Function Expression :
\[f(x)=1+(x^2-1 ). e^{-x} \]Domain
\[]-\infty ;+\infty [ \]Limits
\[\lim_{x \rightarrow-\infty}f(x) = +\infty \]\[\lim_{x \rightarrow+\infty}f(x) = 1 \]
\[ \]
Derivate
\[f^{\,\prime}(x)=2 x e^{- x} - \left(x^{2} - 1\right) e^{- x} \]\[f^{\,\prime}(x)=\left(- x^{2} + 2 x + 1\right) e^{- x} \]
\[ \]
Integral
\[F(x) = x + \left(- x^{2} - 2 x - 1\right) e^{- x} \]Sign Table
Variation Table
Plot
Elapsed Time: 0.0152 seconds