Problem 1.the second derivativeConsider the three-point centered difference formula forf"(xo)f(xo-h)-2f(x) + f(xo + h) h²h²12/(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 bytheory.

Centered difference formula:- f''x0 = fx0-h -2fx0 +fx0 +hh2 Approximate error:-ε ≤ h212 f4μ Here,…

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.

Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)

6th Edition

ISBN:9781337111348

Author:Bruce Crauder, Benny Evans, Alan Noell

Publisher:Bruce Crauder, Benny Evans, Alan Noell

Chapter2: Graphical And Tabular Analysis

Section2.1: Tables And Trends

Problem 1TU: If a coffee filter is dropped, its velocity after t seconds is given by v(t)=4(10.0003t) feet per...

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Question

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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