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