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