lim x → 0 (x^4) (sec^5(2x)) csc^4(3x)

Answer 1

x csc(3x) = (1/3)((3x)/(sin(3x))
You know that lim u/sinu = 1
So, your limit is
lim sec^5(2x) * (lim (1/3 (3x/sin3x))^4 = 1^5 * (1/3)^4 = 1/81

Answer 2

Limx->0 (5-4/cosx)^1/sin^2(3x)