This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: 92.131 Calculus1 Newton’s Method 1) Using Newton’s Method, find the first 2 approximations to the positive root of 1 2 = − − x x . Start with 2 = x , calculate 2 1 and , x x . Compare this to the exact solution. 2) Using Newton’s Method, find the first 2 approximations to the positive root of 3 2 4 = − x x . Start with 2 = x , calculate 2 1 and , x x . Compare this to the exact solution. 3) Using Newton’s Method, find the first 2 approximations to the positive root of 2 3 = − x . Start with 1 = x , calculate 2 1 and , x x . Explain your result. 4) There is one value of x in the interval [1, 2] where the functions 2 4 4 x x y − = and x y 2 − = intersect. i) Give the recursion equation for solving this problem using Newton’s method. ii) Starting with 2 = x , approximate the positive solution by 2 x 5) Approximate 3 7 − to four decimal places. 92.131 Calculus1 Newton’s Method Solutions: 1) With 1 ) ( 2 − − = x x x f , 1 2 ) ( − = ′ x x f , and so the recursion relation is...
View
Full
Document
This note was uploaded on 02/13/2012 for the course MATH 92.131 taught by Professor Staff during the Fall '09 term at UMass Lowell.
 Fall '09
 Staff
 Calculus, Approximation

Click to edit the document details