5. Graphically, or otherwise estimate the number of and values of the root to the function given below, between -10 and +10. 4x f(x) = 8 cos³ x 9. - - - 5 Calculate a root to 4 decimal places using: (a) the Bisector method (use 6 and 9 as initial values)
5. Graphically, or otherwise estimate the number of and values of the root to the function given below, between -10 and +10. 4x f(x) = 8 cos³ x 9. - - - 5 Calculate a root to 4 decimal places using: (a) the Bisector method (use 6 and 9 as initial values)
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
![5. Graphically, or otherwise estimate the number of and values of the root to the function
given below, between -10 and +10.
4x
f (x) = 8 cos³ x
5
-
Calculate a root to 4 decimal places using:
(a) the Bisector method (use 6 and 9 as initial values)
(b) the false position method (use 6 and 9 as initial values)
(c)
the Secant method (use 6 and 9 as initial values)
(d)
the Newton-Raphson method (use 5 as initial value)
Calculate any others roots.
Comment on the results and the accuracy of the various approaches and the impact of the
initial values (e.g. what would have happened with other initial values?). Show your working
and tabulate values at each iteration, and plot a convergence history of each on the same
graph. It is suggested you use EXCEL.
Perform no more than 15 iterations of each method. Comment on the performance of each method.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6ad67ebd-a9fe-4e0c-b036-2be1d0e3b40d%2F891e6543-c5bb-4d30-9272-6284ea637884%2F8qzdxgy_processed.png&w=3840&q=75)
Transcribed Image Text:5. Graphically, or otherwise estimate the number of and values of the root to the function
given below, between -10 and +10.
4x
f (x) = 8 cos³ x
5
-
Calculate a root to 4 decimal places using:
(a) the Bisector method (use 6 and 9 as initial values)
(b) the false position method (use 6 and 9 as initial values)
(c)
the Secant method (use 6 and 9 as initial values)
(d)
the Newton-Raphson method (use 5 as initial value)
Calculate any others roots.
Comment on the results and the accuracy of the various approaches and the impact of the
initial values (e.g. what would have happened with other initial values?). Show your working
and tabulate values at each iteration, and plot a convergence history of each on the same
graph. It is suggested you use EXCEL.
Perform no more than 15 iterations of each method. Comment on the performance of each method.
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