Question

lim -> 0 sin(2x) /(x*cos(x) )

help

Answer 1

sin (2x) = 2sin(x)cos(x)
so sin(2x) /(x*cos(x) =2sin(x)cos(x)/x*cos(x)=2sinx/x
which as x->0 goes to 1

Answer 2

no, answer is 2

Answer 3

ups sry, forgot about 2 multuplying:
lim 2sinx/x=2*1=2
x->0

Answer 4

don't undestand you

Answer 5

sin (2x) can be written like:
sin (2x) = 2sin(x)cos(x)

substituting this expretion in the original one:
sin(2x) /(x*cos(x) =2sin(x)cos(x)/x*cos(x)=2sinx/x

taking limits, and noticing that lim as x->0 of sinx/x=1:
lim 2sinx/x=2*1=2
x->0