Exercise 6.5.1. Consider the function 9 defined by the power series o diw 28x3 g(x) = =x- +3 2 - x4 x5 + 4 5 (a) Is g defined on (-1,1)? Is it continuous on this set? Is g defined on (-1, 1]? Is it continuous on this set? What happens on [-1,1]? Can the power series for g(x) possibly converge for any other points |x| > 1? Explain. (b) For what values of x is g'(x) defined? Find a formula for g'.

Exercise 6.5.1. Consider the function 9 defined by the power series o diw 28x3 g(x) = =x- +3 2 - x4 x5 + 4 5 (a) Is g defined on (-1,1)? Is it continuous on this set? Is g defined on (-1, 1]? Is it continuous on this set? What happens on [-1,1]? Can the power series for g(x) possibly converge for any other points |x| > 1? Explain. (b) For what values of x is g'(x) defined? Find a formula for g'.

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter10: Sequences, Series, And Probability

Section10.3: Geometric Sequences

Problem 49E

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