Example 2.  Error Analysis.  Investigate the error for the Newton polynomial approximations in Example 1.

Solution 2.

2 (a).  Investigate the error over the interval    for the Newton interpolation polynomial  ,  of degree n = 1.

2 (b).  Investigate the error over the interval    for the Newton interpolation polynomial  ,  of degree n = 2.

2 (c).  Investigate the error over the interval    for the Newton interpolation polynomial  ,  of degree n = 3.

2 (d).  Investigate the error over the interval    for the Newton interpolation polynomial  ,  of degree n = 4.

2 (e).  Investigate the error over the interval    for the Newton interpolation polynomial  ,  of degree n = 5.

(c) John H. Mathews 2003