Function Expression :
\[f(x)=\sqrt{x^2+8x} \]Domain
\[\left]-\infty, -8\right] \cup \left[0, \infty\right[ \]Limits
\[\lim_{x \rightarrow-\infty}f(x) = +\infty \]\[\lim_{x \overset{<}{\rightarrow-8} }f(x) = 0 \]
\[\lim_{x \overset{>}{\rightarrow0} }f(x) = 0 \]
\[\lim_{x \rightarrow+\infty}f(x) = +\infty \]
\[ \]
Derivate
\[f^{\,\prime}(x)=\frac{x + 4}{\sqrt{x^{2} + 8 x}} \]\[f^{\,\prime}(x)=\frac{x + 4}{\sqrt{x \left(x + 8\right)}} \]
\[ \]
Integral
\[F(x) = \int \sqrt{x^{2} + 8 x}\, dx \]Sign Table
Variation Table
Plot
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