calculus

posted by .

Find the interval which contains a zero for the given function. The use Newton's method to approximate the zero of the function within 0.001.
a.) f(x)=x^3+x-1
b.)f(x)=2x^3+x^2-x-+1

  • calculus -

    pick some value reasonably close to a root. Start too far away, and you may converge to a different root, or none at all.

    a) since f(0) = -1 and f(1) = 1, start with x = 1.

    The iterations converge quickly:

    1: 1.0000 -> 0.7500 f(x) = 0.1719
    2: 0.7500 -> 0.6860 f(x) = 0.0089
    3: 0.6860 -> 0.6823 f(x) = 0.0000
    4: 0.6823 -> 0.6823 f(x) = 0.0000


    b) Is that -1 or +1 at the end? I'll assume -1.
    f(1) = 1
    f(0) = -1

    1: 1.0000 -> 0.8571 f(x) = 0.1370
    2: 0.8571 -> 0.8304 f(x) = 0.0044
    3: 0.8304 -> 0.8295 f(x) = 0.0000
    4: 0.8295 -> 0.8295 f(x) = 0.0000


    If we use +1 instead of -1, the root has shifted away to the left:

    1: 1.0000 -> 0.5714 f(x) = 1.1283
    2: 0.5714 -> 0.0347 f(x) = 0.9666
    3: 0.0347 -> 1.0814 f(x) = 3.6175
    4: 1.0814 -> 0.6392 f(x) = 1.2916
    5: 0.6392 -> 0.1660 f(x) = 0.8707
    6: 0.1660 -> 1.8980 f(x) = 16.3803
    7: 1.8980 -> 1.2270 f(x) = 4.9735
    8: 1.2270 -> 0.7528 f(x) = 1.6672
    9: 0.7528 -> 0.3260 f(x) = 0.8496
    10: 0.3260 -> -2.6072 f(x) = -25.0408
    11: -2.6072 -> -1.8829 f(x) = -6.9226
    12: -1.8829 -> -1.4635 f(x) = -1.6637
    13: -1.4635 -> -1.2771 f(x) = -0.2575
    14: -1.2771 -> -1.2357 f(x) = -0.0112
    15: -1.2357 -> -1.2338 f(x) = -0.0000
    16: -1.2338 -> -1.2338 f(x) = -0.0000

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. Maths, continuity

    Plz help me out with a solution... f(x) = sin(1/x) when x is not = to 0 and f(0) = 0 Thanx in advance... A function is continuous if Limit of y-->x of f(y) equals f(x) for every x. In this case you have t see if this is the case …
  2. pre-calculus

    the function has a real zero in the given interval. approximate this solution correct to two decimal places: f(x)=x^4-x^3-7x^2+5x+10; (2,3)
  3. Calculus

    Consider the function f(x)=sin(5x)/x. (a) Fill in the following table of values for f(x): x= -0.1 -0.01 -0.001 -0.0001 0.0001 0.001 0.01 0.1 f(x)= ( I need the values of f(x) for each x) (b) Based on your table of values, what would …
  4. Calculus

    Consider the function f(x)=(4^x−1)/x. (a) Fill in the following table of values for f(x): x= -0.1 -0.01 -0.001 -0.0001 0.0001 0.001 0.01 0.1 f(x)= I the the falues of f(x) for each interval... (b) Based on your table of values, …
  5. Calculus

    Consider the function f(x)=(4^x−1)/x. (a) Fill in the following table of values for f(x): x= -0.1 -0.01 -0.001 -0.0001 0.0001 0.001 0.01 0.1 f(x)= I the the falues of f(x) for each interval... (b) Based on your table of values, …
  6. math

    the function has a real zero in the given interval. approximate this solution correct to two decimal places. f(x)=x^4-x^3-7x^2+5x+10; (2,3)
  7. Calculus

    I'm supposed to find the average value of the function over the given interval. f(x) = sin(nx), interval from 0 to pi/n, where n is a positive integer. I know the average value formula, and I know that the integral of that function …
  8. calculus

    Use the Newton method to approximate the indicated zero of the function. Continue with the iteration until two successive approximations differ by less than 0,0001 the zero of: f(x)=x^3+2x^2+x-7 between x=1 and x=2, x0=1
  9. College Algebra

    1. Use the Intermediate Value Theorem to show that the polynomial function has a zero in the given interval. f(x) = 13x^4 - 5x^2 +7x -1; [3,0] Enter the value of (-3). 2. Use the Intermediate Value Theorem to show that the polynomial …
  10. calculus 1

    f(x) = 3x^3 - 9x + 5 find the: 1) zeroes or undefined values 2) intervals where the function is greater than zero 3) intervals where the function is less than zero 4) coordinates of all maxima and minima 5) intervals where the function …

More Similar Questions