Question

Find the approximations T_n, M_n, and S_n for n = 6 and 12. Then compute the corresponding errors E_T', E_M', and E_S.

Answer 1

To find the approximations T_n, M_n, and S_n for n = 6 and 12, we can use the given equations. Then, we can compute the corresponding errors using their actual values and the approximations.

Step-by-step explanation:

To find the approximations T_n, M_n, and S_n, we need to refer to Equations 12.21, 12.22, and 12.23. For n=6:

1. T_n = 91.0
2. M_n = (T_n + S_n) / 2 = (91.0 + 9.0) / 2 = 50.0
3. S_n = 9.0

For n=12:

1. T_n = 15.6
2. M_n = (T_n + S_n) / 2 = (15.6 + 15.6) / 2 = 15.6
3. S_n = 15.6

To compute the corresponding errors E_T', E_M', and E_S, we need the actual values and the approximations. Given the values, we can calculate the errors:

1. E_T' = |T_n - T' n|
2. E_M' = |M_n - T' n|
3. E_S = |S_n - S' n|