a) It is known that x2 x3 In(1 + x) = x - + Write down the generic form of the expansion with summation notation. Derive the Maclaurin expansion for ), (-1 < x < 1), and explain why x takes value in the range (-1,1). b) The Taylor series of fx) about x=a can be expressed as x2 f (a + x) = f(a) + xf'(a) + x3 + ... by using the Taylor series, calculate cos47°, show all the steps of your work (correct to 4 decimal places).

a) It is known that x2 x3 In(1 + x) = x - + Write down the generic form of the expansion with summation notation. Derive the Maclaurin expansion for ), (-1 < x < 1), and explain why x takes value in the range (-1,1). b) The Taylor series of fx) about x=a can be expressed as x2 f (a + x) = f(a) + xf'(a) + x3 + ... by using the Taylor series, calculate cos47°, show all the steps of your work (correct to 4 decimal places).

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter10: Sequences, Series, And Probability

Section10.1: Infinite Sequences And Summation Notation

Problem 72E

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