Function Expression :
\[f(x)=(2x-1 )e^{\frac{1}{x}}+4 \]Domain
\[\left]-\infty, 0\right[ \cup \left]0, \infty\right[ \]Limits
\[\lim_{x \rightarrow-\infty}f(x) = -\infty \]\[\lim_{x \overset{<}{\rightarrow0} }f(x) = 4 \]
\[\lim_{x \overset{>}{\rightarrow0} }f(x) = -\infty \]
\[\lim_{x \rightarrow+\infty}f(x) = +\infty \]
\[ \]
Derivate
\[f^{\,\prime}(x)=2 e^{\frac{1}{x}} - \frac{\left(2 x - 1\right) e^{\frac{1}{x}}}{x^{2}} \]\[f^{\,\prime}(x)=\frac{\left(2 x^{2} - 2 x + 1\right) e^{\frac{1}{x}}}{x^{2}} \]
\[ \]
Integral
\[F(x) = x^{2} e^{\frac{1}{x}} + 4 x \]Sign Table
Variation Table
Plot
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