Function Expression :
\[f(x)=\frac{x^2-4x+3}{x^2+3x-4} \]Domain
\[\left]-\infty, -4\right[ \cup \left]-4, 1\right[ \cup \left]1, \infty\right[ \]Limits
\[\lim_{x \rightarrow-\infty}f(x) = 1 \]\[\lim_{x \overset{<}{\rightarrow-4} }f(x) = +\infty \]
\[\lim_{x \overset{>}{\rightarrow-4} }f(x) = -\infty \]
\[\lim_{x \overset{<}{\rightarrow1} }f(x) = - \frac{2}{5} \]
\[\lim_{x \overset{>}{\rightarrow1} }f(x) = - \frac{2}{5} \]
\[\lim_{x \rightarrow+\infty}f(x) = 1 \]
\[ \]
Derivate
\[f^{\,\prime}(x)=\frac{\left(- 2 x - 3\right) \left(x^{2} - 4 x + 3\right)}{\left(x^{2} + 3 x - 4\right)^{2}} + \frac{2 x - 4}{x^{2} + 3 x - 4} \]\[f^{\,\prime}(x)=\frac{7}{x^{2} + 8 x + 16} \]
\[ \]
Integral
\[F(x) = x - 7 \log{\left(x + 4 \right)} \]Sign Table
Variation Table
Plot
Elapsed Time: 0.0039 seconds