Verified answer

Let Δx = h.

lim_{h->0} ((x + h)^2 - x^2)/h

= lim_{h->0} (x^2 + 2xh + h^2 - x^2)/h

= lim_{h->0} (2xh + h^2)/h

= lim_{h->0} 2x + h

= 2x

check out this site:

http://www.wolframalpha.com/input/?i=lim+%CE%94x+-...

usually can get a breakdown of math problems. I suggest using this for instructional purposes only. :)