1) Which Limit Laws would you use to prove Theorem 4 on page 120?
2) Which Limit Laws guarantee that g(x) = [ f (x)]n is continuous whenever f (x) is continuous?
3) Is it true or false that if h(x) = [ f (x)]2
continuous everywhere, then f (x) is continuous everywhere?
If this is true, prove it. If it is false, give a counter example.
4) Revisit Limit Law 11 on page 110. What must be true to be able to pull the limit through (inside) the root?
Is this true? If this is true, prove it otherwise provide a counter example.