Function Expression :
\[f(x)=\frac{x^2+x-6}{x-2} \]Domain
\[\left]-\infty, 2\right[ \cup \left]2, \infty\right[ \]Limits
\[\lim_{x \rightarrow-\infty}f(x) = -\infty \]\[\lim_{x \overset{<}{\rightarrow2} }f(x) = 5 \]
\[\lim_{x \overset{>}{\rightarrow2} }f(x) = 5 \]
\[\lim_{x \rightarrow+\infty}f(x) = +\infty \]
\[ \]
Derivate
\[f^{\,\prime}(x)=\frac{2 x + 1}{x - 2} - \frac{x^{2} + x - 6}{\left(x - 2\right)^{2}} \]\[f^{\,\prime}(x)=1 \]
\[ \]
Integral
\[F(x) = \frac{x^{2}}{2} + 3 x \]Sign Table
Variation Table
Plot
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