Function Expression :
\[f(x)=\frac{4x^2+7x+1}{x+2} \]Domain
\[\left]-\infty, -2\right[ \cup \left]-2, \infty\right[ \]Limits
\[\lim_{x \rightarrow-\infty}f(x) = -\infty \]\[\lim_{x \overset{<}{\rightarrow-2} }f(x) = -\infty \]
\[\lim_{x \overset{>}{\rightarrow-2} }f(x) = +\infty \]
\[\lim_{x \rightarrow+\infty}f(x) = +\infty \]
\[ \]
Derivate
\[f^{\,\prime}(x)=\frac{8 x + 7}{x + 2} - \frac{4 x^{2} + 7 x + 1}{\left(x + 2\right)^{2}} \]\[f^{\,\prime}(x)=\frac{4 x^{2} + 16 x + 13}{x^{2} + 4 x + 4} \]
\[ \]
Integral
\[F(x) = 2 x^{2} - x + 3 \log{\left(x + 2 \right)} \]Sign Table
Variation Table
Plot
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