1. Prove or give a counterexample: Every sequence of real numbers is a continuous function 2. Consider the formula Let D = {x : f (x) ∈ }. Calculate f (x) for all x ∈ D and determine where f : D → R...

1. Prove or give a counterexample: Every sequence of real numbers is a continuous function

2. Consider the formula

Let D = {x : f (x) ∈
}. Calculate f (x) for all x ∈ D and determine where f : D → R is continuous

3. Define f :

→

by f (x) = 5x if x is rational and f (x) = x²
+ 6 if x is irrational. Prove that f is discontinuous at 1 and continuous at 2. Are there any other points besides 2 at which f is continuous?