1. (a) Approximate f(x) = (1+z)³ by finding Ts(r) (the 5th degree Taylor polynomial of f) centered at 0.(b) Find the remainder Rs(z) for the above approximation and use this to show Ts(z) is not actually anapproximation of f(x), but it is in fact exactly f(x); that is, T5(x) = f(x).(c) Consider instead g(x) = (1+z)5/2. Find Rs(r) of g(x) and use this to show Ts(z) centred at 0 is notexactly g(x). (You only need to find Rs(x), not Ts(z)). Furthermore, deduce that for ze [-0.5, 0.5] theabsolute error in using Ts(z) to approximate g(x) is bounded by 5.81922. (a) Approximate the value of In(?) bu

Note: As per our Guidelines we can solve first parts as your all parts are not small . But I tried…

1. (a) Approximate f(x) = (1+z) by finding Ts(r) (the 5th degree Taylor polynomial of f) centered at 0. (b) Find the remainder Rs(z) for the above approximation and use this to show Ts(r) is not actually an approximation of f(x), but it is in fact exactly f(z); that is, Ts(x) = f(x). (c) Consider instead g(x) = (1+z)5/2, Find Rs(r) of g(x) and use this to show Ts(z) centred at 0 is not exactly g(x). (You only need to find Rs(z), not Ts(z)). Furthermore, deduce that for z € [-0.5, 0.5] the absolute error in using Ts(z) to approximate g(z) is bounded by . 8192

1. (a) Approximate f(x) = (1+z) by finding Ts(r) (the 5th degree Taylor polynomial of f) centered at 0. (b) Find the remainder Rs(z) for the above approximation and use this to show Ts(r) is not actually an approximation of f(x), but it is in fact exactly f(z); that is, Ts(x) = f(x). (c) Consider instead g(x) = (1+z)5/2, Find Rs(r) of g(x) and use this to show Ts(z) centred at 0 is not exactly g(x). (You only need to find Rs(z), not Ts(z)). Furthermore, deduce that for z € [-0.5, 0.5] the absolute error in using Ts(z) to approximate g(z) is bounded by . 8192

College Algebra

7th Edition

ISBN:9781305115545

Author:James Stewart, Lothar Redlin, Saleem Watson

Publisher:James Stewart, Lothar Redlin, Saleem Watson

Chapter3: Polynomial And Rational Functions

Section3.5: Complex Zeros And The Fundamental Theorem Of Algebra

Problem 3E: A polynomial of degree n I has exactly ____________________zero if a zero of multiplicity m is...

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