Find limit as x approaches 0 of (1+sin4x)^cotx

(1+sin4x)^cotx

As x → 0, the function "looks like" lim(x→0)(1 + 4x)^(1/x) = e^4

1 + sin (2x+2x) = 1 + 2sin2xcos2x = sin^2 2x + cos^2 + 2sin2xcos2x = (sin2x + cos2x)^2

(sin2x + cos2x)^2cotx

put x=0

(0 + 1)^2cot0 =

1 to the power of any number will be 1

so 1

Function (1+sin4*x)^cotx
Lim f x→0 = 1