1. Prove that the function f(x) = x if x is rational, x^2 if x is irrational, is continuous at 1 and discontinuous at 2. 2. Show that if two continuous functions f and g agree on all rational numbers, then they are equal everywhere. 3. Show that if a function f is such that the sequence {f(x_n)} converges whenever {x_n} converges to c, then f is continuous at c.