Function Expression :
\[f(x)=\frac{-2x^2+5x+1}{3-x} \]Domain
\[\left]-\infty, 3\right[ \cup \left]3, \infty\right[ \]Limits
\[\lim_{x \rightarrow-\infty}f(x) = -\infty \]\[\lim_{x \overset{<}{\rightarrow3} }f(x) = -\infty \]
\[\lim_{x \overset{>}{\rightarrow3} }f(x) = +\infty \]
\[\lim_{x \rightarrow+\infty}f(x) = +\infty \]
\[ \]
Derivate
\[f^{\,\prime}(x)=\frac{5 - 4 x}{3 - x} + \frac{\left(-1\right) 2 x^{2} + 5 x + 1}{\left(3 - x\right)^{2}} \]\[f^{\,\prime}(x)=\frac{2 \left(x^{2} - 6 x + 8\right)}{x^{2} - 6 x + 9} \]
\[ \]
Integral
\[F(x) = x^{2} + x + 2 \log{\left(x - 3 \right)} \]Sign Table
Variation Table
Plot
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