Function Expression :
\[f(x)=\sqrt{2-\frac{x^2-x-2}{x^2-x+1}} \]Domain
\[\left]-\infty, \infty\right[ \]Limits
\[\lim_{x \rightarrow-\infty}f(x) = 1 \]\[\lim_{x \rightarrow+\infty}f(x) = 1 \]
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Derivate
\[f^{\,\prime}(x)=\frac{\frac{\left(1 - 2 x\right) \left(- x^{2} + x + 2\right)}{2 \left(x^{2} - x + 1\right)^{2}} + \frac{1 - 2 x}{2 \left(x^{2} - x + 1\right)}}{\sqrt{- \frac{x^{2} - x - 2}{x^{2} - x + 1} + 2}} \]\[f^{\,\prime}(x)=\frac{3 \cdot \left(1 - 2 x\right)}{2 \sqrt{\frac{x^{2} - x + 4}{x^{2} - x + 1}} \left(x^{4} - 2 x^{3} + 3 x^{2} - 2 x + 1\right)} \]
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Integral
\[F(x) = \int \sqrt{- \frac{x^{2} - x - 2}{x^{2} - x + 1} + 2}\, dx \]Sign Table
Variation Table
Plot
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