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October 10

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Limit question

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Is there a nice way to show that ? Trying to turn it into 0/0 and using L'Hôpital's rule seems to just get me stuck in a mess of algebra that doesn't seem to be getting me any closer to the nice answer. Double sharp (talk) 14:57, 10 October 2018 (UTC)[reply]

@Double sharp: One way is to first make the substitution and then let Then, you can write each cosecant as its Laurent series around 0: Then you can take the limit easily. –Deacon Vorbis (carbon • videos) 15:13, 10 October 2018 (UTC)[reply]
(Or better, all that matters here is ). –Deacon Vorbis (carbon • videos) 15:21, 10 October 2018 (UTC)[reply]
@Deacon Vorbis: Thank you for your help; that indeed worked perfectly! Clearly I have some more reading to do. ^_^ Double sharp (talk) 15:24, 10 October 2018 (UTC)[reply]
@Deacon Vorbis: I hope you don't mind that I linked to your answer elsewhere, as this limit came up in a forum discussion I was involved in today. ^_^ Double sharp (talk) 15:44, 10 October 2018 (UTC)[reply]
Naw, no worries. –Deacon Vorbis (carbon • videos) 15:59, 10 October 2018 (UTC)[reply]
Thank you! Double sharp (talk) 16:02, 10 October 2018 (UTC)[reply]