Function Expression :
\[f(x)=ln(2x^2-4x ) \]Domain
\[\left]-\infty, 0\right[ \cup \left]2, \infty\right[ \]Limits
\[\lim_{x \rightarrow-\infty}f(x) = +\infty \]\[\lim_{x \overset{<}{\rightarrow0} }f(x) = -\infty \]
\[\lim_{x \overset{>}{\rightarrow2} }f(x) = -\infty \]
\[\lim_{x \rightarrow+\infty}f(x) = +\infty \]
\[ \]
Derivate
\[f^{\,\prime}(x)=\frac{4 x - 4}{2 x^{2} - 4 x} \]\[f^{\,\prime}(x)=\frac{2 \left(x - 1\right)}{x \left(x - 2\right)} \]
\[ \]
Integral
\[F(x) = x \log{\left(x^{2} - 2 x \right)} - 2 x + x \log{\left(2 \right)} - 2 \log{\left(x - 2 \right)} \]Sign Table
Variation Table
Plot
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