5. Using Taylor series, derive the error term for the approximation f' (x) ~ -3 f(x) + 4 f(x + b)...

Question

Question

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

math Advanced-Math

Answer 1

Answer #1

Answer 2

Similar Homework Help Questions

Derive the following numerical approximation to the second derivative of f(x) using Taylor's series. Show all...

Derive the following numerical approximation to the second derivative of f(x) using Taylor's series. Show all of your steps and derive also the order of accuracy of this approximation in terms of h. - f(x + 2h) + 16f(x + h) – 30f(x) + 16 f(x – h) – f(x – 2h) 12h2 1 (C)
Using the Taylor series expansion, derive the following 2nd order central difference approximation for the 4th...

Using the Taylor series expansion, derive the following 2nd order central difference approximation for the 4th derivative. Please provide answer in clear understandable handwriting dx
1) a) Write the Taylor Series for f(x)=5. b) Write the Taylor Series for f(x) =...

1) a) Write the Taylor Series for f(x)=5. b) Write the Taylor Series for f(x) = 5+4x c) Write the Taylor Series for f(x)=5+4x+7x^2 d) Write the Taylor Series for f(x)=5+4x+7x^2 + 3x^3

Question 1 15 Points) It is always desirable to have/ use the finite difference approximation wit...

Question 1 15 Points) It is always desirable to have/ use the finite difference approximation with error term. Please using the Taylor Series: higher order of truncation sw(x) h" +R 2! 3! (I) Derive the following forward difference approximation of the 2nd orde 2) What is the order of error for this case? derivative of f(x). f" derivative off(x) h2 Question 1 15 Points) It is always desirable to have/ use the finite difference approximation with error term. Please using...
1 1 Find the Taylor series for f(x) about <= 5. 3.2 4 The general term...

1 1 Find the Taylor series for f(x) about <= 5. 3.2 4 The general term is an = The first five terms of the Taylor series are Show or upload your work below.
Section A Q1 0 Using the following Taylor series expansion: f(x+h) = f(x)+hf'(x)+22 h 3! f"(x)+...

Section A Q1 0 Using the following Taylor series expansion: f(x+h) = f(x)+hf'(x)+22 h 3! f"(x)+ (+0) (1.1) 4! show that the central finite difference formula for the first derivative can be written as: f'(x)= f(x+h)-f(x-1) + ch" +0(hº) (1.2) 2h Determine cp and of the derived equation. [4 marks] Consider the function: f(x) = sin +COS (1.3) 2 2 Let x =ih with n=0.25, give your answer in 3 decimals for (ii) to (vi): (ii) Evaluate f(x) for i...

Find the Taylor series up to the degree 4 term at a = 3 for f(x)...

Find the Taylor series up to the degree 4 term at a = 3 for f(x) = e.
4. Given a function f(x), use Taylor approximations to derive a second order one-sided ap- proximation to f'(ro...

4. Given a function f(x), use Taylor approximations to derive a second order one-sided ap- proximation to f'(ro) is given by f(zo + h) + cf (zo + 21) + 0(h2). f' (zo) = af(xo) + What is the precise form of the error term? Using the formula approximate f' (1) where r) = e* for h 1/(2p) for p = 1 : 15, Form a table with columns giving h, the approximation, absolute error and absolute error divided by...
(25 pts) For f(x) infinitely continuously differentiable, and C so that the formula Taylor series to...

(25 pts) For f(x) infinitely continuously differentiable, and C so that the formula Taylor series to find A,B, use Af (x 2h)Bf(x) Cf (xh) gives the highest order accurate approximation of f'(x) (for general f and x). What is that order? Remember, Taylor series says h2 |f" (x)^f"(x) h3 f(xh) f(x)hf'(x)+ ... 2! 3! (25 pts) For f(x) infinitely continuously differentiable, and C so that the formula Taylor series to find A,B, use Af (x 2h)Bf(x) Cf (xh) gives the...

5. (10 points) Derive the following formula for f(x) f(4(x+)-3f(x)-f(x+2h)) and show that error is OCh 5. (10 points) Derive the following formula for f(x) f(4(x+)-3f(x)-f(x+2h)) and show th...

5. (10 points) Derive the following formula for f(x) f(4(x+)-3f(x)-f(x+2h)) and show that error is OCh 5. (10 points) Derive the following formula for f(x) f(4(x+)-3f(x)-f(x+2h)) and show that error is OCh