1. Consider the forward-difference approximation f'(x) -3fo + 4f1-f2 2h where f f(x + kh)...

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1. Consider the forward-difference approximation f'(x) ≈ -3fo + 4f1-f2 2h where f f(x + kh) for k = 0, 1, 2. Suppose further that f = yk + ek where yk is the decimal values and ek is the round-off errors. = (a) Find the total error bound (i.e., the sum of the round-off error and the truncation error). (b) Find the value of h that minimizes the total error bound. Hint: This is analogous to the error analysis section in the lecture note. 1. Consider the forward-difference approximation f'(x) ≈ -3fo + 4f1-f2 2h where f f(x + kh) for k = 0, 1, 2. Suppose further that f = yk + ek where yk is the decimal values and ek is the round-off errors. = (a) Find the total error bound (i.e., the sum of the round-off error and the truncation error). (b) Find the value of h that minimizes the total error bound. Hint: This is analogous to the error analysis section in the lecture note.

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