Problem understanding last part of product rule proof

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.

Re: Problem understanding last part of product rule proof

Hey Paze.

It follows directly from the line above: the only difference in the two lines is that the whole thing is now divided by the delta_x (triangle x) term.

Re: Problem understanding last part of product rule proof

Quote:

Originally Posted by

**chiro** Hey Paze.

It follows directly from the line above: the only difference in the two lines is that the whole thing is now divided by the delta_x (triangle x) term.

I still don't understand. It's not supposed to say VX like on my picture, it's supposed to say just V. Which is what baffles me. Also U(x) magically becomes U..