la). Show that f(x)=(x-2)² – Inx =0 has at least one root between 1 and 2. b). Use bisection method to find the first 3- approximations of a solution of the equation f(x) = (x– 2)² – In x = 0 [1,2]. (3- digit rounding) P. f(P,) 1 3 c)Find the minimum number of iterations required to achieve an approximation of a solution of the equation f(x) = (x- 2)² – In x = 0 in [1,2] with an accuracy of 10
la). Show that f(x)=(x-2)² – Inx =0 has at least one root between 1 and 2. b). Use bisection method to find the first 3- approximations of a solution of the equation f(x) = (x– 2)² – In x = 0 [1,2]. (3- digit rounding) P. f(P,) 1 3 c)Find the minimum number of iterations required to achieve an approximation of a solution of the equation f(x) = (x- 2)² – In x = 0 in [1,2] with an accuracy of 10
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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Question
![la). Show that f(x)= (x– 2)² – In x = 0 has at least one root between 1 and 2.
b). Use bisection method to find the first 3- approximations of a solution of the equation
f(x) = (x- 2)² – In x = 0
[1,2].
(3- digit rounding)
b,
Pn
f(p,)
1
3
c)Find the minimum number of iterations required to achieve an approximation of a solution of the
equation f(x)= (x– 2)² – In x = 0 in [1,2] with an accuracy of 104
d)In the graph given below, locate the position of second approximation p, obtained by Bisection
method.
1
0.8
0.6
0.4
a = 0.4
b=1.2
0.2
-0.4
-0.2
0.2
0.4
0.8
1
1.2
1.4
1.6
-0.2
-0.4](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa46d96e9-acf5-4939-bce6-5ea74f2f4622%2F5be43205-ec95-456d-ab96-45b2d47d40c4%2Fvhkgy8_processed.jpeg&w=3840&q=75)
Transcribed Image Text:la). Show that f(x)= (x– 2)² – In x = 0 has at least one root between 1 and 2.
b). Use bisection method to find the first 3- approximations of a solution of the equation
f(x) = (x- 2)² – In x = 0
[1,2].
(3- digit rounding)
b,
Pn
f(p,)
1
3
c)Find the minimum number of iterations required to achieve an approximation of a solution of the
equation f(x)= (x– 2)² – In x = 0 in [1,2] with an accuracy of 104
d)In the graph given below, locate the position of second approximation p, obtained by Bisection
method.
1
0.8
0.6
0.4
a = 0.4
b=1.2
0.2
-0.4
-0.2
0.2
0.4
0.8
1
1.2
1.4
1.6
-0.2
-0.4
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