Function Expression :
\[f(x)=\frac{\sqrt{4x-2}}{\sqrt{-x+2}} \]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
\[f^{\,\prime}(x)=\frac{2}{\sqrt{2 - x} \sqrt{4 x - 2}} + \frac{\sqrt{4 x - 2}}{2 \left(2 - x\right)^{\frac{3}{2}}} \]\[f^{\,\prime}(x)=\frac{3 \sqrt{2}}{2 \left(2 - x\right)^{\frac{3}{2}} \sqrt{2 x - 1}} \]
\[ \]
Integral
\[F(x) = \begin{cases} - \frac{2 \sqrt{2} i \left(x - \frac{1}{2}\right)^{\frac{3}{2}}}{\sqrt{2 x - 4}} + \frac{3 \sqrt{2} i \sqrt{x - \frac{1}{2}}}{\sqrt{2 x - 4}} - 3 i \operatorname{acosh}{\left(\frac{\sqrt{6} \sqrt{x - \frac{1}{2}}}{3} \right)} & \text{for}\: \left|{x - \frac{1}{2}}\right| > \frac{3}{2} \\3 \operatorname{asin}{\left(\frac{\sqrt{6} \sqrt{x - \frac{1}{2}}}{3} \right)} + \frac{2 \sqrt{2} \left(x - \frac{1}{2}\right)^{\frac{3}{2}}}{\sqrt{4 - 2 x}} - \frac{3 \sqrt{2} \sqrt{x - \frac{1}{2}}}{\sqrt{4 - 2 x}} & \text{otherwise} \end{cases} \]Sign Table
Variation Table
Plot
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