Function Expression :
\[f(x)=\frac{x^2}{x-1}e^{\frac{1}{x}} \]Domain
\[\left]-\infty, 0\right[ \cup \left]0, 1\right[ \cup \left]1, \infty\right[ \]Limits
\[\lim_{x \rightarrow-\infty}f(x) = -\infty \]\[\lim_{x \overset{<}{\rightarrow0} }f(x) = 0 \]
\[\lim_{x \overset{>}{\rightarrow0} }f(x) = -\infty \]
\[\lim_{x \overset{<}{\rightarrow1} }f(x) = -\infty \]
\[\lim_{x \overset{>}{\rightarrow1} }f(x) = +\infty \]
\[\lim_{x \rightarrow+\infty}f(x) = +\infty \]
\[ \]
Derivate
\[f^{\,\prime}(x)=- \frac{x^{2} e^{\frac{1}{x}}}{\left(x - 1\right)^{2}} + \frac{2 x e^{\frac{1}{x}}}{x - 1} - \frac{e^{\frac{1}{x}}}{x - 1} \]\[f^{\,\prime}(x)=\frac{\left(x^{2} - 3 x + 1\right) e^{\frac{1}{x}}}{x^{2} - 2 x + 1} \]
\[ \]
Integral
\[F(x) = \int \frac{x^{2} e^{\frac{1}{x}}}{x - 1}\, dx \]Sign Table
Variation Table
Plot
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