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