Function Expression :
\[f(x)=\frac{x-2ln x}{x} \]Domain
\[\left]0, \infty\right[ \]Limits
\[\lim_{x \overset{>}{\rightarrow0} }f(x) = +\infty \]\[\lim_{x \rightarrow+\infty}f(x) = 1 \]
\[ \]
Derivate
\[f^{\,\prime}(x)=\frac{1 - \frac{2}{x}}{x} - \frac{x - 2 \log{\left(x \right)}}{x^{2}} \]\[f^{\,\prime}(x)=\frac{2 \left(\log{\left(x \right)} - 1\right)}{x^{2}} \]
\[ \]
Integral
\[F(x) = x - \log{\left(x \right)}^{2} \]Sign Table
Variation Table
Plot
Elapsed Time: 0.0142 seconds