It is proved that when X - > 0, the function 1 / xsin (1 / x) is unbounded, not infinite

It is proved that when X - > 0, the function 1 / xsin (1 / x) is unbounded, not infinite

First of all, prove that there is no bound
For any M > 0, there is always K, satisfying 2K π + π / 2 > m, taking x0 = 1 / (2k π + π / 2),
Then | f (x0) | = | (2k π + π / 2) sin [1 /) | (2k π + π / 2)] | = 2K π + π / 2 > m, so it is unbounded
Let's prove that it's not infinite
For any δ > 0, there is always K, satisfying 1 / 2K π

Elden Ring Premiere

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