Function Expression :
\[f(x)=1-\frac{7x+13}{(x+1 )^3} \]Domain
\[\left]-\infty, -1\right[ \cup \left]-1, \infty\right[ \]Limits
\[\lim_{x \rightarrow-\infty}f(x) = 1 \]\[\lim_{x \overset{<}{\rightarrow-1} }f(x) = +\infty \]
\[\lim_{x \overset{>}{\rightarrow-1} }f(x) = -\infty \]
\[\lim_{x \rightarrow+\infty}f(x) = 1 \]
\[ \]
Derivate
\[f^{\,\prime}(x)=- \frac{3 \left(- 7 x - 13\right)}{\left(x + 1\right)^{4}} - \frac{7}{\left(x + 1\right)^{3}} \]\[f^{\,\prime}(x)=\frac{2 \cdot \left(7 x + 16\right)}{\left(x + 1\right)^{4}} \]
\[ \]
Integral
\[F(x) = x + \frac{7 x + 10}{x^{2} + 2 x + 1} \]Sign Table
Variation Table
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