Final answer:
The limit of cos⁻¹(x) as x approaches infinity is undefined, because the arccosine function is only defined for x values between -1 and 1.
Step-by-step explanation:
The question addresses the behavior of the function cos⁻¹(x) (also known as the inverse cosine or arccosine function) as x approaches infinity. However, this limit does not exist as the domain of the cos⁻¹(x) function is restricted to values between -1 and 1 inclusive.
The limit of cos⁻¹(x) as x approaches infinity is undefined, because the arccosine function is only defined for x values between -1 and 1.
This is because the cosine function only takes values in the range [-1, 1], hence its inverse function, the arccosine, is only defined within that interval. As such, a limit involving the arccosine function approaching infinity does not exist, making the premise of the question incorrect.