I'm trying to find the following
$$\lim_{n\to \infty} \Bigg(1-\frac{|x|}{\pi}\Bigg)^n$$
Any hints please ?
2026-05-16 19:54:35.1778961275
Find the limit : $\lim_{n\to \infty} \Bigg(1-\frac{|x|}{\pi}\Bigg)^n$
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Hint:
Notice that if $a$ is independent of $n$, then $$\lim_{n \to \infty} a^n= \begin{cases} 0 , & -1 < a < 1 \\ 1, & a=1\\ \text{diverges,} & \text{Otherwise}\end{cases}$$
In the event that $\pi$ is a typo and it is suppose to be $n$, then
$$\lim_{n \to \infty} \left( 1-\frac{|x|}{n}\right)^n=\exp(-|x|)$$