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