QuestionQuestion

1. Consider a function f(x) = ln x. Find the fifth order Taylor polynomial about the point x0 = 2. Then determine the minimum number of terms (i.e. n) that would guarantee an absolute error of no more than 10⁻³ in the Taylor approximation for f(x) for all x in the interval [1,2].

4. Type the following Matlab function
function fixed(g, x0, tol, Nmax)
iter = 0;
u = feval(g, x0);
err = abs(u - x0);
disp(--------------------------')
disp(' iter      x g(x)    |x_(n+1)-x_n|')
fprintf('%2.0f %12.6f %12.6f\n', iter, x0, u)
while(err > tol) & (iter <= Nmax)
x1 = u;
err = abs(x1 - x0);
x0 = x1;
u = eval(g, x0);
iter = iter + 1;
fprintf('%2.0f %12.6f %12.6f\ %12.8f \n', iter, x0, u, err)
end
if(iter > n)
disp('Method failed to converge')
end

Include comments on each line of code to explain the purpose. Use this code to find the rooot of f(x) = 5/x² + 2, using x0 = 2.5, tol = 10⁻⁴ and Nmax = 100. Change Nmax if it does not converge.

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Numerical Analysis Problems
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