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