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what will be if we find the $\lim_{x\to \infty}(e^{-x} -1 )$ from right side such as

$$\lim_{x\to \infty}(e^{-x}-1) = \lim_{x\rightarrow \infty}\left( - x + \frac{x^2}2 - \frac{x^3}6 + \frac{x^4}{24}-\cdots\right)$$

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    Hmmmm.... That seems to be an objectively terrible idea. Instead, examine the end behavior of $f(x)=e^{-x}-1$ as $x\to\infty$. Use the fact that $e^x$ is a strictly increasing positive function (for $x\in\Bbb R$) that tends to $\infty$ as $x$ tends to $\infty$.2012-09-29

2 Answers 2