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Taylor Polynomials and Approximations (BC Calculus - Unit 10)

Jean Adams
5.3k Followers
Grade Levels
11th - 12th, Higher Education
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Pages
10 + 28 Slides
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Jean Adams
5.3k Followers

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Description

Taylor Polynomials and Approximations Lesson:
Your AP Calculus BC students will find Taylor and Maclaurin polynomial approximations of functions.

What is included in this resource?

⭐ Guided Student Notes

Fully-editable SMART Board® Slides

⭐ Homework/Practice assignment

⭐ Content quiz

⭐ Full solution set

Lesson Objective:

★ Find polynomial approximations of functions and compare them with the elementary functions

★ Find Taylor and Maclaurin polynomial approximations of elementary functions

★ Use the remainder of a Taylor polynomial

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NOTE: This lesson has been updated to reflect the changes in the AP Calculus CED Binder .

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College Board® Topics:

Topic 10.11: Finding Taylor Polynomial Approximations of Functions

College Board® Learning Objectives:

LIM-8.A: Represent a function at a point as a Taylor polynomial. (BC Only)

LIM-8.A.1: The coefficient of the nth degree term in a Taylor polynomial for a function f centered at x = a is (f^n (a))/(n! ).
(BC Only)

LIM-8.A.2: In many cases, as the degree of a Taylor polynomial increases, the nth degree polynomial will approach the original function over some interval. (BC Only)

LIM-8.B: Approximate function values using a Taylor polynomial. (BC Only)

LIM-8.B.1: Taylor polynomials for a function f centered at x = a can be used to approximate function values of f near
x = a. (BC Only)

The unit includes the following topics:

1. Series and Convergence

2. The Integral Test and p-Series

3. Comparison of Series

4. Alternating Series

5. Ratio and Root Tests

6. Taylor Polynomials and Approximations

7. Lagrange Error Bound and Accuracy

8. Power Series and Interval of Convergence

9. Taylor and Maclaurin Series

10. Representing Functions by Power Series


Click HERE to SAVE 20% by buying all INFINITE SEQUENCES & SERIES products, including cooperative activities, in the UNIT 10 MEGA BUNDLE.

You may also be interested in:

Sequences & Series Essentials

Sequences & Series Assessments

Sequences & Series Homework

AP® is a registered trademark of the College Board® which was not involved in the creation of, and does not endorse this product.

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Total Pages
10 + 28 Slides
Answer Key
Included
Teaching Duration
Lifelong tool
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