Q. 7 What is a difference between the... [FREE SOLUTION]

Chapter 8: Q. 7 (page 679)

What is a difference between the Maclaurin polynomial of order n and the Taylor polynomial of order n for a function f ?

Short Answer

Expert verified

$From Maclaurin series and Taylor series, a Maclaurin polynomial is approximation to the function f at x = 0 while a Taylor polynomial at x_{0} is approximation to the function f at x = x_{0} .$

Step by step solution

Step 1. Given information is:

A function f with the Maclaurin polynomial of order n and the Taylor polynomial of order n

Step 2. Maclaurin polynomial

$For any function f with derivatives of all orders at the point x_{0} = 0, then the Maclurin polynomial of degree n is, f (x) = f (0) + f' (0) x + \frac{f'' (0)}{2!} x^{2} + \frac{f''' (0)}{3!} x^{3} + . . . . + \frac{f^{n} (0)}{n!} x^{n} The general form Maclurin polynomial of degree n of the function f is : f (x) = {鈭�}_{k = 0}^{n} \frac{f^{k} (0)}{k!} x^{k}$

Step 3. Taylor polynomial

$For any function f with derivative of order n, then the Taylor polynomial of degree n at x = x_{0} is, P_{n} (x = x_{0}) = f (x_{0}) + f' (x_{0}) (x - x_{0}) + \frac{f'' (x_{0})}{2!} {(x - x_{0})}^{2} + . . . . + \frac{f^{n} (x_{0})}{n!} {(x - x_{0})}^{n} The general form Taylor polynomial of degree n of the function f is : P_{n} (x) = {鈭�}_{k = 0}^{n} \frac{f^{k} (x_{0})}{k!} {(x - x_{0})}^{k}$

Step 4. Result

$From Maclaurin series and Taylor series, a Maclaurin polynomial is approximation to the function f at x = 0 while a Taylor polynomial at x_{0} is approximation to the function f at x = x_{0} .$

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91影视

What is a difference between the Maclaurin polynomial of order n and the Taylor polynomial of order n for a function f ?

Short Answer

Step by step solution

Step 1. Given information is:

Step 2. Maclaurin polynomial

Step 3. Taylor polynomial

Step 4. Result

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