It is proved that the function y = (1 / x) sin (1 / x) is unbounded in the interval (0,1], but it is not infinite when x tends to positive infinity

When 1 / x = 2K π + π / 2, k > = 0 is an integer
When x = 1 / (2k π + π / 2) -- > 0,
y=2kπ+π/2--->+∞,
Therefore, when X -- > 0, the function is unbounded
When X -- > + ∞, | y | = (1 / x) | sin (1 / x) | 0, so when x tends to positive infinity, the function tends to 0

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