Function Expression :
\[f(x)=\sqrt{\frac{3x^2+1}{x-1}} \]Domain
\[\left]1, \infty\right[ \]Limits
\[\lim_{x \overset{>}{\rightarrow1} }f(x) = +\infty \]\[\lim_{x \rightarrow+\infty}f(x) = +\infty \]
\[ \]
Derivate
\[f^{\,\prime}(x)=\frac{\sqrt{\frac{3 x^{2} + 1}{x - 1}} \left(x - 1\right) \left(\frac{3 x}{x - 1} - \frac{3 x^{2} + 1}{2 \left(x - 1\right)^{2}}\right)}{3 x^{2} + 1} \]\[f^{\,\prime}(x)=\frac{\sqrt{\frac{3 x^{2} + 1}{x - 1}} \left(- 3 x^{2} + 6 x \left(x - 1\right) - 1\right)}{2 \left(x - 1\right) \left(3 x^{2} + 1\right)} \]
\[ \]
Integral
\[F(x) = \int \sqrt{\frac{3 x^{2} + 1}{x - 1}}\, dx \]Sign Table
Variation Table
Plot
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