NEW FUNCTION

Function Expression :

\[f(x)=1-\frac{1}{x-2} \]

Domain

\[\left]-\infty, 2\right[ \cup \left]2, \infty\right[ \]

Limits

\[\lim_{x \rightarrow-\infty}f(x) = 1 \]
\[\lim_{x \overset{<}{\rightarrow2} }f(x) = +\infty \]
\[\lim_{x \overset{>}{\rightarrow2} }f(x) = -\infty \]
\[\lim_{x \rightarrow+\infty}f(x) = 1 \]
\[ \]

Derivate

\[f^{\,\prime}(x)=\frac{1}{\left(x - 2\right)^{2}} \]
\[f^{\,\prime}(x)=\frac{1}{\left(x - 2\right)^{2}} \]
\[ \]

Integral

\[F(x) = x - \log{\left(x - 2 \right)} \]

Sign Table


Variation Table


Plot


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