Function Expression :
\[f(x)=\frac{x^2-5}{x^2-2x-3} \]Domain
\[\left]-\infty, -1\right[ \cup \left]-1, 3\right[ \cup \left]3, \infty\right[ \]Limits
\[\lim_{x \rightarrow-\infty}f(x) = 1 \]\[\lim_{x \overset{<}{\rightarrow-1} }f(x) = -\infty \]
\[\lim_{x \overset{>}{\rightarrow-1} }f(x) = +\infty \]
\[\lim_{x \overset{<}{\rightarrow3} }f(x) = -\infty \]
\[\lim_{x \overset{>}{\rightarrow3} }f(x) = +\infty \]
\[\lim_{x \rightarrow+\infty}f(x) = 1 \]
\[ \]
Derivate
\[f^{\,\prime}(x)=\frac{2 x}{x^{2} - 2 x - 3} + \frac{\left(2 - 2 x\right) \left(x^{2} - 5\right)}{\left(x^{2} - 2 x - 3\right)^{2}} \]\[f^{\,\prime}(x)=\frac{2 \left(- x^{2} + 2 x - 5\right)}{x^{4} - 4 x^{3} - 2 x^{2} + 12 x + 9} \]
\[ \]
Integral
\[F(x) = x + \log{\left(x^{2} - 2 x - 3 \right)} \]Sign Table
Variation Table
Plot
Elapsed Time: 0.0011 seconds