Function Expression :
\[f(x)=\sqrt{\frac{(4x-2 )}{-x+2}} \]Domain
\[\left[\frac{1}{2}, 2\right[ \]Limits
\[\lim_{x \overset{>}{\rightarrow\frac{1}{2}} }f(x) = 0 \]\[\lim_{x \overset{<}{\rightarrow2} }f(x) = +\infty \]
\[ \]
Derivate
\[f^{\,\prime}(x)=\frac{\sqrt{\frac{4 x - 2}{2 - x}} \left(2 - x\right) \left(\frac{2}{2 - x} + \frac{4 x - 2}{2 \left(2 - x\right)^{2}}\right)}{4 x - 2} \]\[f^{\,\prime}(x)=- \frac{3 \sqrt{2} \sqrt{- \frac{2 x - 1}{x - 2}}}{4 x^{2} - 10 x + 4} \]
\[f^{\,\prime}(x)=- \frac{3 \sqrt{2} \sqrt{- \frac{2 x - 1}{x - 2}}}{2 \cdot \left(2 x^{2} - 5 x + 2\right)} \]
Integral
\[F(x) = \sqrt{2} \int \sqrt{\frac{2 x}{2 - x} - \frac{1}{2 - x}}\, dx \]Sign Table
Variation Table
Plot
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