We need to find the value of lim x-->0 [ tan 4x / tan 2x]

If we substitute x = 0, we get the indeterminate form 0/0. This allows us to use l'Hopital's rule and substitute the numerator and the denominator with their derivatives.

=> lim x-->0 [ 4*(sec 4x)^2...

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We need to find the value of lim x-->0 [ tan 4x / tan 2x]

If we substitute x = 0, we get the indeterminate form 0/0. This allows us to use l'Hopital's rule and substitute the numerator and the denominator with their derivatives.

=> lim x-->0 [ 4*(sec 4x)^2 / 2* (sec 2x)^2]

substitute x = 0

=> 4*1 / 2*1

=> 4/2

=> 2

**The required value of lim x-->0 [ tan 4x / tan 2x] = 2.**