Use a relative error in pn (relative error= abs(pn- pn-1)/abs(pn)) of 0:0001 to find the root...

Use a relative error in p_n (relative error= abs(p_n- p_n-1)/abs(p_n)) of 0:0001 to find the root of f(x) = x + exp(x) = 0 using both the Bisection method, the Fixed Point method and Newton's method. How many iterations are required for each method

Expert Solution

Colby Messinger answered 2 years ago

Use Newton-Raphson to find the real root to five significant figures 64x^3+6x^2+12-1=0

1. The equation 8?2 − 3?? = 0 has three roots. Find: (i) The first root,...

1. The equation 8?2 − 3?? = 0 has three roots. Find: (i) The first root, which is between -1 and 0, by the bisection method; (ii) The second root, which is between 1 and 2, by Newton’s method; (iii) The third root, which is between 3 and 4, by both the bisection method and Newton’s method. All the answers should be correct to 2 decimal places.

use bisection to find the real root x = sin(x) + 1 with the initial guesses...

use bisection to find the real root x = sin(x) + 1 with the initial guesses of x l = 0 and x u = 3. perform the computation until the approximate error falls below 5%

Use the Newton’s method to find the root for ex+1 = 2 + x, over [−2,...

Use the Newton’s method to find the root for ex+1 = 2 + x, over [−2, 2]. Can you find a way to numerically determine whether the convergence is roughly quadratic using error produced at each iteration? Include your answers as Matlab code comments

USING BISECTION METHOD, FIND THE ROOT OF 0.5e^x - 5x + 2 = 0 ON THE...

USING BISECTION METHOD, FIND THE ROOT OF 0.5e^x - 5x + 2 = 0 ON THE INTERVAL [ 0 , 1 ] UP TO 3 DECIMAL PLACES. USE NEWTON'S METHOD TO APPROXIMATE THE ROOT OF f(x)=x^2-5 IN THE INTERVAL [ 2 , 3 ] UP TO 4 DECIMAL PLACES.

Use Newton-Raphson to find the real root to five significant figures 64x^3+6x^2+12-1=0. First graph this equation...

Use Newton-Raphson to find the real root to five significant figures 64x^3+6x^2+12-1=0. First graph this equation to estimate. Use the estimate for Newton-Raphson

Use false position method to find the root of ?(?) = −sin(? − 5) + ?...

Use false position method to find the root of ?(?) = −sin(? − 5) + ? with initial guesses of 0.2 and 1. Show up to three iterations and calculate the relative percent error ?? for each iteration possible? Show full details for at least one iteration to get full points. Also, if three significant figure accuracy is required, show if the value after third iteration is acceptable or not.

PLEASE USE PYTHON CODE 2. Find the smallest positive (real) root of x^3-3.23x^2-5.54x+9.84 = 0 by...

PLEASE USE PYTHON CODE 2. Find the smallest positive (real) root of x^3-3.23x^2-5.54x+9.84 = 0 by the method of bisection

for parts 1-2 for use these answers/rules Find the relative extrema of the function Specifically: The...

for parts 1-2 for use these answers/rules Find the relative extrema of the function Specifically: The relative maxima of f occur at x = The relative minima of f occur at x = The value of f at its relative minimum is the value of f at its relative maximum is Notes: Your answer should be a comma-separated list of values or the word "none". part 1) f(x)=9x−(4/x)+6 part 2) f(x)=(8x^2−7x+32)/(x) part 3) Use the derivative to find the vertex...

Let X~N(-5,9). Find P(abs(X)<2) P(abs(X)>1) My stats professor gave this as an extra credit assignment but...

Let X~N(-5,9). Find P(abs(X)<2) P(abs(X)>1) My stats professor gave this as an extra credit assignment but never went over it in class and said she won't answer any questions about it in her office hours so I'm completely lost. Help please!

Question