Function Expression :
\[f(x)=\frac{x^3-1}{(x-2 )^2} \]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
\[f^{\,\prime}(x)=\frac{3 x^{2}}{\left(x - 2\right)^{2}} + \frac{\left(4 - 2 x\right) \left(x^{3} - 1\right)}{\left(x - 2\right)^{4}} \]\[f^{\,\prime}(x)=\frac{- 2 x^{3} + 3 x^{2} \left(x - 2\right) + 2}{\left(x - 2\right)^{3}} \]
\[ \]
Integral
\[F(x) = \frac{x^{2}}{2} + 4 x + 12 \log{\left(x - 2 \right)} - \frac{7}{x - 2} \]Sign Table
Variation Table
Plot
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