Proving these two statements using Epsilon-Delta

Hi,

I believe I have the right answers for these two questions, but any corrections/clarifications would be very helpful. The two questions, I'm looking at are:

1) Prove that the distance function defined as is continuous. Use the two versions of the triangle inequality.

For this one I proved it using Epsilon=Delta. Is this correct?

2) Prove that the dot product in is continuous. Use Cauchy-Schwartz inequality.

Again, I believe I proved this using Epsilon=Delta. Is this correct as well?

Thanks a lot