Function Expression :
\[f(x)=\frac{8(x-2 )(x^2-2x+4 )e^{x-4}}{x^3} \]Domain
\[\left]-\infty, 0\right[ \cup \left]0, \infty\right[ \]Limits
\[\lim_{x \rightarrow-\infty}f(x) = 0 \]\[\lim_{x \overset{<}{\rightarrow0} }f(x) = +\infty \]
\[\lim_{x \overset{>}{\rightarrow0} }f(x) = -\infty \]
\[\lim_{x \rightarrow+\infty}f(x) = +\infty \]
\[ \]
Derivate
\[f^{\,\prime}(x)=\frac{\left(2 x - 2\right) \left(8 x - 16\right) e^{x - 4} + \left(8 x - 16\right) \left(x^{2} - 2 x + 4\right) e^{x - 4} + \left(8 x^{2} - 16 x + 32\right) e^{x - 4}}{x^{3}} - \frac{24 \left(x - 2\right) \left(x^{2} - 2 x + 4\right) e^{x - 4}}{x^{4}} \]\[f^{\,\prime}(x)=\frac{8 \left(x^{4} - 4 x^{3} + 12 x^{2} - 24 x + 24\right) e^{x - 4}}{x^{4}} \]
\[ \]
Integral
\[F(x) = \frac{\left(8 x^{2} - 32 x + 32\right) e^{x - 4}}{x^{2}} \]Sign Table
Variation Table
Plot
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