IIO 



a) Ponatur (px m log. x; obtinetnr notissima séries, 

 quae " per logarithmum ( i H- ^) ope seriei infinitae ex- 

 primitur : 



h) PonaUir x^z=:<Px', coefficientes seriei, qna Ax 

 exponitur, erimt functiones m; atque x in denominatoreni 

 abit; coëtTicientibas his per F''m, ¥''m, F^'^^m notatis, ob- 

 tinetnr : 



^ = (f/) + r//)^,F^»-4-r^t7F-m etc. . . . 

 positis m :=: 2 ; ACpr, abit in (2xH-Ax)Ax; atque si 

 Axizzi sumatur, obtinetnr factis substitutionibiis commo- 

 dis , séries : 



Z HZ Z . (Z + 1) — 2 . î . Z^ (Z H- i)^ 



~i^^^-^.|.Z4.(Z+i)4 



c) Ponatur Cl)x=zsin.x; prodit 

 Axzn — h ( -) . n te. X 



COS. X ' ^cos.x/ '2 O 



H-0^t4'5+|tg.^:^4-itang.''x] 



