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