Function Expression :
\[f(x)=\frac{\sqrt{4x-2}}{-x+2} \]Domain
\[\left[\frac{1}{2}, 2\right[ \cup \left]2, \infty\right[ \]Limits
\[\lim_{x \overset{>}{\rightarrow\frac{1}{2}} }f(x) = 0 \]\[\lim_{x \overset{<}{\rightarrow2} }f(x) = +\infty \]
\[\lim_{x \overset{>}{\rightarrow2} }f(x) = -\infty \]
\[\lim_{x \rightarrow+\infty}f(x) = 0 \]
\[ \]
Derivate
\[f^{\,\prime}(x)=\frac{2}{\left(2 - x\right) \sqrt{4 x - 2}} + \frac{\sqrt{4 x - 2}}{\left(2 - x\right)^{2}} \]\[f^{\,\prime}(x)=\frac{\sqrt{2} \left(x + 1\right)}{\left(x - 2\right)^{2} \sqrt{2 x - 1}} \]
\[ \]
Integral
\[F(x) = \begin{cases} - 4 \sqrt{x - \frac{1}{2}} + 2 \sqrt{6} \operatorname{acoth}{\left(\frac{\sqrt{6} \sqrt{x - \frac{1}{2}}}{3} \right)} & \text{for}\: \left|{x - \frac{1}{2}}\right| > \frac{3}{2} \\- 4 \sqrt{x - \frac{1}{2}} + 2 \sqrt{6} \operatorname{atanh}{\left(\frac{\sqrt{6} \sqrt{x - \frac{1}{2}}}{3} \right)} & \text{otherwise} \end{cases} \]Sign Table
Variation Table
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