Function Expression :
\[f(x)=\frac{\sqrt{x-2}+3}{x-1} \]Domain
\[\left[2, \infty\right[ \]Limits
\[\lim_{x \overset{>}{\rightarrow2} }f(x) = 3 \]\[\lim_{x \rightarrow+\infty}f(x) = 0 \]
\[ \]
Derivate
\[f^{\,\prime}(x)=- \frac{\sqrt{x - 2} + 3}{\left(x - 1\right)^{2}} + \frac{1}{2 \sqrt{x - 2} \left(x - 1\right)} \]\[f^{\,\prime}(x)=\frac{- x - 6 \sqrt{x - 2} + 3}{2 \sqrt{x - 2} \left(x^{2} - 2 x + 1\right)} \]
\[ \]
Integral
\[F(x) = 2 \sqrt{x - 2} + 3 \log{\left(x - 1 \right)} - 2 \operatorname{atan}{\left(\sqrt{x - 2} \right)} \]Sign Table
Variation Table
Plot
Elapsed Time: 0.0063 seconds