Chapter 8: Q. 12 (page 679)

If a function f has a Taylor series at $x_{0}$ , what are the possibilities for the interval of convergence for that series?

Short Answer

Expert verified

$The possible value for the interval of convergence for the series are (- ρ, ρ), (- ρ, ρ], [- ρ, ρ) and [- ρ, ρ], here, ρ > 0 .$

Step by step solution

Step 1. Given information is:

A function f with Taylor series at $x_{0}$

Step 2. Solving for interval

$The taylor series for the function f around x = x_{0} is : P (x_{0}) = \sum_{k = 0}^{\infty} \frac{f^{k} (0)}{k!} {(x - x_{0})}^{k} The possible value for the interval of convergence for the series are (- ρ, ρ), (- ρ, ρ], [- ρ, ρ) and [- ρ, ρ], here, ρ > 0 .$

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If a function f has a Taylor series at $x_{0}$ , what are the possibilities for the interval of convergence for that series?

Short Answer

Step by step solution

Step 1. Given information is:

Step 2. Solving for interval

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Step by step solution

Step 1. Given information is:

Step 2. Solving for interval

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Most popular questions from this chapter

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If a function f has a Taylor series at $x_{0}$ , what are the possibilities for the interval of convergence for that series?