3 x =2y x =-16y 1 4 {0 ;4!;} y=-;4!; y x =y 1 5 5'2 2 (0 0) 4 (3-2) 3 3 x=0 y=0 x=2 y=1 :: 1 4 O x 1 1 -:: y=-:: 4 4 {0 -;2!;} y=;2!; l A y 1

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1 = =-6 {0;!;}=-;!; = 5 5' (00) (-) =0=0 == :: -:: =-:: {0-;!;}=;!; 0 l :: -:: =:: F 5 0cm =- = =- (0)=- =6 =0 =- (0)=- - =- {-;#;0}=;#; =- - =- (0)=- = =8 -:: :: =:: - =- 98

2 R l Q P B S r rb l Q P B lb RS Q =RS =rpq =PS PR =P P l P l l + = = + = (05)(0-5) (0')(0-') '5 ' 5-5 :::;+:::;= 69 0 '5 ' 5 + =5 -' ' + = + = (60)(-60) :::;+::;= = m 8 8U=7_0 m -' -' ('5 0)(-'5 0) 6 +9 =6 + = + = (0'5) (0-'5) 6 :;:+:;:= 9 '5 - -'5 ' '5 99

3 (0) (-0) (-) + =9 (-) + =9 (+) + = (+) + = r P P +P =(7-r)+(+r)=8 P() 8 + = 6 + = = =;#;=-;#; =;!;=-;!; =-:: :;:-:;:= =:: ::;- =- =:: =-:: =- 6 8 P F' F - = - = (00)(-00) (60)(-60) (' 0)(-' 0) (0)(-0) 6 - =- - = (0)(0-) (0'7)(0-'7) '7 (0)(0-) (0')(0-') ' ;9$; -;7$; = - =- 5 (0)(-0) (' 0)(-' 0) =;#; =-;#; - - :;:-:;:= 9 00

4 P F PF P =PF PF' =t P =PF' +F' =t+ PF' -PF = t-(t+) = P FF' F(0)F'(-0) - = 5 - = 5 =+5'=-5' +=5 = =8 0 + = (6') 06 + = 07 =p ` F(p0) (66) 6 =p_6p= F( 0) cm 6 F(p, 0) 6 =p ` ='(æ0), =-'(<0) --=0 '-=0(æ0) - (+0) (+0) + =6 - (+0) +-0=0 '-+=0 5 --=0 +-=0 - (+0) (+0) 9 - (+0) (+0) -+8=0 '5--= % 50 % + -+=0 d d d d ( )+ ( )- ()+ ()=0 d d d d 0

5 d d + -- =0 d d d - = (+) d - () ;@; --=0 --=0 0 t (, ) (-, ) (-, 0)(-, -) (0, 0) (, ) = + =- + = 5 (+t) t - (t+-) (+t) --=0 --=0 +'-=0 5--=0 5 a=b= 5 =t+=t +t- d d = =t+ dt dt d =t+ d t= -=(-) =- t+ +-=0 sin h+cos h= cos h tan h+= cos h sec h-tan h= sec h-tan h= sech=tanh= - = - -=0 d =sech =sech tanh dh d =tanh =sec h dh d d dh sec h sech = = = = (sinh+0) d d sech tanh tanh sinh dh p h= =' sin p p p =sec ='=tan = (') -='(-') '--=0 - -=0 (sin h+0) '--=0 sinh 0 - (+0) - (+0) 0 -t 0-8+7= t d d 08 =t =t+k dt dt d d dt t+k = = (t+0) ` d d t dt t= +k =k= t===_ +_-_ =-6 +6=(-) --8=0 ` ` 0

6 d d 0 % k 0 % 0 % 0 % PF'F 0 % PF'F 0 % d =r(h-sinh) =r(-cosh) dh d =r(-cos h) =rsinh dh d d dh rsinh sinh = = = (cos h+) d d r(-cos h) -cos h dh pr F PM F' P =PF' PF' +PF =F () P F F' P M 0 =6 0 + = + = (+0) {+;!;} - t 0 0 a=- b= =;$;=-;$; 'å7 09 P F'PF PF' :PF =F' :F =: PF' =kpf =k(k>0) PF' -PF =k=_k= ` P'F =8 PF = ' +5= FF' =6 ` PF'F PF' +PF +FF' =8++6=8 ` P B P =PF P l F P PT +PF' =( )PT +PF =( ) PF' -PF =( )-( )=() P FF' 0

DC 0 5 0 ms B B CD CD 5 5 C F ED a+b b C D B 0 0 5 +b +c -d =B +BC +CD -D 5 +b +c -d =(B +BC )+CD -D 5 +b +c -d =C +CD -D 5 +b

7 DC ms B B CD CD 5 5 C F ED a+b b C D B b +c -d =B +BC +CD -D 5 +b +c -d =(B +BC )+CD -D 5 +b +c -d =C +CD -D 5 +b +c -d =(C +CD )-D 5 +b +c -d =D +(-D ) 5 +b +c -d =0 6 CB b a+b C B ' b a+b PBC P BC P P =B -BP = - = P ' ' 0 a-b -b b b C -b B 0

8 p -r =(+b )-(5+7b ) p -r =+b -5-7b p -r =--6b p -r =-(+b ) -(p +q )=p -r p +q p -r 0 b b -::b a+b b -b +5b a+b b k+0 k+lb =0 HjjK k=-lb l k+lb =0 HjjK =- b k k+lb =0 HjjK b k=0 l=0 -b k+lb =0 HjjK k=0 l=0 a-b 8-b b +;#;b p +q =(+b )+(+b ) p +q =+b ++b p +q =+b B 05

9 b +c -b +c 0 ' 0 '5 ' 5 5 ' 0 0 -;$; (+b )-(b -c )=+b -b +c =-b +c b =c +c =c»(+b )-(b -c )»= c = c = c = ` ` ' _ =' ` 0 % c 0 % 0 % b a+b a+b b -b -b a-b -b m - -b -c b + -b BC M Mm b +c m = G M : G B G g M m b c C 06

10 g b +c _ + m + g = = = +b +c + '5 m=-n= (5-) (70) b b + a+b -b a-b BCG b c g +b +c g = +b +c =g G +GB +GC =( -G )+(B -G )+(C -G ) =+b +c -g =0 B b P p =() P +PB =( -P )+(B -P ) P +PB = +B - P P +PB =+b -p P +PB =(0)+(50)-() P +PB =(6--) P +PB = " (6-) +(-) = (6-) +(-) = (-) + = (-) + = P (0) 0 0 F ' = F cos h (650, 000) (m) (m) e +e () e -e (-) '5 5 m=n=- m=n= (5) (-0) 5 +b 6 ()' (-5)' 6' 0-0 = cos0 = _ = 5 -b =(-b ) (-b ) -b =(-b ) -(-b ) b -b = -b - b +b b -b = - b + b (+b ) (-b )=(+b ) -(+b ) b (+b ) (-b )= +b - b -b b (+b ) (-b )= - b 07

11 5 ' 6 '5 7 -;!@; P 8 - -;%; P - ;#;p P p :: ::p P +b =(+b ) (+b ) +b = + b + b +b = + b cosh+ b +b + b + b +b =( + b ) +b æ0 æ0 b æ0 +b + b ::p ::p p :: 5 ::p 07 B cosh s B W W=Fs = B cosh = ` `B b +b ;5$; PQRSPQR -a -b (00)Q'(a -a b -b )R'(a -a b -b ) Q'R' S S=;!; (a -a )(b -b )-(b -b )(a -a ) 08

12 =+ =-+ =-+ (-) +(-) =9 0 8 (-)B() () B =()-(-)=() B =() () - - = - -= -= - d + =-+ =- + =- =5-5+=0 =- 0 ; 7; 5 - ' 0 6 ;5$; ' --' d =(lm) P( ) = l m 8 B =()-(-0)=() 8 B =() () = d=(, ) - 8 =- + -+= +-=0 ;!@; ; ; mm' -n -n' = = m m' d d d =( m) d =( m') d d =0 (m) (m')=0 _+m_m'=0 mm'=- m-+n=0m'-+n'=0 n n n =(m-)n =(m'-) n n =0 (m-) (m'-)=0 mm'+=0 mm'=- 09

13 0 C (-) +(+) = (-) + = = = = =0 08 H(ab) HC d (a-6b-) ()=0 a+b=0 ` ` d =() = H b a= ` ` (-) +(-) = +(-) = a=b= () ` C CP h PC=90 C CP = C CP cosh C CP = C C C CP =r CP c p C CP =r (-c ) (p -c )=r ( -a -b) (-a-b)=r ( -a)(-a)+( -b)(-b)=r =0 -= 0 ;5$; 0 -;!; 0 (+) +(-) = =0 Q =R =r PQ =PR PQ PR ab 0 % ab 0 % 0 % P PQ PR P PQR QR P QR P =n =( ) l l + +a=0 P(, )Q(, ) Q =(, ) QP =P -Q =(, )-(, )=( -, -) (, ) ( -, -)=( -)+( -)= =0 + =r a=-r l + -r =0 0

14 0 Q(t, 0) ;!;e + '- ' ()' 7 (6) 'å (-)(0-6) (0)(0-) (-)' (6-) ' =-;@; ;#; +8 '=- ;!; l l=:)9 æ +{- ;!; } d=:)9 'ƒ+ d Pt v d d v ={ }=(-rsintrcost) dt dt Pt v v =" (-rsint) +(rcost) v =" r (sin t +cos t)=r Pt d d ={ }=(-r cost-r sint) dt dt Pt =" (-r cost) +(-r sint) =" r (cos t +sin t)=r (-rsintrcost)r (-r cost-r sint) r 0 '(e-) : : ;!;{e- } e 5 ;#;+;!;ln l=_;@;[{+} ;#; 0' 0- ]9)= S 0' 0- S= _7=60' 0-6(m ) d d f'() dt dt 0 ()' (6) ' 0 0 e 0 ;@;('-) 0 p 05 : : 06 t=' (60' 0-6) m - 07 '= ` - =ln(- ) =0 =;!; l ;!; - l=:) æ +{ } d ` -

15 ;!; ;!; (+ ) + l=:) æ d=:) d (- ) - ;!; l=:) {-+ }d - ;!; l=:) {-+ + }d + - l=[-+ln(+)-ln(-)] ;!; ) 08 8 l=-;!;+ln;#;-ln;!;=-;!;+ln ' ' -' ` P p 0 vºtsinh-;!;gt =0, t{vºsinh-;!;gt}=0 vºsinh t+0 t= g P p vºsinh =vºtcosh=vºcos h_ g vº sinhcosh vº (sinhcosh+coshsinh) = = g g vº sinh = g sinh p sinh=h= h= p 0 % 5 % 5 % 0 (-) +(-) =5 0 ;#; 05 ' 06 ;@;+;@;b 07 B 0 B =B' =' 'B' 08 P +PB +PC =B P +PB +PC =PB -P P =-PC PC : ` PB PBC P PC S :S =: ` S = ` S 09 F +F +F =0 F =5 F =5' P B P B n P B' n P' m m ' P (, )BP b p =(-, 0)b =(, 0)p =(, ) P : BP =: P = BP (, )-(-, 0) = (, )-(, 0) (+, ) = (-, ) (+, ) ={ (-, ) } (+) + ={(-) + } +++ ={( -+)+ } -+ =0 -+ =0 0 % 5 % S S 5 % P (-) + =

16 D E BC BF CD EF HG CG DH FG EH ab l' mn mb l'm a ll' P m na l'n ln b n m a P l' l 0 DE C BC D BE DF EF CF BCDE FGB FJE BGHC EJID DIHC FGHIJ BCDEF GHIJKL GLF BHIC FLKE CIJD GHIJKL B 5 ab a lb lb 6 la l a la m l mb lm 8 B BC DF DEF D E BC CD ED ED BC CD BCDE lc l a c m lm ln mn B E F C D b l a 7 lm l ma l P n b abp m ab P m abn b l la ma n lnmn a lmlmp a b

17 0 lm M BC BC M BC DBC DM BC BC ( MD) BC ( MD) D MD D BC P a P a P l PH l l P PH PH l PH H l PH lh l l PH H PH l( PH) l PH lp P H P lh a P a ;; 5 ;; 5 6 ;!; 7 a m B ab B=90 B m m a a 8 l P a b m a cn B PÍaPBÍa '6 P a B PPB b c l l a a m b l P B c n BCD H H BC E E BC C BC 5BC =5 E =6 BC BCD EH 0 H =6sin0 = BCD ;!;_0_=0 0 EFH ' 5 'p`cm ' 8+' 8' 0 S S' 0 cm 0 cm S' 00p cm B E 0 H D

18 h 00p=;!;S S=00p (cm ) 00p cm BCD BC M M BC DM BC DM BCD H DM CD N H BN H BCD ' 07 ' BHFGBFGHFGCD(BCD)HCD 0 0 BD EH BD EH =;!;BD CBDFG BD FG =;!;BD ` EH FG EH =FG ` EFGH EFGH ` ' ' 6 EH =;!;BD FG =;!;BD 0 % EH /FG EH =FG 0 % EFGH 0 % ' 5 () (80) {;&;;(;} 0 (,, )B(,, ) 06 B H M C N D P(00)Q(5)R(05) P(-)Q(-0)R(00) (05) (00) (---) (-) z (-) 6' 5' 5 P(00) 5

19 (00) (-0) (--) (---) ( z ) G z +z +z { } G : P B z z (0000) ( ) " {0-(-00)} +{00-(- 00)} +(0-00) =00 () 00 m _ + _ + ª P + + z +z +z _ +z º + P z +z +z +z { } z +z +z { } z +z +z +z { } 0 0 '(0,, 0)B'(,, 0) : (,, 0) (0) (5-6) (-0) (5) (--0) () (-) +(-) +(z+5) =6 (-) +(+) +(z-) = +(-) +(z-) =9 (-0) ' (-) (-) +(-) +(z+) =6 (-) '6 (-) +(+) +(z-) = (+) +(-7) +(z+) =5 (-0) ' C{;#;}D(0) (5) P P (-) P H H 6

20 (-0) Q PHQ HQ HQ =øπpq -PH =" - ='5 5p P(abc) 5p 05 (5) 06 '6 07 (-9) 08 5' z -++z+a =0 (-) +(+) +(z+) =9-a (000)(--) ` " (-0) +(--0) +(--0) = ` +" 9-a =a =5 a='5 ` 0 z 5 P 5 0 % 0 % a 0 % 5 0 Q z 5 PQ Z P± W{;!;;!;} X{;!;;!;0} WX {;!;;!;;!;} 0 (-) 0 z (-) 0 z (-) 0 (---) 0 (-0-) 0 z (0) 0 z (-0) 0 (0-) 0 (00) 0 7 +b b - (-6) (--) (-7)

21 0 E F G H B C D b - -c c - b - (+b )+c =(B +D )+E (+b )+c =(B +BC )+CG (+b )+c =C +CG =G +(b +c )=B +(D +E ) (+b )+c =B +(BC +CG ) (+b )+c =B +BG =G (+b )+c =+(b +c ) +b +c +b -c 5 ' 7 6 p +q =(+b -c )+(-b +c )=-b +c p -r =(+b -c )-(5-5b +c )=-+6b -c p -r =-(p +q ) p +q p -r 7 B =D =b HF =HE +EF =(-EH )+EF =-b +=-b NM =N +M =-N +M NM =-;!; D +;!; B NM =-;!; b +;!; NM =;!; (-b ) NM =;!; HF MN HF '5 ' 9 --c -+b -c b -b 0 =(, )b =(, ) 0 e +e +e () e -e -e (--) 5' (9-) (-89) (0-)5 (--)' b =(a a a )b =(b b b ) (k) b =(ka ka ka ) (b b b ) =ka b +ka b +ka b (kb )=(a a a ) (kb kb kb ) =ka b +ka b +ka b k( b )=k{(a a a ) (b b b )} =k(a b +a b +a b ) =ka b +ka b +ka b (k) b = (kb )=k( b ) p 8 ;#;p c -b BC l BC = (c -b ) = c - b p p BC =l cos -l cos =0 BC 8

22 ' z- = = - z- = = - == ' ;9@; BC SBC=h S=;!; B C sinh S=;!; B C "ç-cos h S=;!;øπ B C - πb C cos h S=;!;øπ B C -(πb C ) BC ;!;øπ B C -(πb C ) - - z+ = = z- = = p 6 0 (, 6, )(, 9, 6) (t, t, t) + - = =z+ - + z- = = - a=0bc+0 - z-z = = b c z a=b=0c+0 = = z + z- =-+= + - = z= 5 - d =(abc) - z- + - =+= = =z - - (abc) (-)=a+b-c=0 (abc) (-)=-a+b+c=0 a:b:c=5:-:7 + + z- = = z- =--= =--= z

23 -+z-=0 z-=0 ++6z-7= z+8=0 (-) (0-) (0-) (00) +-z-6=0 5 (8-) - - z 6 =z=0 =-=- p p 7 n = =() () (-)+(-)+(z-)=0 ++z-9=0 ++z-9= la ll a l' l a h l a p -h l d a n p d n sinh=cos{ -h}= d n p 0 ' (-) +(+) +(z-6) =9 + +z =5 (-) +(+) +(z-) = (-) + +(z-) = z a b a b a b a bz c 5 a(- )b(- )c(z-z ) 0 l=;!;m=n= 0 ' 8 ' 9 0 ' -' - z-5 0 =-= z= z-7=0 -+z+5=0 6+-z-=0 ++z-=0 + z = = - (-) +(+) +(z+) =6 + +z =9 07 +=0 08 H H d =(-) H - - z- = = ` - HH-+z+5=0 - - z- = = =t - =t+ =-t+z=t+ ` 0

(t+)-(-t+)+(t+)+5=0 t=- ` =-=z=0 H (-0) H =" {-(-)} + (- ) +(-0) H =' H 0 % t 0 % H 0 % 09 00km/ cosh= ' ` p ` 07 p z- 08 -+=-= 7' 09 50 0 5'5 0 % cosh 0 % 0 % ' p cm

24 (t+)-(-t+)+(t+)+5=0 t=- ` =-=z=0 H (-0) H =" {-(-)} + (- ) +(-0) H =' H 0 % t 0 % H 0 % 09 00km/ cosh= ' ` p ` 07 p z =-= 7' '5 0 % cosh 0 % 0 % ' p cm ++z=+-z=6-5 = =z = =z+ +=8 - ++z= +-z=6+=8 0 '5 0 {-;@;;$;} 0 ;!; 7+6-9z= a=;!;b=;!;c=;!; 06 B 'B' ' (-0)B'(60) ` B hb 'B' B =5' 'B' =5 B = 'B' cosh 5=5' cosh

25 B b P(z)

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