Question

Answer each of the following in details~: (a) Can the Bisection method be used to find...

Answer each of the following in details~:

(a) Can the Bisection method be used to find the roots of the function ?(?) = 1 + ??? ?? Justify your Answer.

(b) While using the Newton’s method with the initial guess ?0 = 4 and ?(?0) = 1 gives ?1 = 3. Find ?′(?0).

(c) While using the Secant method for finding a root, ?0 = 2, ?1 = −1, ??? ?2 = −2 with ?(?1) = 4. Find ?(?0).

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
Consider the function f(x) = 1 2 |x|. a) Can we use bisection search to find...
Consider the function f(x) = 1 2 |x|. a) Can we use bisection search to find one of its roots? Why or why not? b) Can we use Newton’s method to find one of its roots? Why or why not?
Q1: Use bisection method to find solution accurate to within 10^−4 on the interval [0, 1]...
Q1: Use bisection method to find solution accurate to within 10^−4 on the interval [0, 1] of the function f(x) = x−2^−x Q3: Find Newton’s formula for f(x) = x^(3) −3x + 1 in [1,3] to calculate x5, if x0 = 1.5. Also, find the rate of convergence of the method. Q4: Solve the equation e^(−x) −x = 0 by secant method, using x0 = 0 and x1 = 1, accurate to 10^−4. Q5: Solve the following system using 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.
Consider the function ?(?) = ?^2 − 3? − 2. a) Use Newton’s Method to estimate...
Consider the function ?(?) = ?^2 − 3? − 2. a) Use Newton’s Method to estimate a root for the function given by the above formula. More precisely: Using the initial value of ?1 = 5, calculate ?3. b) Solve the quadratic equation ?^2 − 3?− 2 = 0 and compute the two solutions to 4 decimal places. How do these compare to the approximate root you computed in part (a) above? c) Suppose your friend uses Newton’s Method to...
Given function ?(?) = ?^4 − 2?^3 + 3?^2 − 2? + 1. a) Solve analytically...
Given function ?(?) = ?^4 − 2?^3 + 3?^2 − 2? + 1. a) Solve analytically to find the exact roots of the equation ?(?) = 0. (Hint: ?^4 − 2?^3 + 3?^2 − 2? + 1 = (?^2 − ? + 1)^2) b) Predict if you can find a zero of ?(?) = 0 by using Newton’s method with any real initial approximation Po.
Use the Rational Root Theorem to find all possible rational roots then use Newton’s Method to...
Use the Rational Root Theorem to find all possible rational roots then use Newton’s Method to find one rational root and then synthetic division and the quadratic formula to find the any remaining rational, irrational or complex roots.   Px=3x^5-8x^4-17x^3+38x^2+20x-24
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...
SOMEONE, PLEASE ANSWER This is for Numerical Methods class homework Consider the function ex + x...
SOMEONE, PLEASE ANSWER This is for Numerical Methods class homework Consider the function ex + x - 7 Find an approximation of the root of f(x) with an absolute error less than 0.001 using Newton’s method Please plot the function to choose an initial guess and conduct as many iterations as needed until you reach the specified error
2. (a) For the equation e^x = 3 - 2 x , find a function, f(x),...
2. (a) For the equation e^x = 3 - 2 x , find a function, f(x), whose x-intercept is the solution of the equation (i.e. a function suitable to use in Newton’s Method), and use it to set up xn+1 for Newton’s Method. (b) Use Newton's method to find x3 , x4 and x5 using the initial guess x1 = 0 . How many digits of accuracy are you certain of from these results? (c) Use x1+ ln 2   and show...
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.