NEW FUNCTION
Function Expression :
\[f(x)=\frac{6x+2}{5x-2} \]
Domain
\[\left]-\infty, \frac{2}{5}\right[ \cup \left]\frac{2}{5}, \infty\right[ \]
Limits
\[\lim_{x \rightarrow-\infty}f(x) = \frac{6}{5} \]
\[\lim_{x \overset{<}{\rightarrow\frac{2}{5}} }f(x) = -\infty \]
\[\lim_{x \overset{>}{\rightarrow\frac{2}{5}} }f(x) = +\infty \]
\[\lim_{x \rightarrow+\infty}f(x) = \frac{6}{5} \]
\[ \]
Derivate
\[f^{\,\prime}(x)=\frac{6}{5 x - 2} - \frac{5 \cdot \left(6 x + 2\right)}{\left(5 x - 2\right)^{2}} \]
\[f^{\,\prime}(x)=- \frac{22}{\left(5 x - 2\right)^{2}} \]
\[ \]
Integral
\[F(x) = \frac{6 x}{5} + \frac{22 \log{\left(5 x - 2 \right)}}{25} \]
Sign Table
Variation Table
Plot
Elapsed Time: 0.0478 seconds