Function Expression :
\[f(x)=\frac{(x-1 )^2-1}{(x-1 )^2} \]Domain
\[\left]-\infty, 1\right[ \cup \left]1, \infty\right[ \]Limits
\[\lim_{x \rightarrow-\infty}f(x) = 1 \]\[\lim_{x \overset{<}{\rightarrow1} }f(x) = -\infty \]
\[\lim_{x \overset{>}{\rightarrow1} }f(x) = -\infty \]
\[\lim_{x \rightarrow+\infty}f(x) = 1 \]
\[ \]
Derivate
\[f^{\,\prime}(x)=\frac{\left(2 - 2 x\right) \left(\left(x - 1\right)^{2} - 1\right)}{\left(x - 1\right)^{4}} + \frac{2 x - 2}{\left(x - 1\right)^{2}} \]\[f^{\,\prime}(x)=\frac{2}{\left(x - 1\right)^{3}} \]
\[ \]
Integral
\[F(x) = x + \frac{1}{x - 1} \]Sign Table
Variation Table
Plot
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