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Question 3 Consider the function f(x) = (a + bx)2/3, (a) Find the third-order Taylor polynomial of (1+x)2/3 around z = 0. The coefficients of the Taylor polynomial must be written in the exact form, i.e in form of fractions as neccesary. (b) Rewrite f(z) in a different way to enable you to use the Taylor polynomial of (1+x)2/3 from part (a). Using this result and the answer from (a), write down the third order Taylor polynomial for the function f around x = 0.

Question 3 Consider the function f(x) = (a + bx)2/3, (a) Find the third-order Taylor polynomial of (1+x)2/3 around z = 0. The coefficients of the Taylor polynomial must be written in the exact form, i.e in form of fractions as neccesary. (b) Rewrite f(z) in a different way to enable you to use the Taylor polynomial of (1+x)2/3 from part (a). Using this result and the answer from (a), write down the third order Taylor polynomial for the function f around x = 0.

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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Question 3 Consider the function f(x) = (a + bx)2/3, (a) Find the third-order Taylor polynomial of (1+x)2/3 around z = 0. The coefficients of the Taylor polynomial must be written in the exact form, i.e in form of fractions as neccesary. (b) Rewrite f(x) in a different way to enable you to use the Taylor polynomial of (1+x)2/3 from part (a). Using this result and the answer from (a), write down the third order Taylor polynomial for the function f around x = 0.
Transcribed Image Text:Question 3 Consider the function f(x) = (a + bx)2/3, (a) Find the third-order Taylor polynomial of (1+x)2/3 around z = 0. The coefficients of the Taylor polynomial must be written in the exact form, i.e in form of fractions as neccesary. (b) Rewrite f(x) in a different way to enable you to use the Taylor polynomial of (1+x)2/3 from part (a). Using this result and the answer from (a), write down the third order Taylor polynomial for the function f around x = 0.
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