The arcsine is the inverse sine function. Since x can be in the range of [-1,1], arcsin (x) is undefined outside the range of [-1,1]. So the limit of arcsine of x when x is approaching infinity is undefined:

The limit of Arcsin (x) as x approaches infinity is undefined, or does not exist. This is because the inverse sine function, Arcsin (x), can only take values between -π/2 and π/2, and as x approaches infinity, the values of Arcsin (x) become increasingly large and undefined.