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