(adsbygoogle = window.adsbygoogle || []).push({}); lim x->0 (sin x / x) =1......contradiction?

sin(x)/x =1 (limit x to 0)

this is an identity proved by using geometry and squeeze theorem ...right?

now today i came across another question and doing it my way ....gives me two answers;)

the question is limit x-->0 of [ x*sin(1/x)]

my first approach was using the above identity by rewriting the question as follows:

sin(1/x)/(1/x)....it means the same thing and is now in the form so that we can use the identity....so limiting x->0 must give us 1 according to the identity

now i thought to use the squeeze theorem as shown below:

-1≤sin(1/x)≤1

-x≤x*sin(1/x)≤x

now x goes to 0 so:

0≤x*sin(1/x)≤0

so x*sin(1/x)=0 as x goes to 0

now which method which is correct ?

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# Lim x->0 (sin x / x) =1 contradiction?

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