Function Expression :
\[f(x)=\frac{x^2-4x^2+3x+1}{(x-2 )^2} \]Domain
\[\left]-\infty, 2\right[ \cup \left]2, \infty\right[ \]Limits
\[\lim_{x \rightarrow-\infty}f(x) = -3 \]\[\lim_{x \overset{<}{\rightarrow2} }f(x) = -\infty \]
\[\lim_{x \overset{>}{\rightarrow2} }f(x) = -\infty \]
\[\lim_{x \rightarrow+\infty}f(x) = -3 \]
\[ \]
Derivate
\[f^{\,\prime}(x)=\frac{3 - 6 x}{\left(x - 2\right)^{2}} + \frac{\left(4 - 2 x\right) \left(\left(-1\right) 4 x^{2} + x^{2} + 3 x + 1\right)}{\left(x - 2\right)^{4}} \]\[f^{\,\prime}(x)=\frac{9 x - 8}{x^{3} - 6 x^{2} + 12 x - 8} \]
\[ \]
Integral
\[F(x) = - 3 x - 9 \log{\left(x - 2 \right)} + \frac{5}{x - 2} \]Sign Table
Variation Table
Plot
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