Problem 3 (hand-calculation): Consider a two-dimensional function: f(x, y)- sin(x)cos() where x and y are in radi ans (a) Evaluate a f/oz, f / ду, and /(8z0) at x = y = 1 analytically. (b) Evaluate a...
Problem 3 (hand-calculation): Given f(x) = In (5-z) for x E [0,2], apply Taylor's theorem with zo = 1 in the following (a) Find the lowest-order Taylor polynomial approximation that is accurate to within (b) Find the actual errors at x = 0, 1 and 2. exercises. 10-3 Take a photo of your work. Include all pages in a single photo named problem3.jpg. Set the following in your homework script: figure(3); imshow (imread('problem3.jpg'); p3 = 'See figure 3'. Problem 3...
Problem 3 (hand-calculation): Consider the functiong() 1 +e. Show that, for any initial guess zo on the interval r E [1,2], the fixed-point iteration converges. How many iterations does the theory ow that, for anv initia predict thatt will take to achieve 10- accuracy? Take a photo of your work. Include all pages in a single photo named problem3.jpg. Set the following in your homework script: figure(3); imshow(imread('problem3.jpg')); p3 'See figure 2. Problem 3 (hand-calculation): Consider the functiong() 1 +e....
Problem 2 (hand-calculation): Consider the function f(x) tabulated in table 1. Apply improved trapezoid rule to estimate the integral, If) J ) dz, by using the following number of subintervals, n (a) n-3. Use grid points at i0, 4, 8 and 12 (b) n- 6. Use grid points at i0, 2,4, 6, 8, 10 and 12 (c) n = 12, Use all grid points For each part, compute the integral, T(f) and the corresponding absolute error Er(f), and the error...