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