Function Expression :
\[f(x)=\frac{\sqrt{x}}{x-3} \]Domain
\[\left[0, 3\right[ \cup \left]3, \infty\right[ \]Limits
\[\lim_{x \overset{>}{\rightarrow0} }f(x) = 0 \]\[\lim_{x \overset{<}{\rightarrow3} }f(x) = -\infty \]
\[\lim_{x \overset{>}{\rightarrow3} }f(x) = +\infty \]
\[\lim_{x \rightarrow+\infty}f(x) = 0 \]
\[ \]
Derivate
\[f^{\,\prime}(x)=- \frac{\sqrt{x}}{\left(x - 3\right)^{2}} + \frac{1}{2 \sqrt{x} \left(x - 3\right)} \]\[f^{\,\prime}(x)=\frac{- x - 3}{2 \sqrt{x} \left(x - 3\right)^{2}} \]
\[ \]
Integral
\[F(x) = 2 \sqrt{x} + \sqrt{3} \log{\left(\sqrt{x} - \sqrt{3} \right)} - \sqrt{3} \log{\left(\sqrt{x} + \sqrt{3} \right)} \]Sign Table
Variation Table
Plot
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