# How do I solve this limit: $\lim_{x \to \infty } \sqrt{n}\sin(\sin(\sin … (\sin (1))…))$ [duplicate]

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 StackExchange.ready(function() { if (StackExchange.options.isMobile) return; $('.dupe-hammer-message-hover:not(.hover-bound)').each(function() { var$hover = $(this).addClass('hover-bound'),$msg = $hover.siblings('.dupe-hammer-message');$hover.hover( function() { $hover.showInfoMessage('', { messageElement:$msg.clone().show(), transient: false, position: { my: 'bottom left', at: 'top center', offsetTop: -7 }, dismissable: false, relativeToBody: true }); }, function() { StackExchange.helpers.removeMessages(); } ); }); }); Jan 3 '15 at 15:24

• Presumably $x$ and $n$ are somehow related... – GEdgar Jan 3 '15 at 15:21
• It should be $n \to +\infty$ instead of $x \to +\infty$, no? – Ivo Terek Jan 3 '15 at 15:21