Given the function f(x) = cos(x) - sin(x) defined on the interval [0.0, n/2]. The angle is in radain. a) Start with initial value x = 0.0. Find the approximated root after 5 iterations, using the Flxed Point iteration method. Show your result for 5 iterations. Show your results in a table. b) Start with initial value x = 0.0. Use the Newton-Raphson method to find the root of the function f(x). Stop running after 5 iterations. Show your results in a table. c) Start with 0.0 and 1/3 and find the root of the function using the SecantMethod. Stop running after 5 iterations. Show your results in a table.
Given the function f(x) = cos(x) - sin(x) defined on the interval [0.0, n/2]. The angle is in radain. a) Start with initial value x = 0.0. Find the approximated root after 5 iterations, using the Flxed Point iteration method. Show your result for 5 iterations. Show your results in a table. b) Start with initial value x = 0.0. Use the Newton-Raphson method to find the root of the function f(x). Stop running after 5 iterations. Show your results in a table. c) Start with 0.0 and 1/3 and find the root of the function using the SecantMethod. Stop running after 5 iterations. Show your results in a table.
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter6: Vector Spaces
Section6.7: Applications
Problem 18EQ
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Numerical analysis
![Given the function f(x) = cos(x) - sin(x)
defined on the interval [0.0, 1/2]. The
angle is in radain.
a) Start with initial value x = 0.0. Find the
approximated root after 5 iterations,
using the Flxed Point iteration method.
Show your result for 5 iterations. Show
your results in a table.
b) Start with initial value x = 0.0. Use the
Newton-Raphson method to find the root
of the function f(x). Stop running after 5
iterations. Show your results in a table.
c) Start with 0.0 and 1/3 and find the root
of the function using the SecantMethod.
Stop running after 5 iterations. Show your
results in a table.
d) Based on your results in a), b), and c)
above, which one may converge first?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6cb92734-11bc-4efa-8500-0b764026aaa8%2Ffaeaf919-2970-48e7-8202-f3bbc0dd6803%2Fj7jkko5_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Given the function f(x) = cos(x) - sin(x)
defined on the interval [0.0, 1/2]. The
angle is in radain.
a) Start with initial value x = 0.0. Find the
approximated root after 5 iterations,
using the Flxed Point iteration method.
Show your result for 5 iterations. Show
your results in a table.
b) Start with initial value x = 0.0. Use the
Newton-Raphson method to find the root
of the function f(x). Stop running after 5
iterations. Show your results in a table.
c) Start with 0.0 and 1/3 and find the root
of the function using the SecantMethod.
Stop running after 5 iterations. Show your
results in a table.
d) Based on your results in a), b), and c)
above, which one may converge first?
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