Calculus

You are using Newton's method to solve

e^x - 2. If you first guess is x1=1, what value will you calculate for the next approximation x2?

...I don't know what Newton's method is, so I looked it up...and I'm still confused. Help plz?

Thx

  1. 👍 0
  2. 👎 0
  3. 👁 152
  1. first of all, to "solve" we need an equation.
    You have the expression e^x - 2
    Are you solving e^x - 2 = 0 ?

    I will assume you are.

    let f(x) = e^x - 2
    f ' (x) = e^x

    Newton's method says ...

    xn+1 = xn - f(xn)/f ' (xn)

    so x2 = 1 - (e^1 - 2)/e^1
    = .73576

    x3 = .73576 - (e^.73576 - 2)/e^.73576 = .69404

    x4 = .69404 - (e^.69404 - 2)/e^.69404 = .69314758

    notice we are rapidly approaching some kind of fixed value.
    If the value of x of our input returns as output, we have the solution.
    A most remarkable procedure.

    Using logs I get x = .69314718 , so our method was accurate to 6 digits after only 3 iterations.

    1. 👍 0
    2. 👎 0
    posted by Reiny

Respond to this Question

First Name

Your Response

Similar Questions

  1. calculus

    Use Newton's method to solve the equation sec x = 4 in the interval x in (0, pi/2). In other words, use Newton's Method to compute arcsec(4). (You need to make a good initial guess for the root otherwise Newton's method will

    asked by Anonymous on April 13, 2011
  2. Grade 12 AP calculus

    You are using Newton's method to solve x3-5x-2=0. If your first guess is x1=2, what value will you calculate for the next approximation x2?

    asked by Alannah on December 2, 2012
  3. calculus

    You are using Newton's method to solve x^3-5x-2=0. If your first guess is X1=2, what value will you calculate for the next approximation X2?

    asked by Anonymous on March 2, 2008
  4. Math

    use newton's method to estimate all real solutions of the equation x^3. I am having trouble coming up with a good guess. I went with x1=1, but that doesn't seem to be working. Any thoughts on which number should be the best first

    asked by Betty on February 15, 2016
  5. MATH STUCK:-(

    I am having some difficulties factoring polynomials and I use only one method to figure the stuff out, which is the guess and check method because it's just mental math work and not that complicating. Here is a question that I

    asked by Anonymous on November 15, 2010
  6. Calculus 1

    Use Newton's method to approximate the root of the equation x^3+x+2=0 with initial guess x1=-1 gives:

    asked by Olivia on October 31, 2011
  7. Calculus 1 Newton's Method

    Using Newton's method, approximate the root of the equation x^3+x+2=0 with the initial guess x1=-1 gives: x2=? and x3=? answers are not 0 or -1

    asked by Olivia on October 31, 2011
  8. Math/ Calculus

    Given an initial guess of x1 = 1, use the Newton-Raphson Method to fi nd the second approximation x = x2 of the solution of the equation: sqrt(x+3)=x

    asked by Angela on April 16, 2013
  9. math help

    2x^4-3x^2-7x+1=0 Estimate what the real solution will be using Newton's method. Answers must be 4 decimal places. Let the first guess be x=1.75

    asked by Rachel on January 19, 2016
  10. Math Help

    2x^4-3x^2-7x+1=0 Estimate what the real solution will be using Newton's method. Answers must be 4 decimal places. Let the first guess be x=1.75

    asked by Rachel on January 19, 2016

More Similar Questions