Question #e9f07

1 Answer
Dec 10, 2017

First, we know that #lim_(x->0) sinx/x=1#
and the greatest integer function returns the largest integer less than or equal to #x# for all real number #x#, for example, #[1]=1#, #[2.5]=2# and #[-2.5]=-3#

#lim_(x->0) [(sin(2x)/x)]#
#=lim_(x->0) [(sin(2x)/(2x)*2)]#
#=[1*2]#
#=[2]#
#=2#

Here is the answer. Hope it can help you.