Function Expression :
\[f(x)=\frac{x^2+12x+2}{x^2-4x+2} \]Domain
\[\left]-\infty, 2 - \sqrt{2}\right[ \cup \left]2 - \sqrt{2}, \sqrt{2} + 2\right[ \cup \left]\sqrt{2} + 2, \infty\right[ \]Limits
\[\lim_{x \rightarrow-\infty}f(x) = 1 \]\[\lim_{x \overset{<}{\rightarrow2 - \sqrt{2}} }f(x) = +\infty \]
\[\lim_{x \overset{>}{\rightarrow2 - \sqrt{2}} }f(x) = -\infty \]
\[\lim_{x \overset{<}{\rightarrow\sqrt{2} + 2} }f(x) = -\infty \]
\[\lim_{x \overset{>}{\rightarrow\sqrt{2} + 2} }f(x) = +\infty \]
\[\lim_{x \rightarrow+\infty}f(x) = 1 \]
\[ \]
Derivate
\[f^{\,\prime}(x)=\frac{\left(4 - 2 x\right) \left(x^{2} + 12 x + 2\right)}{\left(x^{2} - 4 x + 2\right)^{2}} + \frac{2 x + 12}{x^{2} - 4 x + 2} \]\[f^{\,\prime}(x)=\frac{16 \cdot \left(2 - x^{2}\right)}{x^{4} - 8 x^{3} + 20 x^{2} - 16 x + 4} \]
\[ \]
Integral
\[F(x) = x + \left(8 + 8 \sqrt{2}\right) \log{\left(x - 2 - \sqrt{2} \right)} + \left(8 - 8 \sqrt{2}\right) \log{\left(x - 2 + \sqrt{2} \right)} \]Sign Table
Variation Table
Plot
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