Hey, I need help on a couple of problems in my proof class. If anyone can help, it would be highly appreciated, Thank you!

1. Prove that S = { n−1 |n ∈ N} is bounded above and that its supremumn

is equal to 1.

2.Use the Intermediate Value Theorem to show that the polynomial x4 +

x3 − 9 has at least two real roots.

3.Use the Mean Value Theorem to prove that |sin(b) − sin(a)| ≤ |b − a|

for all a, b ∈ R.