Question

求极限((1-根号下x^2y+1)/x^3y^2)sin(xy),当x,y趋于0时

Answer 1

lim((1-√(x^2y+1))/x^3y^2)sin(xy),有理化1-√(x^2y+1))：

=lim(-x^2y)/(1+√(x^2y+1))/x^3y^2)sin(xy)

=lim(-sin(xy))/(1+√(x^2y+1))/(xy)

=-1/2 (利用limsin(xy)/(xy)=1)