Hello Everyone! I have 2 questions that I am extremely stuck on and I was wondering if anyone knew how to help! Anything would be great. Here they are:

(1) Use Bolzano Weierstrass to prove the intermediate value theorem. "If f is a continuous function on a,b and f(a) & f(b) have opposite signs, then there is a point c on (a,b) such that f(c)=0.

(2) Prove that every convergent sequence has an increasing or decreasing subsequence, or maybe both. Do so using the limi as n goes to infinity of x(sub n) is equal to l.

Thank you!