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Problem 1. the second derivative Consider the three-point centered difference formula for f"(x) = f(xo-h)-2f(x) + f(xo + h) h² h² + 12/¹) (4) where lies between xo - h and xo + h. (a) Approximate f"(2), where f(x) = In(x + 1). Use h = 0.1. (b) Compute the actual error in the approximation. (c) Find the approximation error and verify the error estimate predicted by theory.

Problem 1. the second derivative Consider the three-point centered difference formula for f"(x) = f(xo-h)-2f(x) + f(xo + h) h² h² + 12/¹) (4) where lies between xo - h and xo + h. (a) Approximate f"(2), where f(x) = In(x + 1). Use h = 0.1. (b) Compute the actual error in the approximation. (c) Find the approximation error and verify the error estimate predicted by theory.

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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Problem 1. the second derivative Consider the three-point centered difference formula for f"(xo) f(xo-h)-2f(x) + f(xo + h) h² h² 12/(4) where lies between xo - h and xo + h. 0.1. (a) Approximate f"(2), where f(x) = ln(x + 1). Use h (b) Compute the actual error in the approximation. (c) Find the approximation error and verify the error estimate predicted by theory.
Transcribed Image Text:Problem 1. the second derivative Consider the three-point centered difference formula for f"(xo) f(xo-h)-2f(x) + f(xo + h) h² h² 12/(4) where lies between xo - h and xo + h. 0.1. (a) Approximate f"(2), where f(x) = ln(x + 1). Use h (b) Compute the actual error in the approximation. (c) Find the approximation error and verify the error estimate predicted by theory.
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