Function Expression :
\[f(x)=\frac{4x+2}{5x-3} \]Domain
\[\left]-\infty, \frac{3}{5}\right[ \cup \left]\frac{3}{5}, \infty\right[ \]Limits
\[\lim_{x \rightarrow-\infty}f(x) = \frac{4}{5} \]\[\lim_{x \overset{<}{\rightarrow\frac{3}{5}} }f(x) = -\infty \]
\[\lim_{x \overset{>}{\rightarrow\frac{3}{5}} }f(x) = +\infty \]
\[\lim_{x \rightarrow+\infty}f(x) = \frac{4}{5} \]
\[ \]
Derivate
\[f^{\,\prime}(x)=- \frac{5 \cdot \left(4 x + 2\right)}{\left(5 x - 3\right)^{2}} + \frac{4}{5 x - 3} \]\[f^{\,\prime}(x)=- \frac{22}{\left(5 x - 3\right)^{2}} \]
\[ \]
Integral
\[F(x) = \frac{4 x}{5} + \frac{22 \log{\left(5 x - 3 \right)}}{25} \]Sign Table
Variation Table
Plot
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