8
Muskr&h.r.rslr EJ \E- @Snt. kctn(org Toutroerrerl"e. au f , (-t-r,r,l-rfR, {(*)= t**,r1i^ rpt*) =E^.*uik" mrt e:#§1«tu'%*, vert. ln uqqgreln@{. f tn= (x+4)e'*- i..*i ?re Tunbt§-ron Q st berels tn dsr tu(Tr u äffili;§ä&n folnerTd.e flur $, kmnrrsn L;rr. ( ryt d* den \,ornp&xen ?our*r[«{f ucn Prl d,.= * $ g,c*tX = * $ *e't-**d* : ; j *n* " - u'ä* u Utr unilerscRdgn ?rxr tdlte, I fr"L( : Q-/ A , @ A [x(r-rortr ,, ätx(,i-k)\ i7*r€x ) Gr)e dxJ x=-lf ! A (r ixrr-ur7ir r 4 ,li"-,r" -iT :ffi«ru.l 1, Lg'x'J tä,,gt^({-FC'J ) 1AiaX=-ri*-_-. ' .---- .X=--ä = = - - (- iiT[r-p) - -iar,r-r.l \ =O, do (xrt-k) Oä-pnodtsch r§] d rr t({ -t.) \itg +lie. ) 4 f =' : (8s:6tf t-k\\ ='Ü : - r) ( cost rr4^ur) r'ffii " ffi]);,*,.,.ffi1)) fii (l-t = L., frcos(nrl-k)) :- -L cos(fl-r4-k)' " +(-1 i I fl,tr-u) ' a*Y#(r;_,-for-a):Ä.ri &Ta(l: k--r , R',,- d,n= xei*c'b*:#jxd, :#tä*,1'= L/r__,1 rrrsE»om,t $rr t asc Tq cr) =,4 tffn,*J.; er ( * iia al)=o 't kez kta I€(x)= T.f., rx) +ffi(x) = ei* * I_ k€z kl4 tkv o ff""l - $ r"l +t'orx) 0rrch T lx(,t-u) dr=*§

r'ffii ffi]);,*,.,.ffi1)) - TU DortmundMuskr&h.r.rslr EJ\E-@Snt. kctn(org Toutroerrerl"e.au f , (-t-r,r,l-rfR, {(*)= t**,r1i^rpt*) =E^.*uik" mrt e:# 1«tu'%*, vert.ln uqqgreln@{.f

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Page 1: r'ffii ffi]);,*,.,.ffi1)) - TU DortmundMuskr&h.r.rslr EJ\E-@Snt. kctn(org Toutroerrerl"e.au f , (-t-r,r,l-rfR, {(*)= t**,r1i^rpt*) =E^.*uik" mrt e:# 1«tu'%*, vert.ln uqqgreln@{.f

Muskr&h.r.rslr EJ

\E-

@Snt. kctn(org Toutroerrerl"e. au f , (-t-r,r,l-rfR, {(*)= t**,r1i^rpt*) =E^.*uik" mrt e:#§1«tu'%*, vert.

ln uqqgreln@{. f tn= (x+4)e'*- i..*i?re Tunbt§-ron Q st berels tn dsr tu(Tr u äffili;§ä&n folnerTd.eflur $, kmnrrsn L;rr. ( ryt d* den \,ornp&xen ?our*r[«{f ucn Prl

d,.= * $ g,c*tX = * $

*e't-**d* : ; j *n* " - u'ä*

u

Utr unilerscRdgn ?rxr tdlte,I fr"L( : Q-/ A ,

@

A [x(r-rortr ,, ätx(,i-k)\i7*r€x ) Gr)e dxJx=-lf -ä! A (r ixrr-ur7ir r 4 ,li"-,r" -iT

:ffi«ru.l 1, Lg'x'J tä,,gt^({-FC'J )1AiaX=-ri*-_-. ' .---- .X=--ä

= = - - (- iiT[r-p) - -iar,r-r.l \ =O, do (xrt-k) Oä-pnodtsch r§]d rr t({ -t.) \itg +lie. )

4 f =' : (8s:6tf t-k\\ ='Ü: - r) ( cost rr4^ur) r'ffii

" ffi]);,*,.,.ffi1))fii (l-t

= L., frcos(nrl-k)) :- -L cos(fl-r4-k)' " +(-1 i Ifl,tr-u) ' a*Y#(r;_,-for-a):Ä.ri

&Ta(l: k--r ,R',,-

d,n= #§ xei*c'b*:#jxd, :#tä*,1'= L/r__,1

rrrsE»om,t $rr

t asc Tq cr) =,4 tffn,*J.; er ( * iia al)=o

't kezkta

I€(x)= T.f., rx) +ffi(x) = ei* * I_k€zkl4

tkvo

ff""l - $ r"l +t'orx) 0rrch

T lx(,t-u)dr=*§

Page 2: r'ffii ffi]);,*,.,.ffi1)) - TU DortmundMuskr&h.r.rslr EJ\E-@Snt. kctn(org Toutroerrerl"e.au f , (-t-r,r,l-rfR, {(*)= t**,r1i^rpt*) =E^.*uik" mrt e:# 1«tu'%*, vert.ln uqqgreln@{.f

AutmbeA, &»uCht st effa-fud-€'tP:iR dWf =-rx^tl I

tP'c*rE+1F =. **'*' vxe'R-cx

@nrt-

@

g-,*,* p,

0

e9

*{cr(z1t«,:a;*

: Qiut(a t6tla

Ir$eß r

I ie,:

G»ucht,

-'

t

(,rpdsrhd$y§

II P: glcor = TLPJ(cJ) rklcu) - frr$rr^,)T[P'J(t^.r) = iurflco) -

>LC'"J(o) = ä,L,r Lx€rr{(o) = ,ä.0,u,c.c)=+ F[xe,",J (.,) :

_rtr f, (fuJ = ai"_(-.L

[1nurendulg d-or TorruSror$ornncs\ch *F ort

F L d'''* p'] (uJ) = FLXE tx\1 [b){€

,F.-," - it» $'cu-rt :

ln rer€ Toururfrcnprmcron 0r{erf

(o(acs- rrffirefle Xs) =,c[y$ (s) der dxusxdj.,t y"u§ct=tVrsy;,=cost, t)o

y'ca) = ^vl ,y, (o)=o_ &)

Es rsl §

( {- r)}r=la, =- t"x yct).LDrpcbrhrdurs:

{,t P x 8} cs) = Kt93 csl' ,({g3 rs)d t y"3 (s) : s"X=r - q@ -*C - suyrs) + s

Page 3: r'ffii ffi]);,*,.,.ffi1)) - TU DortmundMuskr&h.r.rslr EJ\E-@Snt. kctn(org Toutroerrerl"e.au f , (-t-r,r,l-rfR, {(*)= t**,r1i^rpt*) =E^.*uik" mrt e:# 1«tu'%*, vert.ln uqqgreln@{.f

o t{ cos{J rst = A" , t{t'J(s) = 0F v)

Anuendilru dsr lcpke.Tu*{*mcdron m4 ft) -)tt y" ] cr) + t I, t** yc+rl (s) : / { cos*J rst

c=» fXr)+s+& Xs):rio

b) oe»utcht tnverm lc(ffi{rrnsicrmrp/b zu frs)= ;!g*,%,- ' s3+ VSt tQs

?:1.ff_:Tn ery-e tor{rc,rb,'_rct4)$&furs vm r dturch

@ Ntttl§etlen dls Nlorrrus, stnqs.-q: = s( sl Qs +Q)

T li slQs +Q = ts*r)} o[sc ss*Qs1§= s(s*r)zo?ßa u; §::ffi;;ä, b r.r'trrsre.ü:'-*

sa+ Q. A .-, st- t'Yq s!3.

Uoe#i?renhn*,6r.A = ?A= Q. k>.A= äArB=4 t3 g= &4'A +&B +c = o ^& ?+Arc =o=-äFrs):Ä+Ä 3

Tc=_sunu^f

*{{,tl,.i'-:}ilr,.+a) ."ffh ( s*E )

""@ "tttus)+ *L{"c'nJsl -aLt"re-ü 3

:,/{ ä*}e-nts_31n+}Cs)

-s'/'[ +s L

Page 4: r'ffii ffi]);,*,.,.ffi1)) - TU DortmundMuskr&h.r.rslr EJ\E-@Snt. kctn(org Toutroerrerl"e.au f , (-t-r,r,l-rfR, {(*)= t**,r1i^rpt*) =E^.*uik" mrt e:# 1«tu'%*, vert.ln uqqgreln@{.f

Inwme-1

{ Fts)l c+) : ot * *C{t+* sr* o*

@

z'C

,_.4

D,

t*'(ola) affi dos nrdcngs^nßpnmrn y' :e-t( A+ yo ), yä =ö

[:,HW[:$ uYrt T1a"

,T::n0,uuore)ccr rnrü ffimrinnnV.0ro. ndg\Ct$rn

Y,+ (A+y*)

gcf) hU) *

Pry src g,hr.-(r(xi t]Y g,h, q{,qant rP Qd-rnrefi und hryt toVyef{.Er ne yosu'1i i.t .nä&är*ilduc,Cds5 ö : Sg(s)dsäds t

Yo t(=a ö ds i s\-/

) A.. : §e'ds(ä arcfqn (y) - gF,-hng : e*- dte orclony = "*-i"6 Y(tl = {on (ef-,a)

Ztrrn rdsungs,nder vof( a Der Toq4«i:tri dr{rnref$ pür-x€ R\ t r.Y"g I kszJ. porn\ü L=o rrn LosuqQsrndernttl^Wü

,(da e14 =rl,l'i,nbn cr,i eü ;;ä'ür,rrtret*A 6 (-n,Ti) c) ,e$e {p, B)

<o

T: et>o vfe R tsy dres

ffnarn^ctcnq cou Tau, ffiffi

=+) /fu\Trnhrvoll , te [-*,, !^(rr+a))b) &-bucrnt-' Allpnrefiu orfr ür, yn n - vy'* 3, :ett----^./^

€s oi'li- y(r) = Zb§) + ya(ilLr A,,ffi horrq5enursg ' ürnu,*to\- lsg-

Page 5: r'ffii ffi]);,*,.,.ffi1)) - TU DortmundMuskr&h.r.rslr EJ\E-@Snt. kctn(org Toutroerrerl"e.au f , (-t-r,r,l-rfR, {(*)= t**,r1i^rpt*) =E^.*uik" mrt e:# 1«tu'%*, vert.ln uqqgreln@{.f

§ght§; qorno&ne {tg.utr brdrr\m dp }.rutssthnndl} churohh -fW^ p(A)=

^{- eA+3

Es grll-, p(^)=o c= [^o-(f ^

+q) -! +B =eLa ( Ä-cla =/16

^-- &t/1 =3 OdOr

^= &--/ =,1

=ä lt'grrert (sgctor horno6na,n @{chunO § sornrh),h (O = q e5** q.et , ä,c.€tp betre$

{§g\§ ?orürkutdre r1g.4ltq#"hksif : Vanqhch det t«a^rs-tontengr(Wrcnkt,. Spaettler frnsafu, ye(f) =,A{ef mt AeR

%t{) ts#r-e& donn,sg dg} lnhtrno6n0n ?roffi*s,(arrn ye,, ,r) _ A 4,+) * 34 (t) = eF E:Fs,qiji-:- ü 1' c0 = Aer* /teL ,4 et (l+11

/r" r l)lllso is) h I?'e'

C€F

ALso

e) -JA= A=o e- As -*

,4e+ (a++) - ? AE ffl*1)

* 3A1EF : efAtaut) - +^(r+r)+ 34+ =A

L( 1__!/ + 34) + fi(o - v) =- t

ntöu tsn yp(fl) : - {nn anepordr"«rtire dp3§qU§ : fl lE rnerrv xr*r, l*,

Y &) = Y,ft) * x(r) = cräun + cnet -*lf*f ) cr,e6R kkug

tsü

@

Page 6: r'ffii ffi]);,*,.,.ffi1)) - TU DortmundMuskr&h.r.rslr EJ\E-@Snt. kctn(org Toutroerrerl"e.au f , (-t-r,r,l-rfR, {(*)= t**,r1i^rpt*) =E^.*uik" mrt e:# 1«tu'%*, vert.ln uqqgreln@{.f

ftulqoh-s @

-

Qqachh, fuuUu fundmrcunhh,Akm du * = (X [ )f-_-z^. - .\-lMll-''u-.--Üvl\l|l x.z\zr-

r§üniü BmLylnury &r e6znb€{"Eiro}n A =7*0 = prz\) :3 drf ( A-arl : dp{-(yr\) : (&-afug

C:) ( Ä-"?)a= -$ €: ,\ = & t &ri)cmiü,srnd Äa=&"&r, &=d.-ar 4eLrctb kcn@re {*(ofu)^,att§)etbn

t rnc{ dornrt r,gnnu#..ää.&Schlt{ trr,«nwb.bau .A,^=**ai,o[so eln f = (UJ) r-nr{,-^ (ä fi*-nirc),2

= öi(:o

( i' :' ) (YJ) : (3) c€ :':y,*QK = o (€ v= *,( = -ir,,vn, _ V4 _ Qt,q=6

Irl I te F 6r nuekoaen (p*6nxl snc y,nßm. rön l:; = i:^r;

= Erneson@,e$ d$ sUSbß\, j gq;l =t;")

3fuA eoz[teDTS

da+aix (-Xi) {? cos(a+)* ßrncor)( i' )

zuhrcch'rgh sne( cry 6«7ripfu* &a^uywnrn\ratea) *S ( A +

"+ ) at,' b) S rozrsrnt)d?, Lrbo ldo.qatr?-'rt =t \ t-l r+/ / "'' r D)

d,';;ä;. i?(=& rsü (posrhvor.)

6fur rfl c{sr unhrcn HotEbire h$

:et, ('&srn(ac')- ö"Zcosfart\ _ oef 1asinforl\ A+l_,lacs(ap\ .os(or)+rsn(a+) /-\-]_grrrnlf *,: \SD(Q*),

br tdan ern r€r[tes f,s.

Page 7: r'ffii ffi]);,*,.,.ffi1)) - TU DortmundMuskr&h.r.rslr EJ\E-@Snt. kctn(org Toutroerrerl"e.au f , (-t-r,r,l-rfR, {(*)= t**,r1i^rpt*) =E^.*uik" mrt e:# 1«tu'%*, vert.ln uqqgreln@{.f

eu e)

%stnq«:Wrßet

De Tutn&$lon * ,d hobnprü

ry( C\{al, rnslwscndsre e*{-doq vCn lt+,rl=l umfonAdehßeb§{-,

Ccutchu-*'\ S äA, _Clnqrohou l?+.l=,1

Oefunkfrcn *i ,s, hr{oTrprolra$.1, oomD\e l"(trvue l?+41=l uTtciqp d.lnflrY$S

C h6rnmPh.Vrq -- -A

nct t L €loTfio\ trrnlsl.orurn .

§**i}+.4l = 4

2-

CEdt: f z-(-,r)l?+,t l=1

i, t *)df :

, -^: äTIt g

§(l?+41 ='t

009 1-

Oiit.o\-

q,i,o

tt+ 4!1

lnsglcmt {cp}

?re Tunkrrorr t\ srnt sl auf Qon? Choeornorp, nflrf SarnmtU+

t \l

F(z) = Jr' - cos?. Scmtt ,gill- ncrt ds.mlücuurplsahr (t1r ß.onpexe örwn rnsote.

Ser P()) = äffi) .

A) EeNrnrc\e dte SQßr(.onlq,+en uon Y und- dre 0q&dum.E-S tst Z(?L+?-e) =O Gl Q=o Cdsf ?'tt-Q. -O

*>d b t=o o@r (? "ä)" - i -A =o

nu/qcbq .7

e-- A

Page 8: r'ffii ffi]);,*,.,.ffi1)) - TU DortmundMuskr&h.r.rslr EJ\E-@Snt. kctn(org Toutroerrerl"e.au f , (-t-r,r,l-rfR, {(*)= t**,r1i^rpt*) =E^.*uik" mrt e:# 1«tu'%*, vert.ln uqqgreln@{.f

e> (7+ i)*: a) ?=-§+f=/odgr?=-*-ä=-Q, @oJ(j

ocrnrt $nd de isüsfbn rybn{-c$envcn F \,=crä=l,§=d

Dcber snd k=,t ur,rct h=-0?{mtffi / Qrdnunound Z,q=q_rst€rru I''rSbo* Srpr(clnh{,da u

-" d-4 : f 2r-a:]-,%--:* bl "z _ ,f=; k! '=' L ä, , a(so hc«:mor$

RB,urdu€fi;---%-- res#(+rHu + =o rffiryrffi.r'o)

res,Jtt)= resnfc,H*u 4y^c"-r)f(?)= /un *.

t->,t ZfaU)

3*tf,*)= Esofl?) @ Zro [?+c1fl(1)- &rn fu: g L

t-» I n a:) -ol ?(3-l)

e5ffi",r: e -r€

b) @sS s f,rrdzlb-a1 =q

ote [arrw t]-rl.Q -,ry?!^#t dre SrphnLi{,rr?, t srn,mot /rnlrslranmn.

^ , . --' LJCl Y't I l.

lQ)tduen .souä ,),Yl.ld+

- &rrt'(ftqf(?)+§f,ur) :&iii e-.1n\,

= aznte-r1i