Function Expression :
\[f(x)=\frac{5x}{(x+2 )} \]Domain
\[\left]-\infty, -2\right[ \cup \left]-2, \infty\right[ \]Limits
\[\lim_{x \rightarrow-\infty}f(x) = 5 \]\[\lim_{x \overset{<}{\rightarrow-2} }f(x) = +\infty \]
\[\lim_{x \overset{>}{\rightarrow-2} }f(x) = -\infty \]
\[\lim_{x \rightarrow+\infty}f(x) = 5 \]
\[ \]
Derivate
\[f^{\,\prime}(x)=- \frac{5 x}{\left(x + 2\right)^{2}} + \frac{5}{x + 2} \]\[f^{\,\prime}(x)=\frac{10}{\left(x + 2\right)^{2}} \]
\[ \]
Integral
\[F(x) = 5 x - 10 \log{\left(x + 2 \right)} \]Sign Table
Variation Table
Plot
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