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