Function Expression :
\[f(x)=\frac{e^{(\frac{5}{x} )}}{x-4} \]Domain
\[\left]-\infty, 0\right[ \cup \left]0, 4\right[ \cup \left]4, \infty\right[ \]Limits
\[\lim_{x \rightarrow-\infty}f(x) = 0 \]\[\lim_{x \overset{<}{\rightarrow0} }f(x) = 0 \]
\[\lim_{x \overset{>}{\rightarrow0} }f(x) = -\infty \]
\[\lim_{x \overset{<}{\rightarrow4} }f(x) = -\infty \]
\[\lim_{x \overset{>}{\rightarrow4} }f(x) = +\infty \]
\[\lim_{x \rightarrow+\infty}f(x) = 0 \]
\[ \]
Derivate
\[f^{\,\prime}(x)=- \frac{e^{\frac{5}{x}}}{\left(x - 4\right)^{2}} - \frac{5 e^{\frac{5}{x}}}{x^{2} \left(x - 4\right)} \]\[f^{\,\prime}(x)=\frac{\left(- x^{2} - 5 x + 20\right) e^{\frac{5}{x}}}{x^{2} \left(x^{2} - 8 x + 16\right)} \]
\[ \]
Integral
\[F(x) = \int \frac{e^{\frac{5}{x}}}{x - 4}\, dx \]Sign Table
Variation Table
Plot
Elapsed Time: 0.0031 seconds