Function Expression :
\[f(x)=\frac{3x^3-3x+1}{x-2} \]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
\[f^{\,\prime}(x)=\frac{9 x^{2} - 3}{x - 2} - \frac{3 x^{3} - 3 x + 1}{\left(x - 2\right)^{2}} \]\[f^{\,\prime}(x)=\frac{6 x^{3} - 18 x^{2} + 5}{x^{2} - 4 x + 4} \]
\[ \]
Integral
\[F(x) = x^{3} + 3 x^{2} + 9 x + 19 \log{\left(x - 2 \right)} \]Sign Table
Variation Table
Plot
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