Final answer:
The Simpson's rule error bound involves the fourth derivative, and while the references provided are not directly applicable, they suggest using computational tools to find the necessary sample size n.
Step-by-step explanation:
In order to determine the required sample size n for the Simpson's rule approximation to be accurate within a certain tolerance, it is important to consider the error bound formula for Simpson's rule. Unfortunately, the given reference information seems mostly unrelated to the problem of approximating integrals with Simpson's rule. However, the typical way to guarantee that the Simpson’s rule approximation for ∢01 15ex2 dx is accurate within 0.0001 would involve estimating the fourth derivative of the function to find the maximum value on the interval [0, 1], then using that value in the error estimate formula for Simpson's rule:
ES ≤ ⅔ ⅔4 |f(4)(z)| ≠b - a180n4
Since the calculation of the fourth derivative of 15ex2 and its maximum value on the interval [0, 1] can be complex and is usually done with the aid of a calculator or computer, it is suggested to use such tools to compute the necessary sample size n.