Function Expression :
\[f(x)=\frac{2}{e^x-1} \]Domain
\[\left]-\infty, 0\right[ \cup \left]0, \infty\right[ \]Limits
\[\lim_{x \rightarrow-\infty}f(x) = -2 \]\[\lim_{x \overset{<}{\rightarrow0} }f(x) = -\infty \]
\[\lim_{x \overset{>}{\rightarrow0} }f(x) = +\infty \]
\[\lim_{x \rightarrow+\infty}f(x) = 0 \]
\[ \]
Derivate
\[f^{\,\prime}(x)=- \frac{2 e^{x}}{\left(e^{x} - 1\right)^{2}} \]\[f^{\,\prime}(x)=- \frac{1}{2 \sinh^{2}{\left(\frac{x}{2} \right)}} \]
\[ \]
Integral
\[F(x) = - 2 x + 2 \log{\left(e^{x} - 1 \right)} \]Sign Table
Variation Table
Plot
Elapsed Time: 0.0110 seconds