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Newton's Method Worksheet for Calculus I - MA 111, Assignments of Calculus

Solutions and exercises for newton's method in calculus i, specifically for the function f(x) = x² − 2 and the cubic function x³ + x + 15. The document also includes instructions for writing maple programs to implement newton's method.

Typology: Assignments

Pre 2010

Uploaded on 08/13/2009

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MA 111 - Calculus I
Worksheet #6- Newton’s method
Professor Broughton Fall 03-04
Name: Section: Box #:
1. Let f(x) = x2
2.The solution to f(x)=0,for positive xis 2.Approx-
imate the root of f(x) = 0 by using several iterations of Newton’s method
per the table below
n xnf(xn)f0(xn)xnf(xn)/f0(xn)
0 1
2. Solve the following cubic x3+x+ 15. using several iterations of Newtons
method. Get an initial estimate plotting.
n xnf(xn)f0(xn)xnf(xn)/f0(xn)
0 1
3. Write a Maple program that will iterate Newton’s Method in a certain
number of step (done in class).
4. Write Maple program to implement Newtons’ method that stops when the
value of f(x) is less that a prescribed error ².

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MA 111 - Calculus I

Worksheet #6- Newton’s method

Professor Broughton Fall 03-

Name: Section: Box #:

  1. Let f (x) = x^2 − 2. The solution to f (x) = 0, for positive x is
  1. Approx- imate the root of f (x) = 0 by using several iterations of Newton’s method per the table below

n xn f (xn) f ′(xn) xn − f (xn)/f ′(xn) 0 1

  1. Solve the following cubic x^3 + x + 15. using several iterations of Newtons method. Get an initial estimate plotting.

n xn f (xn) f ′(xn) xn − f (xn)/f ′(xn) 0 1

  1. Write a Maple program that will iterate Newton’s Method in a certain number of step (done in class).
  2. Write Maple program to implement Newtons’ method that stops when the value of f (x) is less that a prescribed error ≤.