How do I solve this limit: $ \lim_{x \to \infty } \sqrt{n}\sin(\sin(\sin ... (\sin (1))...)) $

Asked Jan 03 '15 at 15:19

Active Jan 03 '15 at 15:23

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I have been strugling a lot to solve this question, but couldn't figure out where to start.

$$ \lim_{x \to \infty } \sqrt{n} . \underbrace {\sin(\sin(\sin ... (\sin (1))...))}_{n...times..} $$

I think maybe I should assume the part inside brackets as $y$.

But what next??

Any hints/suggestions?

edited Jan 03 '15 at 15:23

Asaf Karagila

asked Jan 03 '15 at 15:19

user63762453

1

http://math.stackexchange.com/questions/276135/calculating-lim-n-to-infty-sqrtn-sin-sin-sinx?rq=1 – math110 Jan 03 '15 at 15:20
Presumably $x$ and $n$ are somehow related... – GEdgar Jan 03 '15 at 15:21
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It should be $n \to +\infty $ instead of $x \to +\infty $, no? – Ivo Terek Jan 03 '15 at 15:21
@IvoTerek yes, sorry. – user63762453 Jan 03 '15 at 15:24
@math110 I saw that link but didn't understand the solution as it involves range, domain etc. and more concerned with analysis. Can I xpect a bit easier solution? something more basic? – user63762453 Jan 03 '15 at 15:26

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