Function Expression :
\[f(x)=\frac{2x-ln x}{2x^{\frac{1}{2}}} \]Domain
\[\left]0, \infty\right[ \]Limits
\[\lim_{x \overset{>}{\rightarrow0} }f(x) = +\infty \]\[\lim_{x \rightarrow+\infty}f(x) = +\infty \]
\[ \]
Derivate
\[f^{\,\prime}(x)=\frac{1}{2 \sqrt{x}} \left(2 - \frac{1}{x}\right) - \frac{x^{\frac{1}{2}} \cdot \left(2 x - \log{\left(x \right)}\right)}{4 x^{2}} \]\[f^{\,\prime}(x)=\frac{2 x + \log{\left(x \right)} - 2}{4 x^{\frac{3}{2}}} \]
\[ \]
Integral
\[F(x) = \frac{2 x^{\frac{3}{2}}}{3} - \sqrt{x} \log{\left(x \right)} + 2 \sqrt{x} \]Sign Table
Variation Table
Plot
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