Final answer:
The limit of cos(x) as x approaches infinity does not exist because the cosine function oscillates between -1 and 1 indefinitely, never settling at a single value.
Step-by-step explanation:
The question pertains to the behavior of the cosine function as the variable x approaches infinity. It is important to understand that for trigonometric functions like cosine, the limit does not exist as x goes to infinity.
This is because the cosine function oscillates between -1 and 1 for all real number inputs. No matter how large x becomes, cosine of x will continue to fluctuate and will never settle at a single value.
Cos(0) equals 1, which is a specific value at a certain point. However, the cosine function can take on any value between -1 and 1 infinitely many times as x increases without bound.
Since trigonometric functions are periodic, as x becomes very large, all possible angle measures are indeed covered, but this does not lead to a single limit value at infinity.