Function Expression :
\[f(x)=\frac{(x^2-4x+3 )}{(x-2 )^2}-1 \]Domain
\[\left]-\infty, 2\right[ \cup \left]2, \infty\right[ \]Limits
\[\lim_{x \rightarrow-\infty}f(x) = 0 \]\[\lim_{x \overset{<}{\rightarrow2} }f(x) = -\infty \]
\[\lim_{x \overset{>}{\rightarrow2} }f(x) = -\infty \]
\[\lim_{x \rightarrow+\infty}f(x) = 0 \]
\[ \]
Derivate
\[f^{\,\prime}(x)=\frac{\left(4 - 2 x\right) \left(x^{2} - 4 x + 3\right)}{\left(x - 2\right)^{4}} + \frac{2 x - 4}{\left(x - 2\right)^{2}} \]\[f^{\,\prime}(x)=\frac{2}{x^{3} - 6 x^{2} + 12 x - 8} \]
\[ \]
Integral
\[F(x) = \frac{1}{x - 2} \]Sign Table
Variation Table
Plot
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