Misplaced Pages

This is an old revision of this page, as edited by Hayson1991 (talk | contribs) at 02:31, 11 April 2008. The present address (URL) is a permanent link to this revision, which may differ significantly from the current revision.

${\displaystyle f(x)=\ln(5-x)\,}$
${\displaystyle {\frac {d}{dx}}f(x)=-{\frac {1}{5-x}}=-{\frac {1}{1-(x-4)}}=-\sum _{n=0}^{\infty }(x-4)^{n}\,}$
${\displaystyle \int df(x)=\int \left(-\sum _{n=0}^{\infty }(x-4)^{n}\right)dx\,}$
${\displaystyle f(x)=C-\sum _{n=0}^{\infty }{\frac {(x-4)^{n+1}}{n+1}}\,}$
${\displaystyle f(x)=C-\sum _{n=1}^{\infty }{\frac {(x-4)^{n}}{n}}\,}$