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