Question

Let f(x) = 1/x², 0.6 ≤ x ≤ 1.4. Suppose that we approximate f(x) by the 3rd-degree Taylor polynomial T₃(x) centered at a = 1. Taylor's inequality gives an estimate.

Answer 1

The question involves calculating the third-degree Taylor polynomial for f(x) = 1/x² centered at a = 1 and using Taylor's inequality to estimate the approximation error on the range 0.6 to 1.4.

Step-by-step explanation:

The question is asking to define the third-degree Taylor polynomial (T₃(x)) of the function f(x) = 1/x² centered at a = 1, and to use Taylor's inequality to give an estimate for the approximation on the interval 0.6 ≤ x ≤ 1.4.

To find T₃(x), we calculate the derivatives of f(x) at x = 1 and use them to construct the polynomial. Taylor's inequality can then help estimate the maximum error between f(x) and T₃(x) for values of x in the specified range.