Taylor Polynomials

Table of Contents

Taylor Polynomials

The Best Functions...

Polynomials Are Easy to Evaluate

They Are Easy to Differentiate

Polynomials Are Easy to Integrate

It’s Easy to Find the Limit of a Poly

Compare Polys to Other Functions

Even Worse Functions

And Others...

If We Could...

Begin With a Line

The Tangent!

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Linear Approximation at a Point

To Find It

An Example

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The Slope

The Equation for the Line

The General Procedure

Second Degree Approximations

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The Tangent Line

The Degree Two Approximation

Our Example

How?

This Gives Us

Thus

Compare

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Notice

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Implications

Compare

Take x Closer to Zero

Better Approximations

Definition

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Why Use Derivatives?

The Taylor Polynomial

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Home Page: http://www2.spsu.edu/math/Dillon/2254/2254.html

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