Let

Q:

a) Prove that g is continuous at c=0

b) Prove that g is continuous at a point . (The identity will be helpful.)

A: a) Let . Then, we have to show that, if it follows that

.

So, if , then implies . Therefore, is ontinuous at 0.

b) Given I am not sure about the first part, I am pretty stuck on the (b). I am not sure how to use the identity in my scratch work; I keep hitting a brick wall. Some help would be great.

Thanks