Function Expression :
\[f(x)=1-2+ln\sqrt{x-1} \]Domain
\[\left]1, \infty\right[ \]Limits
\[\lim_{x \overset{>}{\rightarrow1} }f(x) = -\infty \]\[\lim_{x \rightarrow+\infty}f(x) = +\infty \]
\[ \]
Derivate
\[f^{\,\prime}(x)=\frac{1}{2 \left(x - 1\right)} \]\[f^{\,\prime}(x)=\frac{1}{2 \left(x - 1\right)} \]
\[ \]
Integral
\[F(x) = \frac{x \log{\left(x - 1 \right)}}{2} - \frac{3 x}{2} - \frac{\log{\left(x - 1 \right)}}{2} \]Sign Table
Variation Table
Plot
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