现代数值数学和计算习题答案(同济版)(13)

x0,x1,···,x20

k=10,

max|(x xk)(x x20 k)|≤1;

x

k=10

,

|x x10|≤1.

|R20(x)|<

1

9,0≤t≤9.

R(x)=R(x0+th)=

f(10)(ξ)

x10

|f(10)(ξ)|<9!.

,

R¯(t) <

1

10·910

=

1

2

Mh.8

f(x)=sin(x),

h

13