Write a C program that uses Newton's Method to solve an equation in one variable.
Try solving x^x = ln2
the deriviative of x^x is x^x(lnx + 1). The 'ln' function in C is log(), and the value
for ln2 is approximately .693147180559945 (to 15 places, about the limit of double precision).
Test for convergence using a tolerance of about 1e-10 (that is, look at the absolute value of
new_x - old_x and require this to be less than 1e-10 to say it has converged). Also keep a count
of the number of iterations; if this goes over 100, announce that there is no convergence. Otherwise
once you have convergence, print the solution (say to 15 places) and the number of iterations
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how to write this function in c++ by using Newtton raphson method?
*the question is:
Write a program that uses Newton-Raphson Method to approximate the root of a function
we could execute an infinite number of iterations to find a perfect representation for the root of our function. However, we will assume that the process has worked accurately when x = xk+1- xk becomes less than 0.1
To see how this works, we will perform the Newton-Raphson method on the function f(x) = x2-4. Below are listed the values that we need to know in order to complete the process:
f(x) = x2-4
f'(x) = 2x
x1 = 6
*the answer should be:
Newton-Raphson Method to approximate the root of a function
- Enter precision (1/10, 1/100, 1/1000,...): 0.1
xk f(x) derived_f(xk) xk+1 dx
6.000 32.000 12.000 3.333 2.667
3.333 7.111 6.667 2.267 1.067
2.267 1.138 4.533 2.016 0.251
2.016 0.063 4.031 2.000 0.016
- Enter your choice: (q) to quit, (c) to continue: c
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