Question

Using newton's method calculate to the first 3 iterations.

Foject Goals and Tasks Your goal is to implement Newton's Method in Java for various functions, using a for loop. See the last page of this document for help writing the code. Task 1: (a) Apply Newton's Method to the equation x2 - a = 0 to derive the following square-root algorithm (used by the ancient Babylonians to compute Va): 1 In+1= (b) Use part (a) to compute v1000 correct to at least six decimal place in the following way: Change the code in the program to use the formula you derived in part (a), with .Choose an initial guess by graphing f (x) = x2 - 1000 and choosing an x-value that appears to be near the root Edit the line that assigns "root" within the for loop to correctly approximate your root using Newton's 1000. .

DO NOT WORRY ABOUT THE CODING OR ANYTHING. IHAVE ALREADY COMPLETED THAT. ONLY HAND WRITTEN CALCULATIONS.

Answer 1

1000 1000 let 31.6 000/ +318ノこyor 31-6 SBLTT9-1 3).22785 らこ(3)-62277)十 )622ノ -ろ1. 622777 So a 3. 622777