Function Expression :
\[f(x)=\frac{(\sqrt{x}-3 )}{2x-2} \]Domain
\[\left[0, 1\right[ \cup \left]1, \infty\right[ \]Limits
\[\lim_{x \overset{>}{\rightarrow0} }f(x) = \frac{3}{2} \]\[\lim_{x \overset{<}{\rightarrow1} }f(x) = +\infty \]
\[\lim_{x \overset{>}{\rightarrow1} }f(x) = -\infty \]
\[\lim_{x \rightarrow+\infty}f(x) = 0 \]
\[ \]
Derivate
\[f^{\,\prime}(x)=- \frac{2 \left(\sqrt{x} - 3\right)}{\left(2 x - 2\right)^{2}} + \frac{1}{2 \sqrt{x} \left(2 x - 2\right)} \]\[f^{\,\prime}(x)=\frac{6 \sqrt{x} - x - 1}{4 \sqrt{x} \left(x^{2} - 2 x + 1\right)} \]
\[ \]
Integral
\[F(x) = \sqrt{x} - \log{\left(\sqrt{x} - 1 \right)} - 2 \log{\left(\sqrt{x} + 1 \right)} \]Sign Table
Variation Table
Plot
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