Hi. I'm having a problem why v(x+deltaX) and u(x) become V and U respectively.

The problem is highlighted in my calculations:

http://s7.postimage.org/gqdjxm263/MITprodprood.png

Thanks you very much!

I should probably note that the problem ends as the definition:

And I don't understand how they become V and U in the end.

Bonus question: The teacher keeps saying that for example in the quotient rule proof that v(v+deltaV) becomes v^2 because "they are continuous". I just can't get that part either. Thanks.