1. The problem statement, all variables and given/known data #1. If limit[x->a]f(x) exists, but limit[x->a]g(x) doesnt, limit[x->a](f(x)+g(x)) doesn't exist. T/F? (Proof or example please) #2. prove that if f is continuous, then so is |f| #3. f(x) = [[x]]+[[-x]] for what a does limit[x->a]f(x) exist? Where is f discontinuous? 2. Relevant equations 3. The attempt at a solution #3 confuses me the most; my first thought is the function = 0 for all x so the limit should exist for all a and it should be 0, which means it should be continuous everywhere, but there is a theorem that states if f(x) is disc. on (a,b) and g(x) is disc. on (a, b) then f(x) + g(x) is disc. on (a,b) and since they are both disc. on integer values so should be their sum...so which thought is correct and why?