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