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