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Homework Statement:

Prove that if for any two sequences (xn), (yn) Which are sustained lim(ynxn)=0 Happening
limf(yn)f(xn)=0, Then f is uniformly continuous at R (hint: Use proof of Heine–Cantor theorem)
Relevant Equations:
 Heine–Cantor theorem
The first thing I thought about doing was to prove that f is continuous using the Heine–Cantor theorem proof.
But I do not know at all whether it is possible to prove with the data that I have continuous.
I would love to get help.
Thanks
But I do not know at all whether it is possible to prove with the data that I have continuous.
I would love to get help.
Thanks