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