1(a) Let f(x) = x – 5 cos(x). By calculating f(1) and f(2), show that there is an a e [1, 2] such that f(æ) = 0. You should give your values of f to four significant figures. (b) With a = 1 and b = 2, the first two iterations of the bisection method for the function given in part (a) are shown in the following table. Do two more iterations to find the missing values in the table which are denoted by ???. bn f(æn) 1.1463 n An an 1 1 2 1.5 1 1.5 1.25 -0.3266 ??? ??? 3 ??? ??? ??? 4 ??? ??? ??? (c) For the function f of part (a), write down the corresponding Newton-Raphson method. Then take xo = 1 and do two iterations of this method. You should give your values of x1 and x2 to six significant figures.
1(a) Let f(x) = x – 5 cos(x). By calculating f(1) and f(2), show that there is an a e [1, 2] such that f(æ) = 0. You should give your values of f to four significant figures. (b) With a = 1 and b = 2, the first two iterations of the bisection method for the function given in part (a) are shown in the following table. Do two more iterations to find the missing values in the table which are denoted by ???. bn f(æn) 1.1463 n An an 1 1 2 1.5 1 1.5 1.25 -0.3266 ??? ??? 3 ??? ??? ??? 4 ??? ??? ??? (c) For the function f of part (a), write down the corresponding Newton-Raphson method. Then take xo = 1 and do two iterations of this method. You should give your values of x1 and x2 to six significant figures.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![1(a) Let f(x) = x – 5 cos(x). By calculating f(1) and f(2), show that there is an a e [1, 2]
such that f(æ) = 0. You should give your values of f to four significant figures.
(b) With a = 1 and b = 2, the first two iterations of the bisection method for the function given
in part (a) are shown in the following table. Do two more iterations to find the missing
values in the table which are denoted by ???.
bn
f(æn)
1.1463
n
An
an
1
1
2
1.5
1
1.5
1.25
-0.3266
???
???
3
???
???
???
4
???
???
???
(c) For the function f of part (a), write down the corresponding Newton-Raphson method.
Then take xo = 1 and do two iterations of this method. You should give your values of x1
and x2 to six significant figures.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F61ea2a1d-9910-4619-bb6c-59888ed96708%2F25a56740-68ef-48d5-ada7-efbf38d19381%2Fnjod8_processed.png&w=3840&q=75)
Transcribed Image Text:1(a) Let f(x) = x – 5 cos(x). By calculating f(1) and f(2), show that there is an a e [1, 2]
such that f(æ) = 0. You should give your values of f to four significant figures.
(b) With a = 1 and b = 2, the first two iterations of the bisection method for the function given
in part (a) are shown in the following table. Do two more iterations to find the missing
values in the table which are denoted by ???.
bn
f(æn)
1.1463
n
An
an
1
1
2
1.5
1
1.5
1.25
-0.3266
???
???
3
???
???
???
4
???
???
???
(c) For the function f of part (a), write down the corresponding Newton-Raphson method.
Then take xo = 1 and do two iterations of this method. You should give your values of x1
and x2 to six significant figures.
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