Function Expression :
\[f(x)=\frac{1}{x^2}e^{\frac{1}{x}} \]Domain
\[\left]-\infty, 0\right[ \cup \left]0, \infty\right[ \]Limits
\[\lim_{x \rightarrow-\infty}f(x) = 0 \]\[\lim_{x \overset{<}{\rightarrow0} }f(x) = 0 \]
\[\lim_{x \overset{>}{\rightarrow0} }f(x) = +\infty \]
\[\lim_{x \rightarrow+\infty}f(x) = 0 \]
\[ \]
Derivate
\[f^{\,\prime}(x)=- \frac{e^{\frac{1}{x}}}{x^{2} x^{2}} - \frac{2 e^{\frac{1}{x}}}{x^{3}} \]\[f^{\,\prime}(x)=\frac{\left(- 2 x - 1\right) e^{\frac{1}{x}}}{x^{4}} \]
\[ \]
Integral
\[F(x) = - e^{\frac{1}{x}} \]Sign Table
Variation Table
Plot
Elapsed Time: 0.0027 seconds