Question

Evaluate √167 by Newton Raphson method correct up to four decimal places.​

Answer 1

Step-by-step explanation:

Given Evaluate √167 by Newton Raphson method

• We need to find the √167 to 4 decimal places.
• So let f(x) = x^2 – 167
• So f’(x) = 2x
• So writing x n+ 1 = x n – xn^2 – 167 / 2 xn
• Or x n + 1 = 1/2 ( x n + 167 / xn)
• So if we take a square number previous and successor of 167 we get  144 and 169
• So it will be 12 < √167 < 13
• Consider some number as 12.6 closer to 13 since 167 is near to 169
• So we can write this as x 1 = 1/2 (12.6 + 167 / 12.6 ) = 12.9270
•                         Also for x 2 = 1/2 (12.9270 + 167 / 12.927) = 12.9228
•                        For x3 = 1/2 (12.9228 + 167 / 12.9228) = 12.9228
• Therefore √167 = 12.9228

Reference link will be

https://brainly.in/question/14305251

Answer 2

Given :   √167   , Newton-Raphson method

To find :   Evaluate √167 to four decimal places upto fourth iterations

Solution:

x = √167

x² =  167

f(x) =  x² - 167

f'(x) = 2x

x₀  = 13      as  13² = 169

xₙ₊₁  = xₙ ​− f(xₙ​) / f'(xₙ​)​.

x₁  = 13 -   ( 13² - 167) /(2 *13)        

x₁  =   13 - 1/13

x₁  =   12.923

x₂ =  12.923  -   ( 12.923² - 167) /(2 * 12.923)

x₂ =   12.9228

x₃ =   12.9228   -   (  12.9228 ² - 167) /(2 *  12.9228 )

x₃ =   12.9228

x₂ =  x₃

=> √167 = 12.9228  

Learn more:

Find the approximate value of the expression (1.99)^7 by using ...

brainly.in/question/15853098

If log4=1.3868 ,then the approximate value of log (4.01) 1. 1.3968 2 ...

brainly.in/question/16250601

https://brainly.in/question/17089871