Function Expression :
\[f(x)=\frac{2x^3+x^2-1}{x^2} \]Domain
\[\left]-\infty, 0\right[ \cup \left]0, \infty\right[ \]Limits
\[\lim_{x \rightarrow-\infty}f(x) = -\infty \]\[\lim_{x \overset{<}{\rightarrow0} }f(x) = -\infty \]
\[\lim_{x \overset{>}{\rightarrow0} }f(x) = -\infty \]
\[\lim_{x \rightarrow+\infty}f(x) = +\infty \]
\[ \]
Derivate
\[f^{\,\prime}(x)=\frac{6 x^{2} + 2 x}{x^{2}} - \frac{2 \cdot \left(2 x^{3} + x^{2} - 1\right)}{x^{3}} \]\[f^{\,\prime}(x)=2 + \frac{2}{x^{3}} \]
\[f^{\,\prime}(x)=\frac{2 \left(x^{3} + 1\right)}{x^{3}} \]
Integral
\[F(x) = x^{2} + x + \frac{1}{x} \]Sign Table
Variation Table
Plot
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