Function Expression :
\[f(x)=\frac{x+1}{\sqrt{1-x}} \]Domain
\[\left]-\infty, 1\right[ \]Limits
\[\lim_{x \rightarrow-\infty}f(x) = -\infty \]\[\lim_{x \overset{<}{\rightarrow1} }f(x) = +\infty \]
\[ \]
Derivate
\[f^{\,\prime}(x)=\frac{1}{\sqrt{1 - x}} + \frac{x + 1}{2 \left(1 - x\right)^{\frac{3}{2}}} \]\[f^{\,\prime}(x)=\frac{3 - x}{2 \left(1 - x\right)^{\frac{3}{2}}} \]
\[ \]
Integral
\[F(x) = \begin{cases} - \frac{2 i \sqrt{x - 1} \left(x + 1\right)}{3} - \frac{8 i \sqrt{x - 1}}{3} & \text{for}\: \left|{x + 1}\right| > 2 \\- \frac{2 \sqrt{1 - x} \left(x + 1\right)}{3} - \frac{8 \sqrt{1 - x}}{3} & \text{otherwise} \end{cases} \]Sign Table
Variation Table
Plot
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