ملخص رائع لدروس 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