Function Expression :
\[f(x)=x-1-2\sqrt{x-1} \]Domain
\[\left[1, \infty\right[ \]Limits
\[\lim_{x \overset{>}{\rightarrow1} }f(x) = 0 \]\[\lim_{x \rightarrow+\infty}f(x) = +\infty \]
\[ \]
Derivate
\[f^{\,\prime}(x)=1 - \frac{1}{\sqrt{x - 1}} \]\[f^{\,\prime}(x)=1 - \frac{1}{\sqrt{x - 1}} \]
\[f^{\,\prime}(x)=\frac{\sqrt{x - 1} - 1}{\sqrt{x - 1}} \]
Integral
\[F(x) = \frac{x^{2}}{2} - x - \frac{4 \left(x - 1\right)^{\frac{3}{2}}}{3} \]Sign Table
Variation Table
Plot
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