Question

Let f(x) = x^3 + x - 4 a. Show that f(x) has a root on...

Let f(x) = x^3 + x - 4

a. Show that f(x) has a root on the interval [1,4]

b. Find the first three iterations of the bisection method on f on this interval

c. Find a bound for the number of iterations needed of bisection to approximate the root to within 10^-4

Homework Answers

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
1. Use the Intermediate Value Theorem to show that f(x)=x3+4x2-10 has a real root in the...
1. Use the Intermediate Value Theorem to show that f(x)=x3+4x2-10 has a real root in the interval [1,2]. Then, preform two steps of Bisection method with this interval to find P2.
public static int newtonCount​(double x, double err) Determines the number of iterations of Newton's method required...
public static int newtonCount​(double x, double err) Determines the number of iterations of Newton's method required to approximate the square root of x within the given bound. Newton's method starts out by setting the initial approximate answer to x. Then in each iteration, answer is replaced by the quantity (answer + x / answer) / 2.0. The process stops when the difference between x and (answer * answer) is strictly less than the given bound err. The method returns the...
Find root of the equation cos (x) = xex using Bisection method. Make calculation for 4...
Find root of the equation cos (x) = xex using Bisection method. Make calculation for 4 iterations. Choose xl= 0 and xu= 1. Determine the approximate error in each iteration. Give the final answer in a tabular form.
Solve the following problem using the MATLAB environment Write a function [approx_root, num_its] = bisection(f,a,b,tol) that...
Solve the following problem using the MATLAB environment Write a function [approx_root, num_its] = bisection(f,a,b,tol) that implements the bisection method. You function should take as input 4 arguments with the last argument being optional, i.e, if the user does not provide the accuracy tol use a default of 1.0e-6 (use varargin to attain this). Your function should output the approximate root, approx_root and the number of iterations it took to attain the root, num_its. However, if the user calls the...
Find the root of the function f(x) = 8 - 4.5 ( x - sin x...
Find the root of the function f(x) = 8 - 4.5 ( x - sin x ) in the interval [2,3]. Exhibit a numerical solution using Bisection method.
For the following function, determine the highest real root of f(x) = 2x3 – 11.7x2 +...
For the following function, determine the highest real root of f(x) = 2x3 – 11.7x2 + 17.7x - 5 by using (a) graphical methods, (b) fixed point iteration (three iterations, x0 = 3) (Hint: Be certain that you develop a solution that converges on the root), and (c) Newton-Raphson method (three iterations, x0 = 3). Perform an error check on each of your final root approximations (e.g. for the last of the three iterations).
Let f(x)=sin(x)+x^3-2. Use the secant method to find a root of f(x) using initial guesses x0=1...
Let f(x)=sin(x)+x^3-2. Use the secant method to find a root of f(x) using initial guesses x0=1 and x1=4. Continue until two consecutive x values agree in the first 2 decimal places.
Use the secant method to estimate the root of f(x) = -56x + (612/11)*10-4 x2 -...
Use the secant method to estimate the root of f(x) = -56x + (612/11)*10-4 x2 - (86/45)*10-7x3 + (3113861/55) Start x-1= 500 and x0=900. Perform iterations until the approximate relative error falls below 1% (Do not use any interfaces such as excel etc.)
for f=(x^4)-(6.4*x^3)+(6.45*x^2)+(20.538*x)- 31.752; find the roots using bisection for five iterations
for f=(x^4)-(6.4*x^3)+(6.45*x^2)+(20.538*x)- 31.752; find the roots using bisection for five iterations
1) a) Find the linearization of: f(x) = 3/x (cube root of x) at a =...
1) a) Find the linearization of: f(x) = 3/x (cube root of x) at a = 8. Use it to approximate 3/8.5 (cube root of 8.5). b) Find the absolute maximum and minimum values of f(x) = xe^-x (xe to the power of negative x) on the interval -1<x<1 (x is greater than or equal to -1 but less than or equal to 1)
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT