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central-difference method to approximate the derivative of f(x) = ln x² with value Use of x at 1.8, using a step size of 0.5. Satisfy the 0.05% acceptance criteria.

central-difference method to approximate the derivative of f(x) = ln x² with value Use of x at 1.8, using a step size of 0.5. Satisfy the 0.05% acceptance criteria.

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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2. Use central-difference method to approximate the derivative of f(x) = ln x² with value of x at 1.8, using a step size of 0.5. Satisfy the 0.05% acceptance criteria.
Transcribed Image Text:2. Use central-difference method to approximate the derivative of f(x) = ln x² with value of x at 1.8, using a step size of 0.5. Satisfy the 0.05% acceptance criteria.
3. Approximate the integral of f(x) = x² − 2x + 4 with the following unequally spaced points shown in the table using Trapezoidal rule. What is the absolute relative error? Xo 0 X1 0.1 X2 0.3 X3 0.6 X4 1.0 4. Find f'(5) using backward difference method of the function 7x³5x + 1 f(x) 2x¹ + x² + 1 with a given step size of h = 0.5. Satisfy 0.1% acceptance criteria. 5. Given the function f(x) = 1 + e* sin(4x) with integration limits from a = 0 to b= 1. Use Trapezoidal Rule and Simpson's 1/3 rule to calculate the approximate value with n = 6. Get the relative error of both methods. =
Transcribed Image Text:3. Approximate the integral of f(x) = x² − 2x + 4 with the following unequally spaced points shown in the table using Trapezoidal rule. What is the absolute relative error? Xo 0 X1 0.1 X2 0.3 X3 0.6 X4 1.0 4. Find f'(5) using backward difference method of the function 7x³5x + 1 f(x) 2x¹ + x² + 1 with a given step size of h = 0.5. Satisfy 0.1% acceptance criteria. 5. Given the function f(x) = 1 + e* sin(4x) with integration limits from a = 0 to b= 1. Use Trapezoidal Rule and Simpson's 1/3 rule to calculate the approximate value with n = 6. Get the relative error of both methods. =
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