Solving Limit: Cos(xy) - 1 over x^2 y^2

[Kuma]

Homework Statement

question asks:

lim(x,y) -> (0,0)

cos(xy) -1 / [x^2 y^2]

Homework Equations

The Attempt at a Solution

if you multiply the top and bottom by cos(xy) + 1 you get

-[sin^2(xy)/(xy)^2] * [1/cos(xy) + 1]

but in the solution they somehow got rid of the denominator (xy)^2, because if that's there the denominator is still 0. How do you get rid of that?

 

[Dick]

The limit u->0 sin(u)/u=1. So limit u->0 sin(u)^2/u^2=1. That's what they did with the first term.