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3. Use forward and backward difference approximations of O(h) and a centered difference approximations of O(h²) to estimate the first derivative of the function f(x) = 25x³6x² + 7x-88 at x =2 using a step size h = 0.25. Compare your results with the true value of the derivative. Interpret your results on the basis of the remainder term of the Taylor series expansion.

3. Use forward and backward difference approximations of O(h) and a centered difference approximations of O(h²) to estimate the first derivative of the function f(x) = 25x³6x² + 7x-88 at x =2 using a step size h = 0.25. Compare your results with the true value of the derivative. Interpret your results on the basis of the remainder term of the Taylor series expansion.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Please solve question no.3 and show a clear and readable solution. Thanks!!!

I. Taylor Series Expansion 3. Use forward and backward difference approximations of O(h) and a centered difference approximations of O(h²) to estimate the first derivative of the function f(x) = 25x³6x² + 7x-88 at x =2 using a step size h = 0.25. Compare your results with the true value of the derivative. Interpret your results on the basis of the remainder term of the Taylor series expansion.
Transcribed Image Text:I. Taylor Series Expansion 3. Use forward and backward difference approximations of O(h) and a centered difference approximations of O(h²) to estimate the first derivative of the function f(x) = 25x³6x² + 7x-88 at x =2 using a step size h = 0.25. Compare your results with the true value of the derivative. Interpret your results on the basis of the remainder term of the Taylor series expansion.
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