Function Expression :
\[f(x)=\sqrt{x^2+2}-x \]Domain
\[\left]-\infty, \infty\right[ \]Limits
\[\lim_{x \rightarrow-\infty}f(x) = +\infty \]\[\lim_{x \rightarrow+\infty}f(x) = 0 \]
\[ \]
Derivate
\[f^{\,\prime}(x)=\frac{x}{\sqrt{x^{2} + 2}} - 1 \]\[f^{\,\prime}(x)=\frac{x}{\sqrt{x^{2} + 2}} - 1 \]
\[f^{\,\prime}(x)=\frac{x - \sqrt{x^{2} + 2}}{\sqrt{x^{2} + 2}} \]
Integral
\[F(x) = - \frac{x^{2}}{2} + \frac{x \sqrt{x^{2} + 2}}{2} + \operatorname{asinh}{\left(\frac{\sqrt{2} x}{2} \right)} \]Sign Table
Variation Table
Plot
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