Hello everyone, I have the following function:

I have to find out its continuity and differentiability in (0,0).

Concerning the continuity:

senxy/xy goes to 1. While the other one:

This is what I did so far, is this correct? If it isn't, why? Concerning the differentiability I'll tell how I did as soon as I understand if I did this right (because if I did this wrong is useless to post the other part!). Thanks a lot!