Function Expression :
\[f(x)=\frac{x^2+2x}{e0.5x} \]Domain
\[\left]-\infty, 0\right[ \cup \left]0, \infty\right[ \]Limits
\[\lim_{x \rightarrow-\infty}f(x) = -\infty \]\[\lim_{x \overset{<}{\rightarrow0} }f(x) = \frac{4}{e} \]
\[\lim_{x \overset{>}{\rightarrow0} }f(x) = \frac{4}{e} \]
\[\lim_{x \rightarrow+\infty}f(x) = +\infty \]
\[ \]
Derivate
\[f^{\,\prime}(x)=\frac{2}{e x} \left(2 x + 2\right) - \frac{2 \left(x^{2} + 2 x\right)}{e x^{2}} \]\[f^{\,\prime}(x)=\frac{2}{e} \]
\[ \]
Integral
\[F(x) = \frac{x^{2}}{e} + \frac{4 x}{e} \]Sign Table
Variation Table
Plot
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