There are 25 prime numbers less than 100. The Prime Number Theorem states that the number of primes less than x approaches p(x) ≈ x / lnx . Use this approximation to estimate the rate (in primes per 100 integers) at which the prime numbers occur when (a) x = 1000. (b) x = 1,000,000. (c) x = 1,000,000,000.

Sketch the situation if necessary and use related rates to solve for the quantity. A 6 -ft-tall person walks away from a 10 -ft lamppost at a constant rate of 3 ft/sec. What is the rate that the tip of the shadow moves away from the top of the pole when the person is 10 ft away from the pole? 10 10 6 X + Click here to create a new row The rate that the tip of the shadow moves away from the pole is + ft/sec. © Rice University 201