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