Question

高数多元函数求极限

Answer 1

z= arcsinxy

sinz = xy

cosz dz/dx = y

dz/dx = y/√[1- (xy)^2]

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

=lim(x->0,y->0){ y/√[1- (xy)^2]} /1

= 0/1

=0