Q. 10 What is the relationship between... [FREE SOLUTION]

Chapter 8: Q. 10 (page 679)

What is the relationship between a Maclaurin series and a power series in x?

Short Answer

Expert verified

$The power series in x is same as the Maclaurin series in x if x_{0} = 0 is considered, that is, a_{k} = \frac{f^{k} (0)}{k!} . The Maclaurin series in x is nothing but a special case of power series, that is, a power series calculated about origin is the Maclaurin series of the function .$

Step by step solution

Step 1. Given information is:

A Maclaurin series and a power series in x

Step 2. Maclaurin series and Power series

$The power series of the function f around the point x = x_{0} is : f (x) = {鈭�}_{k = 0}^{鈭�} \frac{f^{k} (x_{0})}{k!} {(x - x_{0})}^{k} The Maclaurin series of the function f around the point x = 0 is : P (x) = {鈭�}_{k = 0}^{鈭�} \frac{f^{k} (0)}{k!} {(x)}^{k}$

Step 3. Result

$Therefore, the power series in x is same as the Maclaurin series in x if x_{0} = 0 is considered, that is, a_{k} = \frac{f^{k} (0)}{k!} . The Maclaurin series in x is nothing but a special case of power series, that is, a power series calculated about origin is the Maclaurin series of the function .$

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91影视

What is the relationship between a Maclaurin series and a power series in x?

Short Answer

Step by step solution

Step 1. Given information is:

Step 2. Maclaurin series and Power series

Step 3. Result

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