solution for limit as delta x approaches 0 (1-cos4x/1-cos2x)

Answer 1

Usually the first step I take in doing a limit question is to actually substitute the approach value, so I got

lim cos 4x/(1- cos 2x) , as x -->0
--> 1/(1-0)
which is undefined,
so there is not limit, or the result is infinity

check: I tried x = .0001
and got 52631574.74

Answer 2

however, a more careful reading reveals :-)

lim (1-cos4x)/(1-cos2x)
= lim 4sin4x/2sin2x
= lim (4sin2x cos2x)/sin2x
= lim 4cos2x
= 4