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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.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter4: Polynomial And Rational Functions
Section4.3: Zeros Of Polynomials
Problem 4E
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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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