Function infinity and unbounded relationship, the best example. Thank you

Function infinity and unbounded relationship, the best example. Thank you

≫ + infinity, X - & gt; + infinity
But in this case, xcosx = 2Kn * cos2kn = 2Kn is unbounded, that is, xcosx has an unbounded subline, so xcos is unbounded
Let x = 2Kn + n / 2, then when k - & gt; + is infinite, xcosx = 0, that is, xcosx has a subsequence that is not infinite, so it does not approach infinity

Must infinity be an unbounded function
Such as the title

Yes!

Why is the sequence 1,0,2,0,3,0. Unbounded but not infinite

Infinity means that when the number sequence reaches a certain length, the last few digits will be very large and close to infinity;
When the sequence reaches a certain length, some of the last few bits are very large, some are still 0, those very large bits make the sequence unbounded, and those still zero bits make the sequence not infinite