Question

use the formal definition of a limit to prove that lim (xy)=ab as (x,y) approaches (a,b)

Answer 1

The δ-ε-definition?

Answer 2

\[\delta=\epsilon/2\]

Answer 3

is this a question from a Calc III course?

Answer 4

yes it is

Answer 5

not really sure on this one, but here's a link to a similar question and the formal proof: http://forums.xkcd.com/viewtopic.php?f=17&t=13883

perhaps this can be modified.

Answer 6

thank you!

Answer 7

no problem, good luck! :)

Answer 8

If we base the proof off of the given answer, it appears we should choose
\[\delta = \min(1, \frac{\epsilon}{a+b+1})\]