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?


marked as duplicate by Belgi, GEdgar, Did calculus Jan 3 '15 at 15:24

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  • 1
    $\begingroup$ math.stackexchange.com/questions/276135/… $\endgroup$ – math110 Jan 3 '15 at 15:20
  • $\begingroup$ Presumably $x$ and $n$ are somehow related... $\endgroup$ – GEdgar Jan 3 '15 at 15:21
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    $\begingroup$ It should be $n \to +\infty $ instead of $x \to +\infty $, no? $\endgroup$ – Ivo Terek Jan 3 '15 at 15:21
  • $\begingroup$ @IvoTerek yes, sorry. $\endgroup$ – Nivedita Jan 3 '15 at 15:24
  • $\begingroup$ @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? $\endgroup$ – Nivedita Jan 3 '15 at 15:26

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