3. Find the Taylor series expansion, up to the seventh (7th) derivative, ofthe following given functions, at the given centre a:(a) f(x) = -√√x at a = 8;(b) g(x) = cos²x at a =(c) f(x) =1(1 + x)³3=;at a = 1;

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Answered: 3. Find the Taylor series expansion, up…

College Algebra

1st Edition

ISBN:9781938168383

Author:Jay Abramson

Publisher:Jay Abramson

Chapter6: Exponential And Logarithmic Functions

Section6.1: Exponential Functions

Problem 60SE: The formula for the amount A in an investmentaccount with a nominal interest rate r at any timet is...

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To calculate f(1.02) from the function f(x) = x 1/2, first write the Taylor expansion of the function at x0 = 1 with 5 terms. Then calculate f(1.02) with an accuracy of two decimal places by error analysis from Taylor expansion.
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3. Find the Taylor series expansion, up to the seventh (7th) derivative, o the following given functions, at the given centre a: (a) f(x) = -√√x at a = 8; (b) g(x) = cos²x at a = (c) f(x) = 1 (1+x)³ at a = 1;