How do you use the Squeeze Theorem to find $limsin(1/x)$ as x approaches zero?

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How do you use the Squeeze Theorem to find $limsin(1/x)$ as x approaches zero?

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Answer 1 · 2015-09-16T18:10:19

The limit $lim_(x->0)sin(1/x)$ does not exist. You can proove this taking two sequences such as $a_n=1/(2pin)$ and $b_n=1/((2n+1)*pi)$ and replacing into the value of x.Hence

$sin(1/(1/((2pin))))=sin(2*pi*n)=1 or -1$ .Hence the values of the limits both sequences are different such limit does not exist

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How do you use the Squeeze Theorem to find $limsin(1/x)$ as x approaches zero?

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