Function Expression :
\[f(x)=\frac{x^3-1}{x^2-1} \]Domain
\[\left]-\infty, -1\right[ \cup \left]-1, 1\right[ \cup \left]1, \infty\right[ \]Limits
\[\lim_{x \rightarrow-\infty}f(x) = -\infty \]\[\lim_{x \overset{<}{\rightarrow-1} }f(x) = -\infty \]
\[\lim_{x \overset{>}{\rightarrow-1} }f(x) = +\infty \]
\[\lim_{x \overset{<}{\rightarrow1} }f(x) = \frac{3}{2} \]
\[\lim_{x \overset{>}{\rightarrow1} }f(x) = \frac{3}{2} \]
\[\lim_{x \rightarrow+\infty}f(x) = +\infty \]
\[ \]
Derivate
\[f^{\,\prime}(x)=\frac{3 x^{2}}{x^{2} - 1} - \frac{2 x \left(x^{3} - 1\right)}{\left(x^{2} - 1\right)^{2}} \]\[f^{\,\prime}(x)=\frac{x \left(x + 2\right)}{x^{2} + 2 x + 1} \]
\[ \]
Integral
\[F(x) = \frac{x^{2}}{2} + \log{\left(x + 1 \right)} \]Sign Table
Variation Table
Plot
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