Final answer:
The limit of cos(5/x) as x approaches 0 does not exist because the argument 5/x causes the function to oscillate increasingly without settling on a single value.
Step-by-step explanation:
The question asks about the limit of the function cos(5/x) as x approaches 0. To find the limit as x approaches zero, we must first understand the behavior of the cosine function. Cosine is a periodic function that oscillates between -1 and 1. Because the argument 5/x becomes infinitely large as x approaches 0, cos(5/x) will oscillate more and more rapidly. As the input value 5/x has no upper bound as x approaches 0, the cosine function will not settle at any particular value. Hence, the limit does not exist because we cannot assign a single number to this behavior as x approaches zero.