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