Function Expression :
\[f(x)=3+\frac{1}{x-3} \]Domain
\[\left]-\infty, 3\right[ \cup \left]3, \infty\right[ \]Limits
\[\lim_{x \rightarrow-\infty}f(x) = 3 \]\[\lim_{x \overset{<}{\rightarrow3} }f(x) = -\infty \]
\[\lim_{x \overset{>}{\rightarrow3} }f(x) = +\infty \]
\[\lim_{x \rightarrow+\infty}f(x) = 3 \]
\[ \]
Derivate
\[f^{\,\prime}(x)=- \frac{1}{\left(x - 3\right)^{2}} \]\[f^{\,\prime}(x)=- \frac{1}{\left(x - 3\right)^{2}} \]
\[ \]
Integral
\[F(x) = 3 x + \log{\left(x - 3 \right)} \]Sign Table
Variation Table
Plot
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