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Chapter 8: Q. 12 (page 679)

If a function f has a Taylor series at x0, what are the possibilities for the interval of convergence for that series?

Short Answer

Expert verified

Thepossiblevaluefortheintervalofconvergencefortheseriesare(-蚁,蚁),(-蚁,蚁],[-蚁,蚁)and[-蚁,蚁],here,蚁>0.

Step by step solution

01

Step 1. Given information is:

A function f with Taylor series atx0

02

Step 2. Solving for interval

Thetaylorseriesforthefunctionfaroundx=x0is:P(x0)=鈭�k=0鈭�fk(0)k!(x-x0)kThepossiblevaluefortheintervalofconvergencefortheseriesare(-蚁,蚁),(-蚁,蚁],[-蚁,蚁)and[-蚁,蚁],here,蚁>0.

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