limitsof a function

Question

find the limit of (1-cos4x) / (1-cos2x) as x approches to 0.

Answer 1

 lim(x--->0) (1-cos4x)/(1-cos2x)

 limits of given functon takes 0/0 form.

Apply L hopitals rule

differentiating numerator and denominator.

 lim(x--->0) (1-cos4x)/(1-cos2x)

= lim(x--->0)4sin(4x)/2sin(2x)

Again differentiating

= lim(x-->0)16cos(4x)/4cos(2x)

by evaluting x = 0

= 16/4

= 4