Final answer:
The limit of the integral of cos as it approaches infinity exists because the amplitude of the oscillations of cos(x) becomes smaller and smaller as x becomes very large.
Step-by-step explanation:
The limit of the integral of cos as it approaches infinity exists because the function cos(x) has a periodic behavior with a range of values between -1 and 1. As x becomes very large, the values of cos(x) oscillate between -1 and 1, but the amplitude of the oscillations becomes smaller and smaller. This means that no matter how large x becomes, the integral of cos(x) will always have a finite value between -1 and 1. Therefore, the limit of the integral as x approaches infinity exists and is equal to this finite value.