Function Expression :
\[f(x)=\frac{(3x-6 )}{(5x+2 )} \]Domain
\[\left]-\infty, - \frac{2}{5}\right[ \cup \left]- \frac{2}{5}, \infty\right[ \]Limits
\[\lim_{x \rightarrow-\infty}f(x) = \frac{3}{5} \]\[\lim_{x \overset{<}{\rightarrow- \frac{2}{5}} }f(x) = +\infty \]
\[\lim_{x \overset{>}{\rightarrow- \frac{2}{5}} }f(x) = -\infty \]
\[\lim_{x \rightarrow+\infty}f(x) = \frac{3}{5} \]
\[ \]
Derivate
\[f^{\,\prime}(x)=- \frac{5 \cdot \left(3 x - 6\right)}{\left(5 x + 2\right)^{2}} + \frac{3}{5 x + 2} \]\[f^{\,\prime}(x)=\frac{36}{\left(5 x + 2\right)^{2}} \]
\[ \]
Integral
\[F(x) = \frac{3 x}{5} - \frac{36 \log{\left(5 x + 2 \right)}}{25} \]Sign Table
Variation Table
Plot
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