Function Expression :
\[f(x)=-\frac{1}{x. x-2x} \]Domain
\[\left]-\infty, 0\right[ \cup \left]0, 2\right[ \cup \left]2, \infty\right[ \]Limits
\[\lim_{x \rightarrow-\infty}f(x) = 0 \]\[\lim_{x \overset{<}{\rightarrow0} }f(x) = -\infty \]
\[\lim_{x \overset{>}{\rightarrow0} }f(x) = +\infty \]
\[\lim_{x \overset{<}{\rightarrow2} }f(x) = +\infty \]
\[\lim_{x \overset{>}{\rightarrow2} }f(x) = -\infty \]
\[\lim_{x \rightarrow+\infty}f(x) = 0 \]
\[ \]
Derivate
\[f^{\,\prime}(x)=- \frac{2 - 2 x}{\left(\left(-1\right) 2 x + x x\right)^{2}} \]\[f^{\,\prime}(x)=\frac{2 \left(x - 1\right)}{x^{2} \left(2 - x\right)^{2}} \]
\[ \]
Integral
\[F(x) = \frac{\log{\left(x \right)}}{2} - \frac{\log{\left(x - 2 \right)}}{2} \]Sign Table
Variation Table
Plot
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