For problem 1, the proof is obvious by definition. If then are all continuous. Let . Now, what are in terms of ? What does that tell you about 's differentiability class?
I have no ideas for problems 2-4.
For problem 1, the proof is obvious by definition. If then are all continuous. Let . Now, what are in terms of ? What does that tell you about 's differentiability class?
I have no ideas for problems 2-4.