Function Expression :
\[f(x)=\frac{1}{3-x}+\sqrt{2x-2} \]Domain
\[\left[1, 3\right[ \cup \left]3, \infty\right[ \]Limits
\[\lim_{x \overset{>}{\rightarrow1} }f(x) = \frac{1}{2} \]\[\lim_{x \overset{<}{\rightarrow3} }f(x) = +\infty \]
\[\lim_{x \overset{>}{\rightarrow3} }f(x) = -\infty \]
\[\lim_{x \rightarrow+\infty}f(x) = +\infty \]
\[ \]
Derivate
\[f^{\,\prime}(x)=\frac{1}{\sqrt{2 x - 2}} + \frac{1}{\left(3 - x\right)^{2}} \]\[f^{\,\prime}(x)=\frac{1}{\sqrt{2 x - 2}} + \frac{1}{\left(x - 3\right)^{2}} \]
\[f^{\,\prime}(x)=\frac{\sqrt{2} \left(x - 3\right)^{2} + 2 \sqrt{x - 1}}{2 \left(x - 3\right)^{2} \sqrt{x - 1}} \]
Integral
\[F(x) = \frac{\left(2 x - 2\right)^{\frac{3}{2}}}{3} - \log{\left(3 - x \right)} \]Sign Table
Variation Table
Plot
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