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