Function Expression :
\[f(x)=\sqrt{\frac{2x+3}{4x-6}} \]Domain
\[\left]-\infty, - \frac{3}{2}\right] \cup \left]\frac{3}{2}, \infty\right[ \]Limits
\[\lim_{x \rightarrow-\infty}f(x) = \frac{\sqrt{2}}{2} \]\[\lim_{x \overset{<}{\rightarrow- \frac{3}{2}} }f(x) = 0 \]
\[\lim_{x \overset{>}{\rightarrow\frac{3}{2}} }f(x) = +\infty \]
\[\lim_{x \rightarrow+\infty}f(x) = \frac{\sqrt{2}}{2} \]
\[ \]
Derivate
\[f^{\,\prime}(x)=\frac{\sqrt{\frac{2 x + 3}{4 x - 6}} \cdot \left(4 x - 6\right) \left(- \frac{2 \cdot \left(2 x + 3\right)}{\left(4 x - 6\right)^{2}} + \frac{1}{4 x - 6}\right)}{2 x + 3} \]\[f^{\,\prime}(x)=- \frac{3 \sqrt{2} \sqrt{\frac{2 x + 3}{2 x - 3}}}{4 x^{2} - 9} \]
\[ \]
Integral
\[F(x) = \frac{\sqrt{2} \int \sqrt{\frac{2 x}{2 x - 3} + \frac{3}{2 x - 3}}\, dx}{2} \]Sign Table
Variation Table
Plot
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