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