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