Chapter 7.4, Problem 1E

For each sequence x, determine whether x is bounded, bounded above, or bounded below.

1. $x_n=10n$
2. $x_n=\frac{10}{n}$
3. $x_n={10}^{-n}$
4. $x_n={\log }_{10}n$
5. $x_n=\frac{10}{n!}$
6. $x_n=\frac{\cos n}{n}$
7. $x_n=n\tan \left(\frac{3n\pi }{4}\right)$
8. $x_n={\left(-1\right)}^{n}n$
9. $x_n={\left(-0.9\right)}^n$
10. $x_n={\left(-1.1\right)}^n$
11. $x_n=\frac{{\left(-1\right)}^n+1}{n}$
12. $x_n=\frac{\left({\left(-1\right)}^n-1\right)\left({\left(-1\right)}^n+1\right)}{n}$
13. $x_n=n+{\left(-1\right)}^{n}n$
14. $x_n=n\sin \frac{n\pi }{2}$