Q2) Find the positive fourth root of 81 using the Newton-Raphson method until percentage relative error is 0 %. employ initial guesses xo=2. - Find the true value (Xtrue) of x and compute percentage relative true error. "You are required to show all steps to arrive at the answer and fill the following a table to show all results". i 0 Xi 2 f(x₁) Ea (%) Et (%)

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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Q2) Find the positive fourth root of 81 using the Newton-Raphson method until
percentage relative error is 0 %. employ initial guesses x₁=2.
- Find the true value (xtrue) of x and compute percentage relative true error.
"You are required to show all steps to arrive at the answer and fill the following a
table to show all results".
0
Xi
2
f(xi)
Ea (%)
Et (%)
Transcribed Image Text:Q2) Find the positive fourth root of 81 using the Newton-Raphson method until percentage relative error is 0 %. employ initial guesses x₁=2. - Find the true value (xtrue) of x and compute percentage relative true error. "You are required to show all steps to arrive at the answer and fill the following a table to show all results". 0 Xi 2 f(xi) Ea (%) Et (%)
Expert Solution
Step 1

Newton-Raphson Method:

The iterative formula for the Newton-Raphson method is,

                        xn+1=xn-fxnf'xn

Absolute Error:

The formula for absolute error is,

εa=approximate value-exact value

Relative Error:

The formula for relative error is,

εt=approximate value-exact valueexact value×100%

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