Let x be a real number. Which of the following statements are true?
1
There exists an integer n ≥ 1 such that n2 sin\(\frac{1}{n}\) ≥ x.
2
There exists an integer n ≥ 1 such that n cos\(\frac{1}{n}\) ≥ x.
3
There exists an integer n ≥ 1 such that ne-n ≥ x.
4
There exists an integer n ≥ 2 such that n(log n)-1 ≥ x.