3. Determine the error for the approximation f'(x) = #[f(x+3h) – f (x - 1)].
please answer q2 with detailed steps, thanks!
2. Calculate the leading truncation error of the following approximation - -3 +3/ 2 3h-1 + f.)/4rs-off /d 3 + e whiere e is the error (Ans:-3 r/2d4f/dr41)
2. Calculate the leading truncation error of the following approximation - -3 +3/ 2 3h-1 + f.)/4rs-off /d 3 + e whiere e is the error (Ans:-3 r/2d4f/dr41)
Please help me solve this. thanks
5. Using Taylor series, derive the error term for the approximation f' (x) ~ -3 f(x) + 4 f(x + b)-f(x + 2h)]. 2h
5. Using Taylor series, derive the error term for the approximation f' (x) ~ -3 f(x) + 4 f(x + b)-f(x + 2h)]. 2h
Determine the degree of the Maclaurin polynomial required for the error in the approximation of the function at the indicated value of x to be less than 0.001. f(x) = 1/(x+1') approximate f(0.2) _______
(a) Find the relative error of approximation of f'(3) by the 3-point symmetric formula with mesh size h = 0.15, where f(x) = 7/(1+3x2)
Determine the degree of the Maclaurin polynomial required for the error in the approximation of the function at the indicated value of x to be less than 0.001. f(x) = 1/(x+1') approximate f(0.3)
Compute the error of each approximation, and then determine which form fits the data the best 3. (20 pts) Consider the nonlinear system 6x1 2 cos(3)-1-0 9r2 + Vr| + sin(za) + 1.06 + 0.9 = 0, Solve this system by i) Newton's method, (ii) Broyden's method. For both methods, use the initial approximation x() = [0,0,0], and the stopping criteria llx(k) X(k 1) I < tol = 10-9. Here 1-1 is the Euclidian 2-norm Display the results for each...
7. Find the linear approximation of f(x,y)=-x’ +2y’ at (3,-1) and use this approximation to estimate f(3.1.-1.04). S (3,-1) = (3.-1) = ,(3,-1) = L(x, y)= L(3.1, -1.04) =
Q5. [8pnts] Use Taylor's formula to find a quadratic approximation of the function f (x, 3) e-2y 1+22-y HE2-7 at the origin. Estimate the error in the approximation if ㈣く.1 and lyl < .1.
Q5. [8pnts] Use Taylor's formula to find a quadratic approximation of the function f (x, 3) e-2y 1+22-y HE2-7 at the origin. Estimate the error in the approximation if ㈣く.1 and lyl
4. Consider the function f(x) = sin(x), x > 0. (a) Estimate f(r) - f(A), where TA is an approximation to rr. (b) Estimate Rel(f(A)) in terms of the error Rel (TA). - f(TA
4. Consider the function f(x) = sin(x), x > 0. (a) Estimate f(r) - f(A), where TA is an approximation to rr. (b) Estimate Rel(f(A)) in terms of the error Rel (TA). - f(TA
h 5. In Homework 8 we looked at the finite difference approximation of f'(x). f(x + 1) = f(x) + f'(z)h + }}" (-x)+2 +0(h2). Rearranging terms, and dividing by h leads to D(h) f(x+h)-f(x) != f'(x) +}s"(x)h + O(n?). Find constants a and 8 such that A(h) = aD(h/2) + BD(h) = f'(x) + (h) (similar to convergence acceleration in Chapter 2, we are using our knowledge of the be- haviour of the error to get a better approximation!)...