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In what follows, the function f is given by f(x) = 3+1, (a) (i) Use Taylor's Theorem to derive a general two-point forward difference formula for approximating f'(zo). (ii) What is the order of the truncation error for this formula? Explain briefly what this means. (iii) Apply the forward difference formula to f(r) for the case where zo-2. Use a step size of h= 0.1. (iv) Calculate the error in the approximation in (a)(iii).

In what follows, the function f is given by f(x) = 3+1, (a) (i) Use Taylor's Theorem to derive a general two-point forward difference formula for approximating f'(zo). (ii) What is the order of the truncation error for this formula? Explain briefly what this means. (iii) Apply the forward difference formula to f(r) for the case where zo-2. Use a step size of h= 0.1. (iv) Calculate the error in the approximation in (a)(iii).

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question 4. Instruction: Apply five decimal place rounding to calculations where applicable. In what follows, the function f is given by f(x) = 3+1, (a) (i) Use Taylor's Theorem to derive a general two-point forward difference formula for approximating f'(zo). (ii) What is the order of the truncation error for this formula? Explain briefly what this means. (iii) Apply the forward difference formula to f(r) for the case where to = 2. Use a step size of h = 0.1. (iv) Calculate the error in the approximation in (a)(iii).
Transcribed Image Text:Question 4. Instruction: Apply five decimal place rounding to calculations where applicable. In what follows, the function f is given by f(x) = 3+1, (a) (i) Use Taylor's Theorem to derive a general two-point forward difference formula for approximating f'(zo). (ii) What is the order of the truncation error for this formula? Explain briefly what this means. (iii) Apply the forward difference formula to f(r) for the case where to = 2. Use a step size of h = 0.1. (iv) Calculate the error in the approximation in (a)(iii).
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