Question

2/v-8

Answer 1

\[\frac{2}{v-8}\]
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Series expansion at V=0
\[-\frac{1}{4}-\frac{V}{32}-\frac{V^2}{256}-\frac{V^3}{2048}-\frac{V^4}{16384}-\frac{V^5}{131072}\]
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Derivative:
\[\frac{d}{dV}\left(\frac{2}{V-8}\right)=-\frac{2}{(V-8)^2}\]
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Indefinite integral
\[\int\limits \frac{2}{V-8} \, dV=2 \ln (V-8)+c\]
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Limit
\[\lim_{V\to \pm \infty } \, \frac{2}{-8+V}=0\]
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Series
\[\frac{2}{-8+V}=\sum _{n=0}^{\infty } V^n (-1) 2^{-2-3 n}\text{ for }|V|<8\]