In Exercises 62–64, use this definition: A prime number is a positive whole number with no factors other than itself and 1. For example, 2, 13, and 37 are primes, but 24 and 39 are not. By convention 1 is not considered prime, so the list of the first few primes is as follows:
2, 3, 5, 7, 11, 13, 17, 19, 23, 29, . . .
Let f be the function that assigns to each natural number x the number of primes that are less than or equal to x. For example, f(12) = 5 because, as you can easily check, five primes are less than or equal to 12. Similarly, f (3) = 2, because two primes are less than or equal to 3. Find f (8), f (10), and f (50).
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