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