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
\[f^{\,\prime}(x)=- - \frac{1}{x} e^{- x} + \frac{-1 + e^{- x}}{x^{2}} \]\[f^{\,\prime}(x)=\frac{\left(x - e^{x} + 1\right) e^{- x}}{x^{2}} \]
\[ \]
Integral
\[F(x) = \log{\left(- x \right)} - \operatorname{Ei}{\left(- x \right)} \]Sign Table
Variation Table
Plot
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