1. In order to make continuous at , the function needs to satisfy the following conditions:

(1) is defined;

(2) exists; and

(3)

To satisfy (1), consider , we need is defined.

To satisfy (2), we need to make sure both and exist, also .

Here we have and .

So we need and .

To satisfy (3), realize that from above, if exists then . Also we have , hence .

In summary, in order to make continuous at , function has to satisfy .

2. Given that , so in order to make differentiable at , we need to show the limit exists. More specifically, we need to show the one-sided limits and exist and are equal. Can you pick up from here?

Roy