f(x)=x^3-3x-1=0
x=[0,2]
epsilon=5*10^-2
1. perform the bisection method for the root in [0,2] until your
root is closer to the real root within epsilon.
Let x_0=1.0, x_1=1.2
2. perform the secant method until your root is closer to the
real root within epsilon.
3. do as in 2. with the Newton's method, with x_0=1.1
Apply Newton’s method and the modified method to the equation
f(x) = 1−cos(x−5) to approximate the a double root 5. Compare the
results and demonstrate the superiority of the modified method.
Numerically identify the rates of convergence of both the
methods.
Using the bisection method, find the root of the following
function:
f(x)=cos(2x) - x
Use the following initial values: xl=0 and xu=2
NOTE: Perform only 3 iterations.
How would the 68, 95, 99% rule apply for measures E and F if for
measure E my mean is 73 and standard deviation of 11 and Measure F
my mean is 27 and standard deviation of 17.4 what each fall
between
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.
Estimate a real root of the polynomial
f(x) = 5x4-2x3-25x2-6x+45 between
x=1 and x=2 (using bisection, Standard Newton-Raphson, Secant, and
modified Newton-Raphson, and modified Secant methods). Show the
detailed calculations for 5 iterations (for each method)