Function Expression :
\[f(x)=\sqrt{x^2+6x+1}-(x+3 ) \]Domain
\[\left]-\infty, -3 - 2 \sqrt{2}\right] \cup \left[-3 + 2 \sqrt{2}, \infty\right[ \]Limits
\[\lim_{x \rightarrow-\infty}f(x) = +\infty \]\[\lim_{x \overset{<}{\rightarrow-3 - 2 \sqrt{2}} }f(x) = 2 \sqrt{2} \]
\[\lim_{x \overset{>}{\rightarrow-3 + 2 \sqrt{2}} }f(x) = - 2 \sqrt{2} \]
\[\lim_{x \rightarrow+\infty}f(x) = 0 \]
\[ \]
Derivate
\[f^{\,\prime}(x)=\frac{x + 3}{\sqrt{x^{2} + 6 x + 1}} - 1 \]\[f^{\,\prime}(x)=\frac{x - \sqrt{x^{2} + 6 x + 1} + 3}{\sqrt{x^{2} + 6 x + 1}} \]
\[ \]
Integral
\[F(x) = \int \left(- (x + 3) + \sqrt{x^{2} + 6 x + 1}\right)\, dx \]Sign Table
Variation Table
Plot
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