do i simplify tan^3 5x to tan(tan^2 5x) as the first step?

lim x0 (tan^3 5x/125x^3)*(4x/sin4x)*(125x/4x)
=lim x0 125/4
since lim x0 tan x/x = x/sin x = 1
what you were thinking was wrong .It would be tan 5x * tan 5x *tan 5x
=lim x0 125/4
since lim x0 tan x/x = x/sin x = 1
what you were thinking was wrong .It would be tan 5x * tan 5x *tan 5x

limit as x>0 of tan^3 5x/ x^2 sin4x = 5^3/4 = 125/4

Ideas" tan 5x ~ 5x, sin 4x ~ 4x as x> 0

Ideas" tan 5x ~ 5x, sin 4x ~ 4x as x> 0