1. Write a delta - epsilon proof that shows that the function f(x)=3x5 is continuous at x=2

2. Write a delta - epsilon proof that shows that the function f(x)=|x| is continuous on its domain.

3. Use a delta-epsilon definition of continuity to argue that f(x) is or is not continuous at x=2 if f(x)=2x when x is rational and f(x)=x when x is irrational.

4. Write a delta - epsilon proof that shows that the function f(x)=x is continuous on its domain.

5. For what values of ARAR is f(x)f(x) continuous at 2 ?

f(x)={Ax x2

(1A)x x>2]