM ln 0 ln a x x og x a l WNH 1 0 1 a a a og og l l 0 0 og og og a a r a x y r x y x y x r x a l l l 0 0 1 a a a r a a a a a a a x y og xy og x og y og x r og x og og x x x og og x og y y l l l l l l l l l l r 1amp 0 1 lt lta a gt 1 l l og x og y x y a a lt lt l l og x og y x y a a gt gt lim lim a x a x og x og x l l lim lim a x a x og x og x l l W7X 1 ln a x og x x a l
26 4 05 2 K c 4 0g lt W1 gtDK gtK exp W C exp x HB x x e WNH x x e gt ln x x e x ln 0 x x e x ln x x y e y x y 2 x y x y x y e e x y e e x y gt gt x y x y x y e e e r x rx r e e 1 x x e e x x y y e e e W WDf 1-2 WD 8Uf x Df f x e u x D x x D f u f x e WA lim x x e lim 0 x x e lim x n x e x lim 0 n x x x e 1 lim 1 x x e x n W41J x 4x e I 3 2Uu OTUI 3 d4u c 8Samp u x I 3 d4x e
27 WS7J x W 6 gx e x x x e e I 3 2Uu W OTUI 3 d 6 g u c 8Samp u x I 3 d6 g x e W u x u x x I u e x e Q Wln a 1 Waa Uh c W1 oga exp W C a q - l a exp x HB x a x a WNH x x a ln x a e x log a x a 0 og x a x a a l 2 x y x y a a x y x y 0 og y a l x a y x 2 x y x y x y a a a r x rx r a a 1 x x a a x x y y a a a W1amp 0 1 lt lta a gt 1 x y a a x y x y lt lt a a x y gt gt lim x x a lim 0 x x a lim 0 x x a lim x x a 1 lim ln x x a a x W 7X ln x x a a a
28 4 05 2 K 7 c z a ib a b 2 i2 1 WD2 Wi7 P 8 a b 2 WM z a ib z vY -a ib Re z W j z Da Im z W j z Db D z OTUIm 0 z WO 8Samp WjNH j Ugt z OTUIm 0 z Re 0 z WO 8Samp WE7 i1 Lz z z z z z Re Re Im Im z z Wi7 Q oJ okamp v 1 2 o e e Wi7 bk a b 2 WM z a ib z a ib Wv z eU Dnlt O M z M z z z z z z z z z n n n z z 1 1 z z z z z z z 0 Dz z z 9gtDz z z z z z 2 Re z z i z 2 Im 2 2 zz z z Re Im Wi7 a b 2 WM z a ib M a b 0 z v M z Wt z gt-M 0 M 0ez OM quoteZ8z OM z Wt z Aff OM P a b 2 W M z a ib z zz a b 2 2 WtD z v
29 n n z z n z z z z z z z 1 1 z z z z z z z z W gtg i7 c 8 Q X M j-gtK z e1 OM Wquot gP z v argz W j arg 2 z Wt K z arg 2 z r z HB W z vDEEp z r i r cos sin WD z v i z re WNH J Ka DEE a lt 0 a gt 0 a a 0 2 ai a a a 2 ai a arg arg arg 2 zz z z arg arg 2 z z arg arg 2 z z arg arg 2 n z n z 1 arg arg 2 z z arg arg arg 2 z z z z r r rr r r r r n n r r n 1 1 r r r r r r i i i re r e rr e i i re re i i re re n i n in re r e 1 1 i i e r e r i i i re r e r e r k r k r 2 د z z k arg arg 2 z z k د ف k WgtA YN Wk YN cos sin cos sin n n i n n i n 1 cos 2 i i e e 1 sin 2 i i e e i Wa a z z a 2 W 32 W S a a a gt 0 S 0 a 0 z z a 2 S i a i a a lt 0
30 a 0 77 Ac b a Waz az bz c 2 0 W W 32 W gt 0 2 2 b b S a a 2 b S a 2 2 4 z az bz c b ac lt 0 2 2 b i b i S a a W7 c 9 6 O6amp quotDC g AB z z B A AB U A B 014I 2 A B I z z z AB AC q g arg 2 c A B A z z AB AC z z C B A C A B A z z z z D C B A D A B C B A D C z z z z z z z z P D A D C B A B C z z z z z z z z g quotDC z z r A r gt 0 AM r r quot A 8r kampD-M z z z z A B AM BM AB kampD-M 2 C A B A z z r z z A a o gMEABC 1 C A B A z z z z A aLg v MEABC 1 2 C A B A z z z z A a o g Lg v MEABC 1 3 C A B A z z z z Av MEABC WJ lt 7 l WvjEx n X Stquot u u quoteb M z z b 0e M z k z k jlt 8vZ h D8 n j X 8vZr O i z e z 0e M
31 quotamp J 2 K 4 05 WA WA y ay b a 0 ax b y x e a WA Wlt- W quot WA gt 0 LL r2 r1 L 1 2 r x r x y x e e 2 WM r 0 rx y x x e 2 WM y ay by 0 2 0 2 4 r ar b a b lt 0 WLUQLL 1r p iq 2r p iq cos sin px y x qx qx e 2 WM
32 4 05 2 K Mmamp Z o i j k ltoJ okamp BZ6 a Y W4 F J OI JQ0 F Q u a b c v a b c Lquot 3 u v aa bb cc u a b c 2 2 2 i a a b b a a a a u v j b b i j k c c c c b b k c c Wk DW B AL0L U AB x x y y z z B A B A B A 2 2 2 DW ax by cz d 0 j P M 0U 2 2 2 ax by cz d M M M d M a b c A u o M 0U DW AM u d A u W n a b c ax by cz d 0 quotP AB AC OTUKC B Ac 8Samp quot ABC WD U 5 ABC ym M ABC AM AB AC 0 Wk WDR quot a b c 8U x a y b z c R 2 2 2 2
33 5 ymAB 0gPPSU M S AM BM 0 WD U quot AB14 8SW 2 AB 0 ax by cz d S R k nR71 8vH d H d WHB P S O h 5 Sq JP H 0a SH0P C eU H W 8 W quot 2 2 r R d W O7 S R k nR71 o8vH d H d WHB oS O h 5 Sq Jo H 0a SH0o LL0a
34 4 05 2 K W0 QM W1 CardE W j E dgt E quot2D Card 0 WNH WNH O quotO 2B A Card A B CardA CardB Card A B W0 O0 W1 E quot2A A W CrdDE lt Ao A x E x A M WI A A A A E cardA cardE cardA W Qc A p p quot t0- Y Fo3 5O 8 ampS n1 8 FoD E 5O 8 n2 8 F o p 5O 8 np 8 W OTU 1 2 3 n n n n p W8 j8 1C - 8 1C W8 1C p n 4 p n W 4n L 4p 3 lt-Q p n
35 W8 j8 1C p n 4 p n W4n L 4p 3-O lt-Q 1 2 1 p A n n n n p n p WNH 4n 3lt-Z8-4n L 4n 3-O lt--8 n n n n 1 2 2 1 W ampW n gt quot2E p n p gt E A8 4n L 4 p 3l- W lZ p p n n A C p Cn p An p n Wc 1 2 2 1 0 1 n n n n n p n n C p n p p n n A n p 1 n C n n n1 Cn 0 1 C n n 1 Cn p n p C C n n C C C n n n p p p 1 1 WB A lt8 p n 4n L 4 p tn W D 3 a t-Q W ltn Wtn D p Cn oquotK p 3T H n quoto 3ampO H p An oquot
36 4 05 2 K J0J 9 W WD 5i04 E8Plt- 8 p p 2D O8 O8A A 4B8 D OaB AO eySamp A B ey PB PAeySamp A B ey An B A A A A و A A B LKO B A oW 40 J o 7 W1 p ampO8 jgaiD 3 pi Wi3 OP3 pi Wt P p i i ZO-r 55 523 O 8SampvP 1 2 3 A n WA3 OTU 1 2 3 p A p p p p n WNH p ampO8 p 1 p 0 A0 1 p A WL y3 B AL p A B p A p B p A B LKB AO 8Samp p A B p A p B 3W B p A p A 1 WA WJ0J i1 quotk W1 quot ampO8p a3 5 5Hzc 8Samp W A83 OTU cardA p A card
37 WE- 7 JQRX 40J p A 0 WMfp G L0lt-LB A W1 We7AOP B 3 p A B p B p B A p A A W p A p B 0 WMfp G L0lt-B AL p A B p A p p B p B A W A B W1 p G L0lt-B AL OO B A p A B p A p B WNH p ampO8 1 2 3 1 2 1 2 WA 1 2 1 2 p A p p p p A A HJ W p j p a A WltB k A ey3 O U n ZPSamp 1 k k n k n k n C p p WQMX gtY 40 jT p ampO8 pKV WL LHltX DpKV3 O gn y 1 2 3 X x x x x n X KV Zlro2W 3 5tw p X x i 12ndi WQMX gtY ip9 qJ JY JQquot c n x 3 x 2 x 1 x i x j g pKVX WD 3 9 pn p3 p2 p1 p X x i WX KVDA 1 1 2 2 3 3 E X x p x p x p x p n n V X E X E X 2 2 WX KV V W1 X V X WX KVvX09w5 j7 WQ n Zp aA3 p p n X-A quotUenr 8 vZX DpKV 012 1 k k n k n k n p X k C p p V X np p 1 E X n p
38 4 05 2 K gt 1 Q W M J O7 4 W B E8 T -1 cos 1 -1 sin 1 cos 2 sin 2 1 x x x x sin tan cos 1 1 tan 2 cos 2 x x x x x cos 2 cos sin 2 sin tan tan x k x x k x x k x WA J cos cos 2 x a x a k P x a k - 2 sin sin 2 x a x a k P x a k - 2 tan tan x a x a k k 2 3 4 6 x 1 3 2 2 2 1 2 sinx 0 1 2 2 2 3 2 cosx 1 1 3 3 3 tanx 0 2 x 2 x x x x sin - sinx sinx - sinx cos x cos x cos cos x - cosx - cosx sinx sinx
39 W0 eN cos cos cos - sin sin sin sin cos cos sin tan tan tan 1 - tan tan a b a b a b a b a b a b a b a b a b cos - cos cos sin sin sin - sin cos - cos sin tan - tan tan - 1 tan tan a b a b a b a b a b a b a b a b a b WLM cos 2 cos 2 - sin 2 2 cos 2 - 1 1 - 2 sin 2 sin 2 2 sin cos 2 tan tan 2 1 - tan 2 a a a a a a a a a a a 1 cos 2 cos 2 2 1 - cos 2 sin 2 2 a a a a tan WHA 2 a t 2 sin 1 2 1 - 2 cos 1 2 2 tan 1 - 2 t a t t a t t a t W F r W r F 1 cos cos cos cos - 2 1 sin sin cos cos 2 1 sin cos sin sin 2 1 cos sin sin - sin 2 a b a b a b a b a b a b a b a b a b a b a b a b cos cos 2 cos cos 2 2 cos cos 2 sin sin 2 2 sin sin 2 sin cos 2 2 sin sin 2 cos sin 2 2 p q p q p q p q p q p q p q p q p q p q p q p q a b 00 a x b x cos sin W cos sin 2 2 cos sin 2 2 2 2 2 2 cos a b a x b x a b x x a b a b a b x WeD M sin 2 2 b a b cos 2 2 a a b
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Youssef el haddioui

Youssef el haddioui

أرسلت .



كلمات مفتاحية :
يحتاجه التلميذ الرياضيات
يحتاجه التلميذ الرياضيات bacdoc bac doc dok document cours bacalaureat bacalauréat baccalauréat bacalauréat bacalaureat baccalauréa baccalaurea maroc باك دوك باكدوك دروس بكالوريا باكلوريا باكالوريا المغرب 2014 2015 2016