Chapter 8: Q. 4 (page 679)

What is a Taylor polynomial for a function f at a point $x_{0}$ ?

Short Answer

Expert verified

$P_{n} (x) = \sum_{k = 0}^{n} \frac{f^{k} (x_{0})}{k!} {(x - x_{0})}^{k}$

Step by step solution

Step 1. Given information is:

$We have a function f (x)$

Step 2. Finding Taylor Polynomial

$Consider that the function f is a function with a derivative of order n, then the taylor polynomial at x = x_{0} is, P_{n} (x) = f (x_{0}) + f' (x_{0}) (x - x_{0}) + \frac{f'' (x_{0})}{2!} {(x - x_{0})}^{2} + . . . . + \frac{f^{n} (x_{0})}{n!} {(x - x_{0})}^{n} The general form of the Taylor polynomial of the function f in the compact form is : P_{n} (x) = \sum_{k = 0}^{n} \frac{f^{k} (x_{0})}{k!} {(x - x_{0})}^{k}$

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What is a Taylor polynomial for a function f at a point $x_{0}$ ?

Short Answer

Step by step solution

Step 1. Given information is:

Step 2. Finding Taylor Polynomial

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What is a Taylor polynomial for a function f at a point x0?

Short Answer

Step by step solution

Step 1. Given information is:

Step 2. Finding Taylor Polynomial

One App. One Place for Learning.

Most popular questions from this chapter

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What is a Taylor polynomial for a function f at a point $x_{0}$ ?