求极限lim (sin2x/sin5x) 当x趋近于0时用lim (sinx/x)=0 当x趋近于0时这一极限来求

问题描述:

求极限lim (sin2x/sin5x) 当x趋近于0时
用lim (sinx/x)=0 当x趋近于0时这一极限来求

lim(x->0) sin2x/sin5x (0/0)
=lim(x->0) 2cos2x/(5cos5x)
=2/5
or
lim(x->0) sin2x/sin5x
=(2/5)lim(x->0) (sin2x/(2x)) ((5x)/sin5x)
=2/5