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In-Depth Information
3
2.5
2
1.5
1
0.5
0
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
t
Fig. 4.11
The graph shows the number of iterations used by Newton's method to solve the system
(
4.171
) at each time level
(a) Sketch the function f for x
2
Œ
1; 1 and verify that f.0/
D
0.
(b) Use Newton's method to solve
f.x/
D
0;
(4.181)
choosing x
0
D
1. Compute x
1
, x
2
, x
3
, x
4
with a calculator.
˘
Exercise 4.2.
Redo Exercise
4.1
using
(a) f.x/
D
x
sin.x/.
(b) f.x/
D
1
cos.x/.
˘
Exercise 4.3.
Consider
f.x/
D
x
2
4;
g.x/
D
x
2
:
(a) Set x
0
D
3 and compute x
1
;:::;x
4
in Newton's method to solve
f.x/
D
0:
(4.182)
