Find horizontal asymptotes of f(x)=sin^2(x)/x?

I think that a horizontal asymptote of a curve requires that x->∞.

So we require limit x->∞ of sin²(x)/x and this =0 since |sin²(x)| ≤1.

Some define an asymptote to be tangential to a curve at infinity.

The horizontal asymptote of this function is its value as it approaches infinity. The envelope of sin² is [0,1]. Thus the limit as x → ∞ is 0.

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