1) lim (3x/sinx) as x approaches 0

We can use L'Hopital's rule to find the limit of the given function:

lim (3x/sinx) as x approaches 0 = lim (3/ cosx) as x approaches 0 = 3

2) lim (sin0.5x/sin4x) as x approaches 0

We can simplify the given function by using trigonometric identities:

lim (sin0.5x/sin4x) as x approaches 0 = lim (sin(0.5x - 4x)) / (sin0.5x) as x approaches 0 = lim (sin(-3.5x)) / sin0.5x as x approaches 0 = lim (-3.5) / 0.5 = -7

3) lim (sin 12x/tg6x) as x approaches 0

Again, we can simplify the given function using trigonometric identities:

lim (sin 12x/tg6x) as x approaches 0 = lim (2sin6x * cos6x) / (sin6x / cos6x) as x approaches 0 = lim 2cos6x as x approaches 0 = 2cos(0) = 2