By A. E. Maurice

A finished software for combating and fixing a spread of moisture difficulties in residential and commmercial basements. particular directions and illustrations on themes together with French drains, leaking basement home windows, stone foundations, downgrade slopes, downspout water, radon, water seepage and extra.

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Konv. f. alle x -I)•I I I x+v :§x+n+I :§n+I' n ( ~ 0 gleichmäßig ist. ~1 37. Nach d. ~o 38. " 1 2 --dx s x - (n + I) n I <-- j" e-s(x+•"> n+I · :rr sinx e-sx x dx = 0 sinx dx x+vn tb d t, 353 L § 8. Funktionenfolgen und Funktionenreihen mit wachsendem v abnimmt, gilt nach d. Leibnizschen Kriterium f (•f+l)n e-sx sinx dx I ~ I" e-s(x+(n+l)n) sinx dx < I/(8)- v=l x x+(n+l)n vn _l_ • n+l 0 39. Wegen l l L -~ 1+-, v=1V 8-l 00 8 40. _) dx. v• x• v• V x• V Hier ist nach d. MWS d. -Rechnung l v• l X-'V x• (x+ 1J)s+1 --- = 8 u.

D. -Darstellung folgt, wenn m. -Variable einführt. D. Formel (I) folgt X dann direkt aus A 75 § 6. , daß aus (3} f. n = 0 u. o = (1-t)ndt l+t' 0 woraus d. Beh. nach A75 § 6 u. A62 § 7 folgt. 67. (3) folgt aus (1) f. k = 1. Ersetzt m. +l ==> 0 (v-.. oo, k ~ 0); ersetzt m. - oo, k ~ 0). Durch Subtraktion v. (I') v. (I") folgt (4). (3) u. + 2k+l-d• ==> 0. Wird in d. +2k-dv-l ==> 0 u. wegen d. + 2 k- d. ==> 0. Damit gilt allgemein dr+s- d. ==> 0 (v -.. oo, s ganz ~ 0 ). Das ist aber d. Cauchy-Bolzanosche Kriterium.

Wie schon in L 103 benutzt wurde. 106. Nach A 103 genügt es, d. Konv. v. _ 1 ( (J(8v-1)-g(8. , u. d. Reihe rechts ist offenbar konv. 107. D. J - - 8v 8v-1 •=2 8, •- 1) · g(x) nimmt mit wachsendem x monoton ab, u. m. ---x g(x) dx = s· (x1) X2 no "• so daß A 106 anwendbar ist. f dx = f1/no f(x) dx, lfv 108. Denn es ist nach d. "endlichen" Hölderschen Ungl. (§ 21 Bd. I): L § 7. Unendliche Reihen e= I09. D. Höldersche Ungl. liefert f. llO. Daher konv. d. ) a•. Andererseits ist •=2 •=1 1) a. e. Majorante v.

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