Calculus

posted by .

Use Newton's Method to approximate the root of the function f(x)=e^x-5x when the intial point chosene is x1=1.5. Do two iterations.

This is what I did, but not working.
f'(x)=e^x-5
x2=1.5 - (e^1.5-(5(1.5))/e^1.5 -(5))
=1.5-(4.4817-7.5/4.4817-5)=1.5-5.8234= -4.3234

x3=-4.3234-(e^-4.3234-(5(-4.3234))/ e^-4.3234-(5)) = -4.3234-(21.630/-4.987)= -4.3234-(-4.337)=.0136

I did another one for x4, but the number was no where near either of these two. Aren't they suppose to be somewhat close? Did I make a dumb algebra mistake or am I not doing this right at all?

  • Calculus -

    On the contrary, your equations and calculations are good.

    For X1=1.5
    I get
    x2=-4.32
    x3=0.01415
    x4=0.250868
    Your x4 is quite close to the exact answer of 0.25917110181907.
    In fact, by x7, you will get the answer accurate to 14 decimal places.

    This exercise is probably to illustrate that the Newton's method converges "no matter what", at least in this case where the function has the same concavity within the range.

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. Calculus

    Use five iterations in Newton’s method to estimate the root of cos(2x)-2x.Use x0 = π/4 and eight decimal places.
  2. Math Gr. 9

    a) Evaluate each power 3^1, 3^2, 3^4, 3^5, 3^6 b) Examine the final digit of each of your answers. What pattern do you notice?
  3. Gr. 9 Math

    a) Evaluate each power 3^1, 3^2, 3^3,3^4, 3^5, 3^6 b) Examine the final digit of each of your answers. What pattern do you notice?
  4. 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=?
  5. general inorganic biochemistry

    you have set up the apparatus for this experiment and collected the following data: Atmospheric pressure- 721.o torr temperature-22.0c Gas constant- 0.0821 L atm/mol K you then ran the experiment using 0.3234 g of alka seltzer and …
  6. Calculus

    Use Newton's Method to approximate the positive root of the function f(x) = (x^5) - 20 Show each iteration until successive iterations agree to six decimal places.
  7. Maths

    Find the smallest whole number n for which 126n is a multiple of 3234. My working: 126=2x3x3x7 3234=2x3x7x7x11 lcm=2x3x3x7x7x11
  8. Calculs

    1)Using Newton's Method with A=5, approximate the square root of 27. Do 2 iterations. 2)Using Newton's Method with A=2, approximate the cube root of 9. Do 2 iterations.
  9. Calculus

    Starting with an initial guess of x=2, use Newton’s method to approximate (Third root of 7). Stop the iterations when your approximations converge to four decimal places of accuracy. Compare with the approximation provided by your …
  10. Calculus - Newton's Method

    Use the Newton's Method to approximate the real root of the equation: f(x)=x-2+cosx=0 a) What is the iterative equation of Newton's method of the given equation?

More Similar Questions