What is $lim_(xtooo)(sin2x)/x$ ?

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Answer 1 · 2018-04-13T07:37:28

$0$

Think of this as:
$lim_(xtooo)sin2x*lim_(xtooo)1/x$

As $x$ tends to $oo$ , $1/x$ gets smaller and smaller, until it is effectively $0$

However, $sin(2x)$ can be be anywhere in the range $[-1,1]$ at infinity.

So, we have: $lim_(xtooo)sin2x*lim_(xtooo)1/x=[0(-1),0(1)]=0$

What is lim_(xtooo)(sin2x)/xlim_(xtooo)(sin2x)/x?