A function limit problem in Advanced Mathematics Complete description of the title: Let y = sin1 / x, prove: for any number a ∈ (0,1), try to find the sequence {xn}, such that LIM (n →∞) xn → 0, and lim (n →∞) yn = LIM (n →∞) sin1 / xn = A. and give a geometric explanation for this conclusion

A function limit problem in Advanced Mathematics Complete description of the title: Let y = sin1 / x, prove: for any number a ∈ (0,1), try to find the sequence {xn}, such that LIM (n →∞) xn → 0, and lim (n →∞) yn = LIM (n →∞) sin1 / xn = A. and give a geometric explanation for this conclusion

For any a ∈ (0,1), there exists u ∈ (0, π / 2) such that sinu = a, then u = arcsina
Let xn = 1 / (2n π + U), then Lim [n →∞] xn = 0
yn=sin(1/xn)=sin(2nπ+u)=sinu=a
So yn is always a, then Lim [n →∞] yn = a
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