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求极限lim(x,y)→(0,0) [1-cos(xy)]/xy^2

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求极限lim(x,y)→(0,0) [1-cos(xy)]/xy^2
求极限lim(x,y)→(0,0) [1-cos(xy)]/xy^2,麻烦写下过程
0/0型,要用洛必达法则了.
lim((x,y)→(0,0)) (1 - cos(xy))/(xy²)
= lim((x,y)→(0,0)) - [(- ysin(xy)dx) + (- xsin(xy)dy)]/(y²dx + x • 2ydy)
= lim((x,y)→(0,0)) [(xy)sin(xy) + (xy)sin(xy)]/(3xy²)
= (2/3)lim((x,y)→(0,0)) sin(xy)/y
= 2/3 • 0
= 0