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