NEW FUNCTION

Function Expression :

\[f(x)=1-x^2. e^x \]

Domain

\[]-\infty ;+\infty [ \]

Limits

\[\lim_{x \rightarrow-\infty}f(x) = 1 \]
\[\lim_{x \rightarrow+\infty}f(x) = -\infty \]
\[ \]

Derivate

\[f^{\,\prime}(x)=- x^{2} e^{x} - 2 x e^{x} \]
\[f^{\,\prime}(x)=x \left(- x - 2\right) e^{x} \]
\[ \]

Integral

\[F(x) = x + \left(- x^{2} + 2 x - 2\right) e^{x} \]

Sign Table

Variation Table

Plot

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