technique-math-2bac.svt


I a a a a a a a a a lim f x g x lim f x g x b g x f x g x f x c 0 limx 0 0 f x a a a g x d 0 0 0 0 limx 0 0 f x a g x quot quot e 2 x x 2 2 x x x x x x 2 0 0 0 1 cos tan sin 1 lim lim 1 lim 1 x 2 x x ax ax ax ax ax ax amp x0 f amp a limx amp f x limx x0 f f x f x -012 f amp b 3amp3quot03amp-4 f f amp 5 x 2 0 amp x limx amp f x limx f x l 2 g f 6 x g x f x x x g x l amp x0 f x l g x a lim 0 x g x x0 f x g x b limx f x x0 f x g x c limx g x x0 g x f x h x amp d 0 0 lim lim x x g x h x l ampII 78a 9798b f amp a lim f a b f a f b a f a b f f b amp f amp b lim lim f a b f b f a b a f a b f f amp a b 0 f amp a f b f a a b 0 f amp b f a f b a b f x 0 amp c a b f a f b 0 quot c 9 f amp III amp 1 I 0 f I 09 f f I J 0 f 1 f J I amp 1 x J y I f x y f y x a 1 f J 0 b 1 f f ltquotamp3 J 09 ampamp c Cf 1 f 6amp amp C y x limx f x l limx g x limx f x limx f x l c a b f c c a b f c 0 J amp I f
3 1 f I 0 9 f amp x I f x 0 1 f J f I 0 1 1 1 x J f x f f x n IV n x - n IR y 7 x 1 n y x 4 16 2 4 2 0 2 16 4 2 16 4 2 16 2 a 0 n 0 b n x x c n n n n x y x y x y x y x y lt lt d n n n n x y x y x y x y x y 1 n e n n n n x y x y x y x y x y n f n n n n x y x y x y x y x y g n n n n x x x x n n n x IR x x p n h b a IN n n n a b ab p np p n n n p a a a a n n p np n n a a a a b b b n p np n p a a a i p n n p n p x x x p p n p x x x n quot n x y x y n n xy n n n x x y y 2 3 3 x x x 0 3 3 3 3 3 3 3 3 x x x x x x x x 3 3 3 3 2 2 2 2 a b a b a b a b a ab b a ab b 4 4 3 2 2 3 a b a b a a b ab b b a j IR r r r r r r a a a r r r r a a r r r r a a a r r r a b a b 1 r r a a r r r a a b b
I I U U I n u n n n I U n I U M n M a n I U m n m quotb quot c M m n n I m u M n n I U k 0 n I U k n n n U n U U n n1 a n U U n n 1 amp b n U U n n1 amp c n U U n n 1 ampamp d n U U n n1 e p n u u p n Un 1 p n u u p n amp Un 2 Un 3 u u n n 1 Un u u n n 1 0 - amp Un u u n n 1 0 - amp Un u u n n 1 0 - ampamp Un u u n n 1 0 - Un u u n n 1 0 - II 1 n n U r n U U r n n 1 r Un a 01 21 u u n n 1 3 Un b 01 u u cte n n 1 43 1 0c a c b 2 2 a b b un 0 1 r 5 u0 n U U nr n 0 1 u1 10 1 1 U U n r n 1 u2 10 2 2 U U n r n U p n U 6 U U n p r n p r 5 58 pn 37 Un 1 r 5 u0 0 1 2 1 2 n n u u S u u u u n u0 S 9 un S 9 S 9 n 1 1 1 2 2 n n u u u u u n 0 1 0 1 1 2 n n u u u u u n 6 1 1 2 p n P p n u u u u u n p III 1 n n u q 1 1 n n n U qU q 1 8 1 7 a 01 21 lt Un1 3 1 Un b Un u q u n n 1 43 1 cba 0c 1 2 ac b
n u0 0 1 q 5 1 u n n n u u q 1 1 u1 10 n p u u q n 1 un p u 6 q 5 n p u u q n p 58 pn 37 Un 0 1 q 5 1 U0 1 q gt 1 0 1 0 1 1 n n q S U U U U q u0 S 9 S 9 n 1 S u u u n u 0 1 0 1 n q 1 0 1 1 0 1 1 1 n n q u u u u q q 1 2 1 1 1 n n q u u u u q 6 1 1 1 1 n p p p n p q u u u u q IV lim n q 0 1 1 1 1 lim 1 1 n q q q q q quot amp4 U l V n n V n U n a lim 0 lim V U l n n amp4U V n n V n U n b lim lim V U n n lim lim U V n n amp4V U W n n n W n V n U n c lim lim lim V W l U l n n n 5 5 Un 5 U Vn n 7U V n n V n U n a amp4 V n U n lim lim U V n n b quotamp c U f U n n 1 I f n n 1 U I U f U f I I - l 5 5 Un I f - f l l
I a1 2 2 z a ib a b 1 i ab z a ib z b i 2 i i 1 z quot z a ib c R z a o z amp a Im z b z amp b z a b 0 - z z ib a 0 b a b a a a a ib a ib b b a a ib b II ab z a ib - z a ib - z z a z z z z z z i b z z z z z z c 1 2 1 2 n n z z z z z z z z z z d 1 2 1 2 n n n n z z z z z z z z z z z z n e 1 1 z z z z z z z x iy f 2 2 2 2 Im z z x R z z z iy i z 2 2 zz x y III ab z a ib - z z 1 2 2 z zz a b quot z a z a a z b z ib b 2 2 2 z z z z zz a b z z z z z z 0 0 c d 1 2 1 2 n n zz z z z z z z z z n n z z e 1 1 z z z z z z 1 1 2 z zz zz z z z z 2 2 a ib a ib c id a ib c id c id c id c id c d amp IV 565 P 2quot34 1 2 o e e M z a ib P M x y a aff M u x y b v u 7 z a ib aff u z z M x y z a ib c M z P u x y 7 z a ib d z 2 u z v a 2 1 aff e i aff e aff o 1 0 b z M z x ox z M z ox z M z x o c z i M z y oy z i M z oy z i M z y o quot a aff M aff M M M aff MM aff M aff M MM aff M aff M b aff u aff v u v aff u v aff u aff v aff u aff u u aff u A B G c 1 aff G aff A aff B AB- I d 1 2 aff I aff A aff B 789C B A e c B A z z z C B A A B C A B A z z z z
- amp V 8z M z z 1 e OM arg z arg 2 z e OM 1 arg 0 2 arg 2 arg z z z z z z k arg 2 2 arg 2 2 arg 2 z i z z i z z i z k z lt arg 2 z z r z r i cos sin quot z r z i z re r r r r 2 a z a ib b 2 2 2 2 2 2 2 2 2 2 cos sin a b z a ib a b i a b a b a b i a b cos sin cos sin i i c cos sin cos sin i i cos sin cos sin i i sin cos cos sin 2 2 i i 1 1 n n r r rr r r n r r r r r r r r arg arg arg 2 arg arg 2 arg arg arg 2 1 arg arg 2 arg arg 2 n zz z z z n z z z z z z z z z i i i e e e n i in e e i i e e i i i e e e 1 i i e e 1 i e 2 i i e 2 i i e 1 arg 2 arg arg 2 e u aff u u v aff v aff u 1 arg 2 arg 2 B A D C B A e AB z z z z AB CD z z 1 C A B A z z z z 1 arg 0 2 C A C A B A B A C A B A AC z z z z AC AB AB z z z z z z AB AC z z Moivrequot cos sin cos sin n i n i n Euler quot 1 cos 2 1 sin 2 ix ix ix ix x e e x e e i 2cos 2 sin ix ix ix ix e e x e e i x 47 gt 1 2 1 i i z e z e 1 2 cos sin cos sin cos cos sin sin 2cos cos 2sin cos 2 2 2 2 2cos cos sin 2 2 2 i i z z e e i i i i i 1 2 cos cos sin sin 2sin sin 2cos sin 2 2 2 2 2sin cos sin 2 2 2 z z i i i A 2 2 2 1 2 2 2cos 2 i i i i i i z z e e e e e e 2 2 2 1 2 2 2 sin 2 i i i i i i z z e e e e e e i - 01 VI z z z n n z Z n a z a Z r A Z 2 01 1 n k k z r k n n n n A 2 1 k k w n k n 01 1
01 5 a Z r Z 2 2 Z r r 1 Z 2 u r u 1 b 02 1 Z a 1 2 Z a a u u a Z 02 2 Z a a 2 2 2 Z a i a i a u u i a Z 023 Z ib b 2 2 2 2 1 1 2 2 2 b b b Z ib i i i 1 Z 2 b u u i 02 4 Z ib b 2 2 2 2 1 1 2 2 2 b b b Z ib i i i 1 Z 2 b u u i b 0 0 a Z a ib 02 5 1 Z i 3 4 z x iy B 2 2 2 z x y ixy 2 2 2 2 Z 5 z x y 2 2 2 2 2 2 2 3 1 2 4 2 5 3 x y z Z z Z xy z Z x y quotECDC 2 x 1quot x 1 2 2 x quotE FC C 2 2 8 y 2 y 4 y 2 quot y 2 quot G47 y x xy 2 0 C9 1 2 x y quot 1 2 x y u u i 1 2 Z II1 4 VII quot 2 a 0 az bz c 0 B 2 b ac 4 1 9 0 H1 2 b z a u u 0 H 19 2 b u z a 2 b u z a 2 a 0 az bz c 0 2 1 1 z z 1 2 1 2 b z z a c z z a 2 a 0 az b z c 2 0 quot b ac 7 0 H b z a 1 97 0 H 1 2 b u z a 2 2 b u z a u
I quot f a 0 x limx x f x f x l x x f x l 0 f b 0 x lim x x f x f x l x x f x l d f c 0 x lim x x f x f x l x x f x l g f d 0 f x 0 x d g 0 0 f x f x quot cf x0 f a amp f x 0 M x f x 0 0 T T y f x x x f x 0 0 0 quot Cf x0 f b amp f x d M x f x 0 0 T1 T y f x x x f x 1 0 0 0 d amp c d lim x x f x f x x x f 0 x Cf -quot 0 0 A x f x e lim x x f x f x x x f 0 x Cf -quot quot 0 0 A x f x f lim x x f x f x x x f 0 x Cf -quot quot 0 0 A x f x g lim x x f x f x x x f 0 x Cf -quot 0 0 A x f x amp quot Cf x0 f 01 032 M x f x 0 0 -amp Cf x0 f 01 02 0 0 M x f x f I g I f I g f x I g f x g f x f x quot I quot f x I f x 0 1 f J f I 1 1 1 x J f x f f x quot amp I quot amp u a amp n D x u x f 0 f x u x amp 5 x0 4 4 amp f b 6amp amp 0 f amp x 0 x 4 quotampquot a a 0 f g f g af af 0 x 1 0 f g f g fg 0 ax a 0 r r 1 r x rx 0 r r 1 f rf f 2 1 1 x x 2 0 f f g g f g g 1 2 x x 2 1 f f f 2 u x u x u x sin cos x x 0 3 2 3 3 u x u x u x cos sin x x 0 1 n n n u x u x n u x 2 2 1 tan 1 tan cos x x x 2 1 tan 1 Arc x x sin cos u x u x u x 2 tan 1 u x Arc u x u x cos sin u x u x u x 0 2 tan 1 tan u x u x u x
I quot amp f 7 I amp f a x I f x 0 7 I f b x I f x 0 7 I f c x I f x 0 - f amp I quot amp f 0 8 946amp f amp x 0 x quot I quot amp f x I f x 0 amp Cf a x I f x 0 Cf b -quot - I quot amp f x I 0 0 f M x f x 8 946amp 0 x amp x0 8 9 4 3 6amp f a 0 0 lt M x f x quot amp 5 ampamp amp5 b gt amp f x II Cf quot x a 6 a 2a x D f Df xquot 017 2 01 f x D f a x f x Cf quot a b b 2a x D Df xquot 017 2 2 01 f x D f a x b f x 1 quot a quot gt 3 quot Cf limx a f x lim 5 x f x b lim 5 x f x 1 2 b lim 0 x a f x quot x a 6 a Cf lim 0 x f x b quot y a 6 Cf lim 0 x f x 6 limx f x x a limx f x x lt quot Cf b lim 0 x f x x quot lt quot Cf c lim 0 x f x a x lim 6 x f x ax lim f x ax b i quot y ax b 6 Cf lim f x ax ii lt quot Cf y ax amp quot y ax b 6 Cf lim 0 f x ax b y ax b 5ltquotA B ltquot f x ax b h x quot f x 5 lim 0 x h x amp quot Cf quot5 lt f x m amp quot a y m 6 Cf quot5lt f x 0 amp quot b quot Cg Cf quot5lt f x g x amp quot c 3 lt f x g x quot d gt Cg Cf 6 y ax b 6 Cf Campquot5e f x y 8 amp amp Cf f x y 0 01 amp Cf f x y 0 01
I o i j k v x y z u x y z 2 2 2 u x y z u v xx yy zz quot B x y z B B B A A A A x x z AB x x y y z z B A B A B A 2 2 2 AB x x y y z z B A B A B A quot n amp P amp amp P a P D amp P ax by cz d 0 b n a b c amp P amp quotamp c A 1 1 2 P amp amp n 21 1 amp amp M x y z P AM n 0 quot 1 2 1 1 0 2 1 2 1 1 2 0 x y z x y z P x y z 2 1 0 n 21 1 quot P amp P amp A P 1 1 2 2 1 0 x y z - P x y z 2 1 0 d 1 2 1 2 0 d quot d u a b c D D v a b c u v quot D D u v 0 aa bb cc 0 quot e u D i w v P quot D P u v u w u v u w u a b c D ii P n amp n u 1quot D P 0 a a b b c c u n 1quot D P 0 u n 0 2 P D iii P amp D amp amp D amp P ampamp f n Q P i n n n quot P Q 0 n n 0 n quot P Q 0 n P ax by cz d 0 ii Q a x b y c z d 0 aa bb cc 0 quot P Q quot g ampquot A P i P A quot H P A amp AH amp d A P AH P ax by cz d 0 ii ampquot 0 0 0 A x y z 0 0 0 2 2 2 ax by cz d d A P a b c II M quot amp 3 r - 34 amp M r 5 3r - a b c 34 S amp amp 2 2 2 2 x a y b z c r - amp - 2 2 2 x y z x y z 0 n P D n P A M n P u D n P D P H A
amp 2 2 2 0 x y z x y z quot63amp ampquotamp 7 quot 2 2 2 d c b a 2 2 2 a b c d 0 2 2 2 2 a b c d lt 0 0 2 2 2 a b c 2 a b c d 0 0 2 2 2 a b c 34 amp 2 a b c d gt 0 - 2 2 2 r a b c - amp quot 2 2 2 x a y b z c k amp3ampquot amp 2 2 2 2 2 X X X 2 k lt 0 0 a b c 2 k 0 0 r k -a b c 2 k gt 0 0 - 63 S amp 9 AB 3quot8 amp S quot quot 0 0 A B A B A B x x x x M x y z S AM BM y y y y z z z z x x x x y y y y z z z z A B A B A B 0 quot amp9 - 0 A B A B A B x x x x y y y y z z z z 0quot amp P r - 34amp S a 1lt63 d d P P S 7quot S 7quotltP S gt P 2 d r gt 1i H ampquotquot S P 2 d r ii quot 3 H B quot H S BP amp A3 P C 5 S 7quot P 2 d r lt 1 iii quot H 334 P -P 2 2 r r d amp A3 P 2 d P 1b 5 S amp 7quot P amp A3quot8 P 3 - 34 P C r x - 34amp S c d P r quotS P i A quot A S P ii A P A A 3 A S amp B iii amp quot 0quot x x t D y y t z z t S amp 2 2 2 S x y z ax by cz d 0 amp D S amp 7quot amp 2 2 2 1 2 3 0 4 x x t y y t z z t x y z ax by cz d amp amp amp 9z y x t amp A34 S 7quotltD B amp 2 lt 0 i S 7quot D amp 2 0 ii H S BD amp A3 H ampquot amp 2 gt 0 iii 2 1 7quotD t t B A 1 9 B A quot S 2 1 t t III o i j k D - x v y z x u y z y y x x x x u v i j k z z z z y y u v u v 0 quot u 1a v u v 2 P P amp AB AC 0 amp Equot C B A b amp AB AC ABC amp 3 ABC amp 1 2 S AB AC S AB AD 3 ABCD F4 amp u amp A D ampquot M AM u d M D u u v v u 0 u v u v u v 0 u v w u v u w 0 u v w u v v w 0 S amp D 7quot amp 7quot gt d D
I F 1 f IR x x Log ln F1 0 ln 0 IR a ln D 0 f x u x ln b f x D u x gt f x u x ln f x D u x ln1 0 c e 271828 ln 1 e ln r r Q e r ln r Q b gt 0 a gt 0 ln ln ln ab a b ln ln r a r a 1 ln ln a a ln ln ln a a b b ln ln a b a b ln ln a b a b lt lt ln ln ln ab a b ab gt 0 quot 0 quot a b ln ln ln gt a a b b 0 quot n ln ln a gt n a n a ln x 4 1 0 ln x x x gt ln u x u x u x ln u x u x u x quot5 lim ln x x a ln lim ln x x b ln0 c ln lim 0 x x x d lim ln 0 x x x e ln1 lim 1 x x x 1 ln lim 1 x 1 x x ln ln 0 ln ln 0 1 t v x t u x v x v x t t w x t v x a t II ln amp x x e a x x e x gt x e b 0 e 1 1 e e ln c x x e x ln 0 x gt x e x 0 d x gt x y e y ln y x r Q x y x y x y e e e x 1 x e e x x y y e e e rx x r e e x y e e x y x y e e x y lt lt x x x e e u x u x e u x e x ln x 0 1
quot lim x x e a e lim 0 x x e b 0 e lim x x e c x lim 0 x x xe d 1 lim 1 x x e e x 1 t v x t t e v x t u x e x v x te w x e v x a t a amp III a 1 a amp log a ln 0 log ln a x x x a gt 10 log log 10 ln 0 log log ln10 x gt x x x e amp - log a ln amp log 1 a log 1 0 a a log1 0 log10 1 -- IV ln 0 x x a gt a x a e y x b gt 0 a gt 0 x y x y a a a xy x y a a x x y y a a a x x x a b ab x 1 x a a x x x a a b b x y a a x y ln ln x a x a
I 1 card E E 2 amp nampamp n quot n quot n 0 -amp n n 123 quot 0 1 3 -amp2amp p 01-amp 1 quot34256 n 2 quot 34256 n np quot p 34256 7amp28amp93ltampgtamp 1 2 n n np quot quot 4 1 2 E a a a n quot p n quotA n E p amp 1 E n CDA p B a BD quot E GHA p BEF- 1 2 n x x x BDampamp7 amp9 b p An amp 1 2 1 p n n facteurs n A n n n n p n p E n CDA n B F- E c 1 21 7I amp9d n A n n n n n E p ampJK1 E n CDA p BJK e BDJKquot E GHA p LMF- 1 2 p x x x BDampamp7JKamp9f p Cn amp 1 2 1 1 21 p facteurs p p n n A n n n n n p C p p n p p p p amp 5 a 0 1 n C C n n 1 1 n C C n n n p n p C C n n 1 1 1 p p p C C C n n n quot quotampNampOAampb n n k n k k n k a b C a b 2 E PampM1quotA n E c n quot II 1 QampR 1 2 n U 7Tamp-S a a a AF-gtDampZ6amp VW Xamp4Y6 i D a 66X i 0 1 p i p 1 2 1 n p p p E i i quot XampampPV p amp quot p a p 2 quot XA XampampPV p quot bquotltampampDTampampX8amp7W Xampa A NampY Xamp -amp 1 2 A a a a n 1 2 p A p a p a p a n quot XampampPV p amp 3 A B CX B A a p A B p A p B p A B p A p B p A B quotCX B A b p A p A 1 A BampNamp A X A c cdcdAJampX1 An quotquotquotquotquot A2 A1 d 1 2 1 2 n n p A A A p A p A p A 01 - 4 Y XTampeJ7T1f g XampampPV p Y XTampeJhampDTampampX8ampfi 1 card quotX A card A p A card Y XTampeJampDTampampX8ampf g-ampa 2quot nombre de cas favorables p A nombre de cas possibles kq rs6gtD1jk Dlampmn1o7W XTamp pb U e DD ampoW7amp-wquOrs6gt4vtuOrsS - 7gtampY xDampDTampampX8ampY Xamp XW1EyquOD0ampz-ampc -ampampY xampOamp YX 1 2 n a a a 1 2 n p A p a p a p a eJhMamp48amptuO 4 ampM 3 34Y XampG M34Y XampY XTampeJhDJamp48ampY XTamp BG34VYANamp A NampY XampE X1 123456 45 quot ampDTampampX8ampY XampE p p p x 2 4 6 2 p p p x 1 3 5 f p p p p p p 1 2 3 4 5 6 1 b x x x x x x 2 2 2 1 b 1 9 x 1 1 3 5 9 p p p 2 2 4 6 9 p p p A 36 1 2 1 3 6 9 9 3 p A p p 6 5 p A 0 CX B A
6 A Namp1 B NampY X1 p A B p B A p A 7 8 9 6 p A 0 CX B A p A B p A p B A 9 7 ampX8ampY6a A1 A2 quotquotquotquotquot An -ampZ6amp B i j i j A A 1 n i i A quot AJz-ampZ6amp B An quotquotquotquotquot A2 A1 ampX8ampb quot ampampX8amp cdcd amp7W XTampO c A1 A2 quotquotquotquotquot An B XFquot B ampX1 1 1 n n p B p A p B A p A p B A quot lt 8 -ampZ6ampI6 B A CNampY6a p A B p A p B p B A p B -ampZ6ampC6 B A Nampb quot 2ampVWX16-ampb p A B p A quot cdcd6 2amp n D Rc p A p Xamp 2ampm66Y XampX A 2amp n YI2Z Dk k 6 A NampNamp B 1 k k n k p B C p A p A n f Y Xamp XFM1JAD 2quot F amp2Tamp1ampE amp-ampa p Cn card A p A card 7amp 2ampkD0amp9J7amp 2ampkD z-ampb BDFquot76 gtamp7 ampY xampE0Xampamp 1 2 n X x x x i quoti 34D0amp0 x quot 6 9 8 III 66XD F-ZD X gtF- ampurO 1 quot X BD X rOamp2Kltamp36 ampurO X 2 1 2 X x x x n 4amp X F Xamp4X4F6 i F p X x -YMmamp9li n 12 n x 2 x 1 x i x n 1 2 i p X x 1 4gt 3 amp E X BDampamp X ampurO pampF8amp 1 1 2 2 1 1 2 2 n n n n E X x p X x x p X x x p X x x x x 98 4 ampV X BDampamp X ampurOkOamp 2 2 XV X E X E X 2 2 2 1 1 2 2 2 2 1 1 2 2 n n n n n n E X x p X x x p X x x p X x x x x A B C 5 amp X BDampamp X ampurOampgtampampTamp X V X DEF 6 amp F BDhltampampamp X ampuamprO 0ampamp lt x F X p X x quot x F F x 4amp F ampampX4Y6 AampR3 3 4 B U N quotAAamp7amp-E quot FAampP amp7ampampD xF-ZDamp ampuamprOamp X X 9 8 GHampIJ K a quot3N VYANampb X 0 quot1 2 B N VYANampb X 1 quot2 1 B N VYANampb X 2 quot3B VYANampb X 3 X 01 23 X LM b 3 4 3 7 4 35 C p X C 1 2 3 4 3 7 18 1 35 C C p X C 2 1 3 4 3 7 12 2 35 C C p X C 3 3 3 7 1 3 35 C p X C 0 1 2 3 i x 1 35 18 35 18 35 4 35 i p X x c 4 4 18 1 49 0 1 2 3 35 35 35 35 35 E X d 2 2 2 2 2 4 4 18 1 75 0 1 2 3 35 35 35 35 35 E X 2 2 2 75 49 224 35 35 352 V X E X E X e 224 35 X V X quot x F F x E quot0ampampf F x p X x p 0 lt x 0 -amp 0 1 lt x -amp 4 35 F x p X x p X lt 1 2 lt x -amp 22 0 1 35 F x p X x p X p X lt 2 3 lt x -amp 34 0 1 2 35 F x p X x p X p X p X lt 3 lt x -amp F x p X x p X p X p X p X 0 1 2 3 1 lt
I I b a I f quot b a f b a f x dx amp b a f x dx F b F a f quot F b b a a f x dx F x F b F a 01- 2 x - b b a a f x dx f t dt II I c b a I g f 0 1 a a f x dx 2 a b b a f x dx f x dx 3 b c b a a c f x dx f x dx f x dx 74563 4 b b b a a a f x g x dx f x dx g x dx 5 b b a a af x dx a f x dx a IR quot 6 x a F x f x dx f quot8 quot 9 a quotlt 0 x a b f x a b gt a7 b a f x dx 0 x a b f x a b gt b b a f x dx x a b f x g x a b gt c b b a a f x dx g x dx a b gt d b b a a f x dx f x dx quot a 8 1 b a f x dx b a f quotAB C b a Fb a E F c quotquotDb b a f x dx b a f c c 1 b a m f x dx M b a C G9 M m a b f quot C C quot GI Jb a 8H quot III amp 1 f FI KC4L5 g f ltquotI b a I g b b b a a a f x g x dx f x g x f x g x dx - 00IV f F 0 1 a 0 ax 1 r x r 1 1 1 r x r 1 r u u r 1 1 1 r u r 2 1 x 1 x u u 1 u 1 x 2 x u u 2 u 1 x ln x u u ln u x e x e ax e 1 ax e a f F u x u e u x e 2 1 1 x arctan x 2 1 u x u x arctan u x cos x sin x sin x cos x 2 2 1 tan 1 cos x x tan x cos ax b 1 sin ax b a sin ax b 1 cos ax b a 2 2 1 tan 1 cos ax b ax b 1 tan ax b a u x u x cos sin u x u x u x sin cos u x 2 u x u x 1 tan tan u x
1V 1 P x I dx ax b ax b P x 5 GU u u 2 2 1 I dx ax bx c C V quotF lt 0 gt a 2 p x ax bx c F 2 1 I dx u x t u x OP GU p x a x x P x gt 0 gt b Wlt 1 1 1 1 P x x x GU u u 0 gt c 2 2 1 1 x I dx dx x x x 3 2 P x I dx ax bx c P x 5 2 GUax bx c u u 2 1 u u 4 n I P x ax bdx n P x I dx ax b OP n t ax b I P x ax dx cos 5 I P x ax dx sin kx I P x e dx OPX D8 cos f x P x g x ax I P x x dx cos ln 6 I P x Arc xdx tan OPX D8 ln arctan f x x ou g x P x cos 7 kx I e ax dx sin kx I e ax dx I A I quot X D8 8 1 x I dx ae b x x x x x e e u I dx dx e ae b a be u 9 ln r x I dx x 1 ln 1 ln ln ln 1 r x r r I dx x x dx x x r 10 n u x v x I dx w x OPX D8 n w x f x w x g x quot 23V quot quot 1 F E a b lt a b f a E F Cf x b x a x Ox AE 9 E F b a f x dx u a 54 EF KquotDCf ltf 0 Ygt AE 8 b a f x dx u a EF YFquotDCf ltf 0 Ygt AE 8 b a f x dx u a 6Z E4 -Ygt AE b a f x dx f x dx E a b lt a b g f b E F F Cf Cg x b x a AE 9 E F b a f x g x dx u a 5 Cg KquotDCf ltf g Ygt AE b a f x g x dx Cg YFquotDCf ltf g Ygt AE b a g x f x dx -Cg NltCf Ogt AE b a g x f x dx f x g x dx i cm gt c j cm 9 N5quot 2 u a cm 8967 quot 2 7V 3 S a E F a GV z b z a S quot Ygt S a b IR t S t V a b b a S t dx u v 7z t c S ObCa 9S t 3 a b f b E Cf E 8 EF R E G quot gt 9G 9G 2 b a V f x dx u v
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technique math 2bac svt
technique math 2bac svt 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