671 - ö^a 



_,,«., ,..- x = (liix = o x=:o 



' -^ ' F (X) = f oi) + (tang (a + du) — tang a) . F' (x) . 

 f (x_), olfe in einzelnen «JjV-UcnA maq «ä i»o^l äfterö ^^^j ^ . 



tnöglic^ n)cr^cn, bcti Wcvtf) v-on a ju fi>»&c»/ bfv) rocl» * _ ' 



«^cm (filc 6ie SBett^e von x innerhalb geiriffcr ©i-cnjcn) J — "" >il^^° vL^^^ 



ein IMaximiim Öcr (louüci-gens in bcc 9\(if)e etatt fiiu p-- ,-<^__ p /t;:^ + n^-^o (,, -l dul — tan» ul F^T^)^ 



6et. e« nui§ nc^tnlid) in fold)en Sauen W gcivoimcne _ (>jjs'^ ,j 1^^^^' ^ r. v o ; v. / • 



SonBcrgcnj an öen gfjid^namigen gactoccn bei einen 2(ct ' , ' ' 



ttc r>ei-loi-eiie (Eonvjcrgcnj an ben gleic^uoraigen gactcrcn vf^'ii' vjr3 ^^"3 



Dec anbern 2trt übevwicgcn. F (x) = F (x) + F'*(x) . Cos« u . d tang u, ba^et 



2(c^n(icf)e ?&etrüd)tungcn fxnben u6ccf)nupt cn ben x = (lu x~o 



nod) ©olbner« gocmcl (ntroicfcUcn unenb(id)cn 9vci[;cn VTx^ — F^ xS 



etfltt. ift d tang u = ——^ ^—^. 



' ° x — o 



F'l^x) . Cos^ u 



Vf. ee|e(f (x) = z = Cos(a + x}, foifl(@tcic^un9i.) ^,^ ^ ^„ 



^_Q ^_o ©ep man FCx) = x, fo erholt man: 



F (x) = F (xT^ (Cos (a + X) - Cos a) t^l^ . ^ tang u = ;\"(~^'u = (^"TT' **'* ^"^ ^'^''""*' 



Sin a 



tid^ au(^ fo i|T. 

 X = o 



©e^4 man F (x) = tang x, fo et^nit man; 



, (Cos(a + x)-Cosa)« . ( -Zrc^^Z". S in a) ©e?t «««« ^ W - ""S '^^ 1" "ijau 



T -;; .Sin 3 ä ' d tans u = tans; u — tan? o dn . ,, 



2 öm a 3 — i: _. __— -, »je worein. 



, (Cos (a + x) — Cos a)' . 7^— r" • Cos =" u ^* " 



■ 2.3 



X = o @e^t man F (x) = Sin x, fo «t^nlt man: 



(— 3 Z'.'c'os» 3 + 2 Z-rCos a . Sin a— Z'". Sin^ a) d tang u Sin du — Sin o _ du „,.„„,. 



+ 



X X* x' 



©c|t man F(x)=e =i+x + — -+ — -4. 



• 22.3 



+ , fo «t^äU man : 



VII. ©c^e f (x) = z = tang . (a + x) , fo t(! (®(ei(^. i.) du^ 



X _ o X = o 3 tang u = i + du + -— + — i = 



F(x) = F(x; + (tang (a + x) — tang a) . Z'.Cos*a+ e« Cos» u 



(tang (a + x) — tan g aj' , du 



+ ^ • = jr-,- , njic }u«or. 



" ~ ^ Unb fo ttciur. 



(— 2 Z' . 5in a Cos ' a + Z" . Cos * a) + 

 (tans (a -I- x) — tan° a)^ 



+ 2.3 



X — o 



. ( 1 2 Z' .Sin*a. Cos* a — 4 Z'TSTn a . CoFÖH- Z'". Cos« a) + 

 + 



Unter anbcrn 33emecFiingen, bcren nf^nlic^c pc^ «ucft 

 fc^on on ben ftuftei- cntiuicfeitcn Steigen mad^en liefen, \\ii\- 

 Un reit {)iec nur fclgenbc onfö^ccn: 



Sffiicb X unenbiid) Itcin onätnommen, }, ©, = du, 

 fo bacf man fag«»: 



