求极限lim(x,y)→(0,0) [1-cos(xy)]/xy^2

问题描述:

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)]/(3x...