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

1. 0
2. 5
1. let f(x) = y = x^3 + x +2
dy/dx = 3x^2 + 1

newton's formula

x new = x old - f(xold/f '(xold)

x2 = -1 - (-1-1+2)/(3+1) = 1-0 = -1

since x1 = x1 exactly, x = -1 is a root

1. 0
posted by Reiny
2. Check for typo's in the question.
I believe there is only one real root for the given equation at -1.

So your initial guesses have to be complex, such as 1+i. Convergence will depend on the form of the iteration equation.
You can try
f(x)=(-2-x)^(1/3)
f(x)=-2-x^3
and all kinds of other ones.
The one that seems to converge best is
first make
x^3=-2-x
divide by x and take the square root to get
f(x)=sqrt(-1-2/x)
With a starting value of 1+i, ou should converge quite well, as the iterations alternate between the targeted root of (1/2)±sqrt(7)/2.

Once you have converged to one, you can take the conjugate for the other, without having to do the same things all over again.

1. 0
posted by MathMate
3. the targeted root of (1/2)±sqrt(7)/2i.

1. 0
posted by MathMate
4. My last line should say:

since x2 = x1 exactly, x = -1 is a root

1. 0
posted by Reiny
5. I'll get it right this time!
the targeted root of (1/2)±isqrt(7)/2.

1. 0
posted by MathMate

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
2. Calculus 1

Use Newton's method to approximate the root of the equation x^3+x+2=0 with initial guess x1=-1 gives:
3. 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
4. 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? b) Iterate the equation with starting point x1=5 until you get a
5. numerical methods

Consider a spherical storage tank containing oil. The tank has a diameter of 8 ft. You are asked to calculate the height h to which a dipstick 10 ft long would be wet with oil when immersed in the tank when it contains 6 3 ft of
6. Calculus 1

Use Newton's method to approximate the indicated root of the equation correct to six decimal places. The root of x^4 − 2x^3 + 5x^2 − 5 = 0 in the interval [1, 2]
7. calculus

Use Newton's method to approximate the indicated root of the equation correct to six decimal places. The positive root of 3sinx = x^2
8. Calculus

Use Newton's method to approximate a root of the equation (2 x^3 + 4 x + 4 =0) as follows. Let (x_1 = -1\) be the initial approximation. The second approximation (x_2) is ? and the third approximation (x_3) is ?
9. calculus

Use Newton's method to approximate a root of the equation 3sin(x)=x as follows. Let x1=1 be the initial approximation. The second approximation x2 is and the third approximation x3 is I got x2=-1.454 but can't get x3 :(
10. calculus

Use Newton's method to approximate a root of the equation 3sin(x)=x as follows. Let x1=1 be the initial approximation. The second approximation x2 is and the third approximation x3 is for x2 I got -1.454 which is right but I can't

More Similar Questions