Function Expression :
\[f(x)=\frac{x^4-16}{x+2} \]Domain
\[\left]-\infty, -2\right[ \cup \left]-2, \infty\right[ \]Limits
\[\lim_{x \rightarrow-\infty}f(x) = -\infty \]\[\lim_{x \overset{<}{\rightarrow-2} }f(x) = -32 \]
\[\lim_{x \overset{>}{\rightarrow-2} }f(x) = -32 \]
\[\lim_{x \rightarrow+\infty}f(x) = +\infty \]
\[ \]
Derivate
\[f^{\,\prime}(x)=\frac{4 x^{3}}{x + 2} - \frac{x^{4} - 16}{\left(x + 2\right)^{2}} \]\[f^{\,\prime}(x)=3 x^{2} - 4 x + 4 \]
\[ \]
Integral
\[F(x) = \frac{x^{4}}{4} - \frac{2 x^{3}}{3} + 2 x^{2} - 8 x \]Sign Table
Variation Table
Plot
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