Question

当xy都趋于0的时候,sin(xy)/x的极限并证明

Answer 1

设z=xy,则当x->0和y->0时,z->0

∵sin(xy)/x=[sin(xy)/xy]*y

∴所求极限=[lim(z->0)(sinz/z)]*[lim(y->0)y]

=1*0 (应用重要极限lim(x->0)(sinx/x)=1)

=0