Question

use the error formula to determine a value of n so that the maclaurin polynomial of degree n of f(x) = E^X Approximates F(2)=e2 with error less than. 001

Answer 1

less than 0.001.

Explanation:

The formula for the error in approximating a function using a Maclaurin polynomial is given by:

|F(x) - Pn(x)| = |Rn(x)| <= M * |x - a|^(n+1) / (n+1)!,

where F(x) is the actual function, Pn(x) is the Maclaurin polynomial of degree n, Rn(x) is the remainder term, a is the center of the approximation (a = 0 for Maclaurin polynomials), x is the point at which the approximation is being made, and M is an upper bound on the absolute value of the function's n+1 derivative on the interval [0, x].

To determine the value of n that satisfies the error condition |F(2) - Pn(2)| <= 0.001, we can rearrange the formula as follows:

n >= log(M * |2 - 0|^(n+1) / 0.001) / log(n + 1)

Unfortunately, without knowing the value of M, it is difficult to determine the exact value of n that satisfies the error condition. However, a common approach is to use numerical methods to estimate M and iteratively calculate the value of n until the error is less than 0.001.