5. (Based on Sydsaeter et al. (2022)) Consider the function f(x) = ln(1 + x). 5.1. Write down the fifth-order Taylor approximation, denoted by T(x), to the given function above about x₁ = 0 (where x₁ is defined as in our lecture slides on Taylor's Theorem). ints) 5.2. How much does your approximation deviate from the exact value when x = 1? (Hint: evaluate the exact value of f(x) when x = 1, and evaluate T(x) when x = 1. Then calculate f(1) - T(1)
5. (Based on Sydsaeter et al. (2022)) Consider the function f(x) = ln(1 + x). 5.1. Write down the fifth-order Taylor approximation, denoted by T(x), to the given function above about x₁ = 0 (where x₁ is defined as in our lecture slides on Taylor's Theorem). ints) 5.2. How much does your approximation deviate from the exact value when x = 1? (Hint: evaluate the exact value of f(x) when x = 1, and evaluate T(x) when x = 1. Then calculate f(1) - T(1)
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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Transcribed Image Text:5. (Based on Sydsaeter et al. (2022)) Consider the function f(x) = ln(1 + x).
5.1. Write down the fifth-order Taylor approximation, denoted by T(x), to the given function
above about x₁ = 0 (where x₁ is defined as in our lecture slides on Taylor's Theorem).
ints)
5.2. How much does your approximation deviate from the exact value when x = 1?
(Hint: evaluate the exact value of f(x) when x = 1, and evaluate T(x) when x = 1. Then
calculate f(1) - T(1)
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