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The function f(x) = Cosh(x) can be expressed by Taylor series as follow: Cosh (xi) 2! f(Xi+1)=Cosh(xi) + Sinh(xi)(h) (h)²+ · (h)³…... Sinh(xi) 3! a) Using three terms of the above expression to estimate Cosh(4.6) centered at 4. (4 b) Calculate the true absolute error. c) Calculate the truncation error R₂. Note: The true value of Cosh(4.6) is 49.747.

The function f(x) = Cosh(x) can be expressed by Taylor series as follow: Cosh (xi) 2! f(Xi+1)=Cosh(xi) + Sinh(xi)(h) (h)²+ · (h)³…... Sinh(xi) 3! a) Using three terms of the above expression to estimate Cosh(4.6) centered at 4. (4 b) Calculate the true absolute error. c) Calculate the truncation error R₂. Note: The true value of Cosh(4.6) is 49.747.

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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The function f(x) = Cosh(x) can be expressed by Taylor series as follow: Cosh (xi) (h)²+ 2! f(Xi+1)=Cosh(Xi) + Sinh(xi)(h) + Sinh(xi) 3! a) Using three terms of the above expression to estimate Cosh(4.6) centered at 4. (4 b) Calculate the true absolute error. c) Calculate the truncation error R₂. Note: The true value of Cosh(4.6) is 49.747. (h)³....
Transcribed Image Text:The function f(x) = Cosh(x) can be expressed by Taylor series as follow: Cosh (xi) (h)²+ 2! f(Xi+1)=Cosh(Xi) + Sinh(xi)(h) + Sinh(xi) 3! a) Using three terms of the above expression to estimate Cosh(4.6) centered at 4. (4 b) Calculate the true absolute error. c) Calculate the truncation error R₂. Note: The true value of Cosh(4.6) is 49.747. (h)³....
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