f(x) = +- 3.437 %3D Find (for your own use) the derivative f' (2) of the function f(2). (i) We claim that the function f(r) has a unique root p in la, b) = [0.5125, 0.525). First, as the product f(0.5125) f(0.525) is . (here and everywhere below in this part, please enter a correct word) and as the function f(x) is . on (0.5125, 0.525), the function f(r) has a root in (0.5125, 0.525). Second, the uniqueness of the root follows then from the fact that f'() is . at all points æ € (0.5125, 0.525), and hence the function f(a) is strictly . on [0.5125, 0.525).
f(x) = +- 3.437 %3D Find (for your own use) the derivative f' (2) of the function f(2). (i) We claim that the function f(r) has a unique root p in la, b) = [0.5125, 0.525). First, as the product f(0.5125) f(0.525) is . (here and everywhere below in this part, please enter a correct word) and as the function f(x) is . on (0.5125, 0.525), the function f(r) has a root in (0.5125, 0.525). Second, the uniqueness of the root follows then from the fact that f'() is . at all points æ € (0.5125, 0.525), and hence the function f(a) is strictly . on [0.5125, 0.525).
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
Numerical analysis
3
![(Bisection Method). Consider the function
f(r) =I+
-- 3.437 a
Find (for your own use) the derivative f'(æ) of the function f(æ).
(i) We claim that the function f(r) has a unique root p in
la, b) = [0.5125, 0.525]. First, as the product f(0.5125) f(0.525)
is . (here and everywhere below in this part, please enter a correct
word)
and as the function f(x) is .
on [0.5125, 0.525], the function f(r) has a root in
(0.5125, 0.525). Second, the uniqueness of the root follows then
from the fact that f' (a) is .
at all points æ E (0.5125, 0.525), and hence the function f(r) is
strictly.
on (0.5125, 0.525).
(ii) Use the Bisection method to find an approximation Py of the root
PE (0.5125, 0.525) of the function f(x) such that
RE(PN PN-1) < 10 *. All calculations are to be carried out in
the FPAG. Show then your work by providing the following inputs.
(a) For every natural number k satisfying 1 <k< N, enter one-by-
one the corresponding terms ak, P. by the Bisection method
generates separated by single spaces in the input field labelled by k,
similar to
5
0.496875 0.497267 0.497657
to stress, the first number in your input must be the term a, the
second one the term P, and the third one the term b; type
unnecessary in the input field labelled by any k with k:> N.
1
3
4
7
8
9
10
(b) You have stopped at the N-th step, because the relative error
RE(PN PN-1) =
given in the stopping criterion became less than the tolerance for the
first time.
(c) The required approximation is therefore
PN -](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7c909ed8-88db-4eee-8878-ac3c652129b1%2Fc8385d40-4551-4bdb-9e81-4530c3d768bf%2F5e3r0z9_processed.jpeg&w=3840&q=75)
Transcribed Image Text:(Bisection Method). Consider the function
f(r) =I+
-- 3.437 a
Find (for your own use) the derivative f'(æ) of the function f(æ).
(i) We claim that the function f(r) has a unique root p in
la, b) = [0.5125, 0.525]. First, as the product f(0.5125) f(0.525)
is . (here and everywhere below in this part, please enter a correct
word)
and as the function f(x) is .
on [0.5125, 0.525], the function f(r) has a root in
(0.5125, 0.525). Second, the uniqueness of the root follows then
from the fact that f' (a) is .
at all points æ E (0.5125, 0.525), and hence the function f(r) is
strictly.
on (0.5125, 0.525).
(ii) Use the Bisection method to find an approximation Py of the root
PE (0.5125, 0.525) of the function f(x) such that
RE(PN PN-1) < 10 *. All calculations are to be carried out in
the FPAG. Show then your work by providing the following inputs.
(a) For every natural number k satisfying 1 <k< N, enter one-by-
one the corresponding terms ak, P. by the Bisection method
generates separated by single spaces in the input field labelled by k,
similar to
5
0.496875 0.497267 0.497657
to stress, the first number in your input must be the term a, the
second one the term P, and the third one the term b; type
unnecessary in the input field labelled by any k with k:> N.
1
3
4
7
8
9
10
(b) You have stopped at the N-th step, because the relative error
RE(PN PN-1) =
given in the stopping criterion became less than the tolerance for the
first time.
(c) The required approximation is therefore
PN -
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