Apply the extrapolation process described in Example 1 to determine N3(h), an approximation to f ′(x0), for the following functions and step sizes.
- a. f (x) = ln x, x0 = 1.0, h = 0.4
- b. f (x) = x + e, x0 = 0.0, h = 0.4
- c. f (x) = 2x sin x, x0 = 1.05, h = 0.4
- d. f (x) = x3 cos x, x0 = 2.3, h = 0.4
Example 1 In Example 1 of Section 4.1, we used the forward-difference method with h = 0.1 and h = 0.05 to find approximations to f′(1.8) for f (x) = ln(x). Assume that this formula has truncation error O(h). Use extrapolation on these values to see if this results in a better approximation.
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