Answered: If you had to compute the numerical…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

See similar textbooks

Related questions

Concept explainers

Question

If you had to compute the numerical value for (1/(10^(1/5)) with accuracy up to 12 decimal points, how would you do it using Newton iteration formula.

Expert Solution

Step 1: Description of given data

Let, $x equals 1 over 10 to the power of 1 fifth end exponent$

$x to the power of 5 equals 1 over 10$

$x to the power of 5 equals 0.1$

$x to the power of 5 minus 0.1 equals 0$

now $bold italic f bold left parenthesis bold italic x bold right parenthesis bold equals bold italic x to the power of bold 5 bold minus bold 0 bold. bold 1$

derivatives, $f apostrophe left parenthesis x right parenthesis equals 5 x to the power of 4$

Newton iteration formula:

$bold italic x subscript bold n bold plus bold 1 end subscript bold equals bold italic x subscript bold n bold minus fraction numerator bold f stretchy left parenthesis x subscript n stretchy right parenthesis over denominator bold f bold apostrophe stretchy left parenthesis x subscript n stretchy right parenthesis end fraction$

Here,

X	0	1
f(x)	-0.1	0.9

Here $f left parenthesis 0 right parenthesis equals negative 0.1 less than 0$ and $f left parenthesis 1 right parenthesis equals 0.9 greater than 0$

therefore, the root lies between 0 and 1

$x subscript 0 equals fraction numerator 0 plus 1 over denominator 2 end fraction equals 0.5$

Step by step

Solved in 3 steps with 21 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Troubleshooting$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, advanced-math and related others by exploring similar questions and additional content below.

Similar questions