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