Function Expression :
\[f(x)=x-\sqrt{x}+\frac{1}{\sqrt{x}} \]Domain
\[\left]0, \infty\right[ \]Limits
\[\lim_{x \overset{>}{\rightarrow0} }f(x) = +\infty \]\[\lim_{x \rightarrow+\infty}f(x) = +\infty \]
\[ \]
Derivate
\[f^{\,\prime}(x)=1 - \frac{1}{2 \sqrt{x}} - \frac{1}{2 \sqrt{x} x} \]\[f^{\,\prime}(x)=1 - \frac{1}{2 \sqrt{x}} - \frac{1}{2 x^{\frac{3}{2}}} \]
\[f^{\,\prime}(x)=\frac{2 x^{\frac{3}{2}} - x - 1}{2 x^{\frac{3}{2}}} \]
Integral
\[F(x) = - \frac{2 x^{\frac{3}{2}}}{3} + 2 \sqrt{x} + \frac{x^{2}}{2} \]Sign Table
Variation Table
Plot
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