Define $f:\mathbb{N} \to \mathbb{R}$ by $f(n)=\frac{sin (\frac{n\pi}{4})}{n}.$
May I know if we can use L'hopital's rule to evaluate $\lim_{n \to 0} f(n)$ ? If not, how can we evaluate the limit without the use of series?
Thank you.
Answer
There is no such ting as $\lim_{n\to0}f(n)$ if $f$ is only defined on $\mathbb N$.
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