2. From the following table of values of f(x) = sinh x find f'(1.4) using: х 1.3 1.4 1.5 1.6 1.2 f(x) 1.5095 1.6984 1.9043 2.1293 2.3756 (a) Backward difference formula based on f(1.3) and ƒ(1.4), and backward difference formula based on f(1.2) and f(1.4). Perform one step of Richardson's extrapolation on these values. (b) Centered difference formula based on f(1.3) and f(1.5), and centered difference formula. based on f(1.2) and f(1.6). Perform one step of Richardson's extrapolation on these values. Compare your results with the exact value f'(1.4) = cosh 1.4 = 2.1509. Comment on the errors of approximations.

2. From the following table of values of f(x) = sinh x find f'(1.4) using: х 1.3 1.4 1.5 1.6 1.2 f(x) 1.5095 1.6984 1.9043 2.1293 2.3756 (a) Backward difference formula based on f(1.3) and ƒ(1.4), and backward difference formula based on f(1.2) and f(1.4). Perform one step of Richardson's extrapolation on these values. (b) Centered difference formula based on f(1.3) and f(1.5), and centered difference formula. based on f(1.2) and f(1.6). Perform one step of Richardson's extrapolation on these values. Compare your results with the exact value f'(1.4) = cosh 1.4 = 2.1509. Comment on the errors of approximations.

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter3: The Derivative

Section3.CR: Chapter 3 Review

Problem 8CR

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