Function Expression :
\[f(x)=\frac{2x2+2}{(x+1 )2} \]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
\[f^{\,\prime}(x)=4 \cdot \frac{1}{2} \cdot \frac{1}{x + 1} - \frac{2 x 2 + 2}{2 \left(x + 1\right)^{2}} \]\[f^{\,\prime}(x)=\frac{1}{\left(x + 1\right)^{2}} \]
\[ \]
Integral
\[F(x) = 2 x - \log{\left(x + 1 \right)} \]Sign Table
Variation Table
Plot
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